After about a month of slow and stubborn progress, I finally scored a million points in Tetris. That’s a lot of points, a full seven digits’ worth of them, and yet there was no champagne and no fireworks. Admittedly, this is not the stuff of Greek myths: single player computer games were definitely not among Hercules’ Twelve Labors, but then again, one of his tasks was shovelling cow dung. So why not just humor me for a moment and play pretend that Tetris is something worth caring about? The worst that can happen is that we forget that we were supposed to just pretend, which I guess must have been what happened with modern art.
There is not going to be much new here if you already care about Tetris, except perhaps the kind of naive enthusiasm that children bring to Christmas. You might have made a wrong turn if you're not even the slightest bit curious about the theoretical foundations of tetromino stacking: follow this link back to safety and please remember to sanitize your browser.
Nonetheless, I hope Tetris can exemplify how even the simplest of systems are more interesting than they might appear, hiding treasures beneath their smooth, featureless surfaces that you will only find if you are willing to drill a bit deeper down than what seems reasonable. My chances of success are much greater, of course, if you take a few liberties with the word interesting.
If you want to skip all the exposition and jump straight to
dessertthe spectacle, there is a video. Why waste time read lot word when short clip do trick?
1 — Antiquity (the age of negative points)
I first played Tetris on my cousin’s Game Boy when I was eight years old, but I didn’t get more into it until my early teens. My parents had an old computer with games like Civilization 1 and the DOS-version of Prince of Persia. The text editor was an early ancestor of Word running inside of Windows 3.1, which I would use for schoolwork or trying to write stories. Strangely, even when you're supposedly writing for pleasure, procrastination still rears its three monstrous heads.
To start most games on this computer of the past, you would have to save your document and exit Windows. Needless to say, this process was nowhere near as seamless as just switching between tabs in a web browser. Today, you can pretend you're just going to check one quick thing and then get back to being productive, but when you're rebooting your computer into a different operating system to start a game of Civilization you get all of the shame upfront. It is much more potent that way, ultimately for the same reasons that clickers help with training a dog.
There was, however, a way to bypass the moat of shame that separates boring text editors from the world of games that make entire weekends vanish in a puff of smoke. Just like subsequent versions, Windows 3.1 came with a few games pre-installed, such as Solitaire and Minesweeper, neither of which really manged to draw me in. More intriguing was the Microsoft Entertainment Pack for Windows version of Tetris.
One of the basics of Tetris is that it starts out easy, with pieces dropping at the same pace that the African Continental Plate drifts, but as you keep playing the gravity grows stronger. This affords you less and less time to solve the miniature puzzle that each new piece represents. As the speed increases, you will find that there is no time to ponder where each piece should go — you just have to try to jam it in somewhere that isn’t outright disastrous. If this phase of the game doesn’t do you in, even later stages put your manual dexterity to the test: you might have less than half a second to input the five left
- and two rotation
-presses it takes to shepherd a piece to its promised land in the rightmost column.
Some versions of Tetris will eventually reach speeds where the mathematics of how fast the computer is willing to read inputs and how many presses it takes to get pieces to the edge spells certain doom. This might seem unfair by modern standards, where players expect to be rewarded with a victory-screen if they play anywhere near half-decently, but Tetris is closely related to arcade games which needed to guarantee an eventual game over to keep the spice flowing coins dropping.
Windows 3.1 had a high score table — another perennial feature of arcade games, trying to tunnel into players’ wallets through their fragile egos. My brother and I would take turns claiming the top position of the high score table from each other. After a fair bit of this back and forth, my brother presented me a supposedly unbeatable high score: he had secretly discovered that he could abuse the pause
function to take timeouts at will, letting him figure out the ideal position for each piece. But in the end, my perseverance trumped his cleverness: pausing does help with thinking, but at very high speeds Tetris requires a continuous stream of rapid and precise keypresses. Frequent pausing does gives you time to think, but it breaks up the rhythm you need to get in the zone and hit the precise timings. Imagine pausing a game of Guitar Hero between every note, and despair.
Unlike most versions of Tetris, the Windows 3.1 version could be wrestled into submission. While it had no literal victory screen, it maxed out its gravity at level 10, which was blazing fast but ultimately completely playable. The score was tracked by a 16-bit signed integer which would would happily roll over from 32,767 to lots of negative points. After I had done a handful of loops around the score tracker in a single game, there wasn’t much more to aspire to. I would occasionally toy around with dropping the first few pieces right down the middle without moving them, or seeing how long I survive while not rotating, but Tetris would eventually be replaced by games like StarCraft which appealed to other parts of my obsessive personality.
2 — Renaissance (old man yells at cloud)
I don’t quite remember what inspired me to try playing Tetris again some twenty years later, but I do remember what had been holding me back. Adjusting to a new version of Tetris is a bit like picking up a new instrument: difficult and frustrating. Muscle memory is critical, for reasons that may be difficult to appreciate from the sidelines: superficially, Tetris at higher levels just looks as if someone quadrupled the playback speed, so you might think that the way to keep up is to just play faster. But reality is full of curve-balls that physicists call phase transitions, which is mostly a fancy name for how walking faster and faster never gets you to running: you will instead be racewalking, which looks stupid definitely deserves to be part of the Olympic Games.
The absolutely slowest way of using a keyboard is to look at your screen, decide you want to type in a U
, turn down to your keyboard and scan through the rows of keys to find the correct button, press it, and then turn back up to the screen to make sure that, yes, where once there was empty space, there now is a U
. A quite evocative term for this technique is hunt and peck, and watching each intermittent keystroke will make your blood boil when you’re waiting for some tech illiterate functionary to process your documents.
Similarly, new Tetris players will have a very slow OODA loop: look at the piece, press an arrow key, verify that it has moved, and repeat until the piece has been maneuvered to the desired column. Relying on visual confirmation every step of the way slows you down — I don’t know much neuroscience and am too busy with more important things to bother with actual sources, but I would guess that the minimum time for this conscious act-observe-respond
loop is somewhere around 100ms. The average is much higher.
I got around to doing the bare minimum of research — the fighting game community obsesses about reaction times, because it defines the boundary between the parts of the game that are played as a rock-scissors-paper guessing game and as a tactical action-reaction game of maneuvering for advantageous distancing. They tend to give numbers somewhere in the vicinity of 200ms for
observe-respond
: see for instance https://gamefaqs.gamespot.com/boards/975211-super-street-fighter-iv/56218919.
The ideal Tetris player would reduce the the game to its three minimal components, which we will name after the most relevant body parts:
Eyes: which pieces the game hands you is the only non-deterministic element that you have to read from the screen. The game’s physics and the effect of your keypresses can in principle be fully simulated in your own mind: theoretically, a blind person could play a flawless game of Tetris given a screen reader setup for the piece preview. This would be very similar to how blindfold chess works, where the player continuously maintain the game state in his mind’s eye. I half expected to be able to find somebody who had decided to specialize in blindfold Tetris, but the closest I can find is this.
Brain: given the current game state and what’s next to be placed, you want to compute the piece’s ideal placement, as well the exact sequence of buttons to get it there and how the playing field will look afterwards. This can all be done in a single step and it can be done in parallel with input and output: the eyes peer into the future by using the piece preview and the brain solves for the upcoming piece while the fingers process the active piece.
Fingers: all that remains is to produce the outputs specified by step 2, like how a telegraphist converts a written message into Morse code by a series of taps. The purely mechanical process of pressing buttons should not require any more conscious thought than speaking the words you’re thinking out loud. It’s still not easy: being able to read sheet music doesn’t mean that you can play the piano and it certainly doesn’t mean you should try your luck with La Campanella.
The actual Tetris player, however, is a puny mortal who can’t live up to this Platonic ideal. Just moving pieces sideways can be a challenge: for longer intervals it is tricky to recognize what exact number of lefts or rights is called for without wasting time waiting for visual feedback. At some point I picked up a somewhat clever, but ultimately counter-productive habit: pieces can be placed in the second-from-the-edge column by moving it all the way to the edge and then one step back. It’s foolproof, because getting a piece to the edge doesn’t require a precise number of shifts, you’re safe as long as you press way too many times. But every unnecessary input costs time, and like how the US dollar is the universal currency of the planet Earth, for Tetris it is the millisecond.
There are many small annoyances when transitioning from one version of Tetris to another, particularly older games from before the Bible was written. The modern guidelines for Tetris games state that the L
and J
pieces should be orange and blue respectively, while in Windows 3.1 Tetris they are yellow and purple. Since we’re a very strange kind of ape that can easily isolate a single voice in a bar full of people but struggle with left and right and mirror images, it can be easier to recognize the tetrominos by their color rather than their actual shape. This works great until you are stuck with a game using a different palette and you get to experience the Tetris equivalent of dyslexia.
But in the end, the colors are not that big of a deal. Even very serious matters like exactly how quickly keypresses get repeated when you hold a button are something you can adjust to in a manner of hours — Windows Tetris was really slow, so you would have to mash the arrow keys instead of holding them down. The real kick in the teeth challenge is rotations. A T
piece has a reasonable center of gravity and rotates the way everyone would expect it to, basically spinning in place. An I
piece, however, doesn’t really have a well defined middle point in the tile-based world of Tetris, because 4 is not an odd number. If you rotate an I
from standing to flat, exactly which row will it be in afterwards?
The truth is as they say weirder than fiction: an I
, despite its obvious 180 degree rotational symmetry, actually has 4 distinct states of rotation. Turning it upside down doesn’t get you back to where you started, but shifts it one step in the left-right
direction: yes, this is just as weird as it sounds. Effectively the same thing happens with the two same-but-different flat orientations. And this is just scratching the surface of all the idiosyncrasies that you must internalize to play Tetris at a very high speed, to know what your fingers will do without having to hunt and peck wait and verify.
My pick for a modern version of the game was Tetris Online, just because it was the first thing I found that runs in a browser. I suspect that Tetris snobs would disapprove of this choice, but it seemed good enough for me — partly because I never leave home without a weapons grade adblocker. While there are many subtle and important differences to adjust to when coming from the old Windows Tetris, for now I’ll just summarize the obvious ones to do with the controls.
A lot of old games were ported between the important systems of the day, like DOS, Nintendo and Amiga, often by single programmer with a tight budget. These ports can be anywhere from faithful re-implementations to bug riddled disasters. If for whatever reason you happen to be familiar with NES Tetris, it is superficially the same game as Windows 3.1 Tetris, but with a number of small but meaningful differences in the speed and scoring systems.
Windows Tetris has only one rotation button, the up
arrow key, which rotates pieces counter-clockwise. Hard-drop was mapped to the down
button: you would play the game with only one hand, unless you have no shame and keep your left index finger on F2
for easy access to pause and unpause. Modern games use up
for clockwise rotation instead, and down
for soft-drop which lets you release the button to resume control of the piece, for instance to tuck it underneath an overhang. Counter-clockwise rotation and hard-drop are by default mapped to the C
and space
buttons, which is where the left hand joins in on the fun.
3 — Mission objective: survive (350k)
The first thing to do in a Tetris game is just to get a feel for the controls, the gravity and the delays and then see how long you’re able to survive. I would describe Tetris Online as comfortable until level 10, increasingly hectic but manageable until level 20, and from there on a seat-of-your-pants rollercoaster. After getting used to the game, I would quite consistently lose the game at level 25, which feels absurdly fast: If you start the game at level 25 with a blank playing field and keep your hands away from the keyboard, you get a game over in less than three seconds. According to the documentation, the game actually keeps scaling all the way to level 30, which I assume must be here-be-dragons territory.
Playing with simple-minded focus on survival until level 25 would score somewhere around 350k points. Starting out, I was mostly curious about seeing how far I could push myself in a game with a higher max speed than my old Windows Tetris. But the game would track and show my high scores after each game, and like some inside-out version of Goodhart’s law, whatever happens to get measured becomes the target.
“What gets measured gets managed — even when it’s pointless to measure and manage it, and even if it harms the purpose of the organisation to do so”.
Ridgway clearly was onto something in 1956. Not everything that matters can be measured. Not everything that we can measure matters.
Danny Buerkli, via Center for Public Impact. Sourced from https://medium.com/centre-for-public-impact/what-gets-measured-gets-managed-its-wrong-and-drucker-never-said-it-fe95886d3df6
The most straightforward way to get a better score is to simply survive past level 25. Scoring in Tetris is progressive, so each extra level of play will add a good chunk of dopamine points. However, it turns out that the high difficulty levels in Tetris Online introduce increasingly unphysical behavior — I’m sure I could have kept beating my head against this wall and I’m sure it has a twisted, Picassoesque form of beauty to it — once Stockholm syndrome kicks in — but I decided that I still appreciate what little remains of my sanity.
I think my grievances with Tetris Online can be traced back to an original sin, namely lock delay. The term is almost self-explanatory: when the live piece makes vertical contact with other pieces or the bottom of the play area, there is a small window of time before it actually locks in. The simplest consequence of this lock delay is that it allows you to tuck pieces into open pockets: for instance, if your very first piece in a game of Tetris is an S
or a Z
, there is no way of placing it without creating a little hole with a roof over it. Lock delay lets you soft-drop another piece down next to the pocket and then tuck it into the side facing opening.
By itself, lock delay is mostly benign. Tetris Online, however, combines it with a generous move reset: this means that every time you successfully move or rotate a piece, your lock delay timer restarts. Because of move reset, you can keep a piece in suspended animation by juggling it against a surface — even the O
piece, which looks the same however much you try to spin it around, can have its lock delay reset by seemingly NOOP rotations.
Intuitively, you would expect lock delay to just be a consequence of gravity — every N frames, gravity moves the live piece one row down, and if this movement is blocked by a piece or the bottom of the play field, the piece locks in instead.
NES Tetris seems to actually work this way, and presumably the same goes for Windows Tetris. With this system, Tetris feels cohesive — pieces drop at a given speed, and collisions cause them to lock in. Unfortunately, it is very much not how it works in modern Tetris: lock-in is a wholly separate subsystem, with its own hidden variables (lock delay) and mechanics (lock delay reset). It can probably be argued that this system produces interesting gameplay, but it pulls the rug out from under the logic of the game.
From my description, it would seem that you can juggle a piece indefinitely, but this doesn’t actually work. Cursory googling suggests that there might be an upper limit of the move resets allowed for a given piece, but I’m not sure about the details, and I’m not sure if I want to know, because move reset juggling isn’t exactly the kind of highly compelling gameplay that I’m looking for. As far as I understand, the reason juggling isn’t considered a bigger problem is that these games are primarily meant to be played as a race, against another player or a timer.
To compensate for how generous the lock delay is, Tetris Online turns the gravity way up past level 20. It feels like new pieces spawn already soft-dropped into contact with a surface, so much so that I think the gravity might be literally instant by the time you reach level 25. Either way, you don’t get to do any moving and rotating while the piece is falling: you are only allowed to play the game inside of the grace periods offered by lock delay and move reset.
In Classic Tetris, time pressure is created by the gravity in a physically reasonable way, and one way of managing it is to maintain a U
-shaped structure: this limits the problem with new pieces locking in prematurely, which can cut off even more of your elbow room and lead into a death spiral. Modern Tetris instead uses lock delay as the primary time constraint, removing most of the value of keeping a low stack. The structure with a well in the middle is undesirable, because pieces get trapped. To maximize your access to all columns, you want the exact opposite structure: an inverted U triggers lock delay early, letting the player take control of the pieces and roll them from the first point of contact and off to either side.
If you want to get serious about playing under these conditions — and by all means, I’m sure it’s got its own charming tricks once you understand all the mechanics — you will also have to read up on something called Super Rotation System. SRS dictates exactly how pieces bounce around when its normal rotation is blocked by the edges of the play area or other pieces. Among other things, it makes it possible to sneak pieces through cracks they have no business fitting through and to roll pieces over obstacles in egregious violation of energy conservation.
If you’d rather play something at least vaguely reminiscent of classic Tetris, however, you have to find some other way of squeezing more points out of the game before reaching level 25.
4 — The subtle art of back-to-back Tetrises (650k)
4.1 — Fantastic points and how to score them
I sometimes have these incredibly outside-of-the-box ideas, such as reading up on how Tetris awards points when trying to improve my high score. You might ask: Where do I find my inspiration? — but as they say, a magician never reveals his secrets. And he certainly doesn’t write fifty pages worth of documentation.
As shown in the above table, Tetris is not just the name of the game itself, but also the term for the aesthetically pleasing quadruple line clear that requires a vertical I
piece. While all line clears are equal, some line clears are more equal than others, so it is only fair that Tetrises give more points. This is not merely because it clears more lines at a time: one Tetris scores twice as many points as four single line clears.
By itself, this discovery doesn’t get us anywhere. It must be combined with understanding that the difficulty level in Tetris only indirectly depends on the player’s score. The current difficulty level is is always 1 per ten full line clears, plus 1 because the game doesn’t 0-index — note in particular that you don’t gain anything by doing a Tetris to jump straight 9 to 13 line clears; the next increment will be at 20 lines regardless.
These two observations — that the kind of line clears determine points per line, while the difficulty system effectively limits total number of lines cleared — give us exactly the tools we need. We can assume that level 25 is effectively our killscreen, seeing as it’s stupidly fast, which means that we have clear 240 line clears available to score points. And since Tetrises score more points per line, they allow us blow our previous high score out of the water.
This equation is just a slightly more convenient reformulation of the information from the previous scoring table. The type multiplier takes values reflecting the per line scoring efficiency: {single: 1, double: 3/2, triple: 5/3, tetris: 2}
. The back-to-back multiplier is normally 1, except in the special case of scoring a Tetris when the previous line clear was also a Tetris. In this case there’s a 50% score bonus to reward you for being awesome, or in other words the back-to-back multiplier is 3/2. This multiplier is what the word difficult in the scoring table above alludes to: we will get more into these weeds in section 6.
With a formula for score per line, we just need to do a sum across all 240 lines while accounting for how the current level factors into the score calculations. The mathematics shows that a level 25 game with only single line clears (minimum efficiency with multipliers of 1) will score 300k points. This is close to the empirical numbers from section 3: the difference is presumably explained by the occasional multi-line clears being mixed in. More importantly, we can see that a perfect 240 lines game will have a combined multiplier of 3 for Tetris type clears, for a total score of 900k points. This is highly dopaminergic number, if still sadly short of the white whale that is seven digits. And if it’s not seven digits, is it really even a score?
Additional details on scoring: Tetris awards 2 points per row when a piece is hard-dropped (1 per row instead if soft-dropped), which among other things is what prevents your score from always being a clean multiple of 100.
\(\text{max drop points} = 240 \frac{\text{lines}}{\text{game}} \cdot \frac{10}{4} \frac{\text{pieces}}{\text{line}} \cdot 20 \, \frac{\text{rows}}{\text{piece}} \cdot 2 \frac{\text{points}}{\text{row}}\)\(\text{max drop points} = 24\,000 \frac{\text{points}}{\text{game}}\)Taking quite unreasonable maximums for all possible values, we obtain an upper bound for the possible drop points scored in a game, which is much too low to be worth thinking about. Unlike line clear points, drop points do not benefit from level-based scaling — they are instead effectively penalized, because higher gravity means that you spend more drop height when maneuvering pieces.
Additional details on speed: I tried using drop points to figure out how high level gravity actually works in Tetris Online. I am completely unable to score even a single hard-drop point at level 25 despite mashing or holding the button. However, holding down the soft-drop button does score 18 points on a clear playing field. This inconsistency is puzzling, to say the least.
Since I was already trying to hold down buttons, I also tried it with
down
,left
,right
androtate
on an empty play field at level 25. In all cases you can clearly see new pieces impacting the bottom of the playing field before any kind of movement or rotation takes place.I suspect the inconsistency between soft-drop and hard-drop scoring at level 25 might be explained by soft-drop being a state that is activated and deactivated, such that holding it down simply enables scoring during vertical movement, whereas hard-drop is a discrete input that the game is not willing to process during the instant gravity drops of level 25.
Hopefully correct information from someone more knowledgeable than me: permalink to a Reddit-post
4.2 — Pits and pockets
To satisfy our hunger for revenge whale oil points, we need to do sixty uninterrupted Tetrises. The basic game plan is easy enough to summarize:
Reserve the rightmost column for vertical
I
pieces: nothing else is ever allowed to touch it. Since lines only clear when a row is filled in all columns, we will never accidentally clear a line with a different piece. Use the other pieces to fill the other nine columns. Only dropI
pieces in the tenth column when the rest of the bottom four rows are completely filled: otherwise, have them contribute to making the rest of the play field Tetris ready.Never create pockets: once an enclosed hole reaches the bottom four rows, it will spoil the next Tetris and drag down our points per line average.
Like in Douglas Adams’ tips on flying, the problem is the second part:
There is an art, it says, or rather, a knack to flying. The knack lies in learning how to throw yourself at the ground and miss. … Clearly, it is this second part, the missing, which presents the difficulties.
Life, the Universe and Everything, Douglas Adams
However, just like hitting the ground is a symptom of an underlying problem of failing to maintain altitude, pockets are just the observed fail state of an unhealthy structure. The main pathogen is pits: single-width holes in the surface that impose constraints on where pieces can be placed, potentially starting a a slow, torturous death by a thousand cuts where the structure gets increasingly jagged until we have no choice but to start papering over unfilled pits and accepting that bad is the enemy of perfect.
The most obvious problem is deep holes: after reaching a depth of 3 on both sides, a pit makes its column off limits until an I
is used to fill it in. However, I
pieces are scarce, by virtue of their obligations with respect to column 10. Only one in seven pieces is an I
, and each Tetris clears four rows which corresponds to ten pieces. In other words, 70% of all I
s must go towards Tetrises to prevent the playing field from gradually filling up and drowning the player. The leftover I
pieces can be used to reclaim pits, but these spares trickle in once per ~23 pieces.
Straining the I
piece budget is however only the most salient problem with pits. More insidious is the effect that pits have until they are filled in, as indicated in the above figure: the two pits reduce the portion of the play field that is actually available to only six columns, a 33% reduction in real estate. While this is already a very meaningful number, it underestimates just how dire the pictured state is. With six live columns, a 3-width piece like a horizontal S
only has four candidate positions that don’t touch pits on either side: in terms of positions this is a 43% reduction: had the pits been more centralized, the effect could have been even worse.
What is the actual significance of losing candidate positions to pits? For lack of quantitative analysis or logical arguments, I will try to share my empirical but admittedly somewhat half-baked intuitions. Let us pretend for a moment that we have the Tetris equivalent of Stockfish, a chess engine that calculates how many «centipawns» white is ahead. We could name it Stavechurch and have it map Tetris playing fields to numbers estimating the health of the structure: near 100 for a very even surface, with mild to moderate to severe penalties for unevenness or jaggedness or deep pits, and approaching 0 as maintaining back-to-back Tetrises goes from challenging to impossible.
Setting the time pressure aside, Tetris is a quite forgiving game, in the sense that there are usually many good moves available. However, this usually comes with an asterisk: the number of good moves has a strong dependence on the number of candidate positions available. The problem with structural weaknesses is not just increased likelihood of a direct catastrophic event as in the above figure. The bigger problem is that as the number of candidate moves drops, the proportion of pieces presenting opportunities to increase the health of the structure decreases, while the likelihood increases that even optimal placements will compound the existing weaknesses.
“How do you go bankrupt?” — “Slowly at first, and then all at once.”
A much repeated quote, especially in the worlds of finance, which also applies to Tetris. It might originate from Ernest Hemingway’s 1926 novel, The Sun Also Rises, in a slightly clumsier form:
“How did you go bankrupt?” — “Two ways,” Mike said. “Gradually and then suddenly.”
Borrowing research from James Hickman via Schiff Sovereign, sourced from https://www.schiffsovereign.com/offshore/slowly-at-first-then-all-at-once-12909/
In practice, there is a generous amount of slack in Tetris — maintaining a reasonably healthy structure doesn’t require anywhere near perfect play, just avoiding unforced errors and being somewhat diligent about recognizing and fixing minor weaknesses as opportunities present themselves. In situations where an I
is needed somewhere else than column 10, many players will prioritize Tetrises over filling in pits, if only because dumping the long bar in the Tetris well is a habit. Square block goes in square hole. This is almost always a mistake: filling in pits opens up more real estate and makes it possible to recover the structure. Only very rarely is clearing rows more urgent than unlocking columns. An unfilled pit is the equivalent of a gaping wound — you don’t want to leave it to fester.
Having introduced this concept of health, it is worth pointing out that the computational element of ideal Tetris play from section 2 is really just optimizing for play field health over all possible actions — placing the currently active piece or the one that is in
HOLD
. While this looks like a single ply optimization problem, we have offloaded all the downstream ramifications to the health estimation. A good way of looking at the probabilistic candidate position argument is that with a higher branching factor, far more future game states can be reached, which in turns greatly lowers the likelihood of catastrophic events.
Strictly speaking, it can be proved that even optimal play cannot survive every possible string of pieces, but this proof relies on astronomically unlikely runs of S
or Z
pieces: a somewhat more practical demonstration of this exists in the form of Hatetris, where the world record for line clears is just some hundred lines. Even our robot overlords cannot maintain perfect back-to-back Tetrises under the classic rules, but there are a number of extra tools available in modern Tetris that make a huge difference:
Multi-piece preview: shows the next three pieces in Tetris Online. This allows you to construct shapes specifically to accommodate the upcoming pieces instead of just following best practice and occasionally finding that you have painted yourself into a corner.
7-bag piece randomization: each group of seven pieces contains one of each tetromino, as if the seven pieces were put in a bag and drawn without replacement. Once empty, the bag is refilled, again with one of each piece. This guarantees a reliable stream of
I
tetrominos, makes long runs of problematic pieces such asS
andZ
literally impossible and leaks some extra knowledge. For instance, when placing the third piece and previewing pieces four through six, the seventh piece can be determined by elimination.HOLD:
allows setting aside the current piece for later: if there is already a piece set aside, this becomes the active piece, and until this piece is placed,HOLD
is disabled. This can be used as a Get Out of Jail Free card for a piece the playing field currently can't accommodate, as a somewhat dangerous panic button when you messed up your inputs, and as a way to keep a solution-oriented piece likeT
orI
in reserve.Generous lock delay: provides an extra grace period, useful for correcting misplacements at lower speed as well as simply stalling by juggling. Lock delay also makes tucking reliable enough to be used to backfill unclosed pockets from the side, a maneuver that feels like backing your car into a parking spot.
4.3 — Shoulders and weaknesses
The key observation in the above table is that, going just by the numbers, the completely flat structure is «strongest», though it’s not entirely clear what that actually means. However, the single offset shoulder is not terrible: it can support most pieces in at least one orientation, the exceptions being O
and one of LJ
depending on whether the offset is left-right or right-left. At the same time, there is significant merit in this height one shoulder, in that it accommodates SZ
which can not fit in the completely flat structure at all. For the double offset, things are much clearer — it fails to fit the majority of the pieces and has nothing to make up for it. The weakness this 2-height shoulder represents may not be very significant: this depends on whether there is sufficient space available on the lower side of the seam to make it possible to deconstruct it from the outside.
These numbers are supposed to illustrate the advantages of flat structures: they hardly prove anything. Indeed, the choice of specifically a shoulder structure is somewhat arbitrary: for example, it is unfavorable to the horizontal, upside-down rotation of T
, a relatively useful shape that doesn’t fit any of these structures. Similarly arbitrary is the way we count the vertical I
: it is so narrow that it cannot be placed across a shoulder seam, but since a shoulder never blocks a candidate placement for a vertical I
it seems most fair to count this in its favor. In general, the numbers will be misleading for answering other questions than those about flatness of structures: for comparisons between pieces, they make OSZ
appear better and LJT
worse than they really are, because we show the fraction of rotations with a valid placement. LJT
’s four distinct rotations offer more possible placements and thus on average better actual placements. We care about the health of the optimal placement, not of the one averaged over all possible rotations.
The following figures showcase a few somewhat subtle examples of structural weaknesses that can occur during play. They assume a single-minded focus on maintaining back-to-back Tetris streaks, but these structures tend to be suboptimal whatever you are trying to accomplish. This is by no means a comprehensive listing, but some illustrate examples of the traps that insufficiently flat structures can spring on you.
4.4 — In theory, there’s no difference between practice and theory
The revised step-by-step guide to back-to-back Tetrises looks like this:
Reserve the rightmost column for vertical
I
pieces.Never create pockets, which are a death sentence for the back-to-back streak.
Avoid creating deep pits, which strain the already limited
I
-piece budget.When they arise, fill them in at the first possible opportunity.
Maintain a healthy structure: it is nearly impossible to make a structure too flat, while
the deviljaggedness hides behind every corner and under every stone.Actively even out the structure with every single piece placement.
When in doubt, place pieces lying down.
Upwards spikes are relatively benign in columns 1 and 9, butting up against the wall or the Tetris well, but much more limiting when in the in-between columns
For a decent while, I struggled to maintain a solid back-to-back streak, tending to stumble somewhere around 40 to 80 lines cleared. One particularly bad habit of mine was making use of how SZO
stack on top of themselves, which can quickly lead to structures chock full of weaknesses that resemble a skyline.
It is difficult to know exactly how I got better — it is tempting to come up with specific ideas and concepts, but perhaps the most important improvements were just the same kind of incremental growth that comes with time when you curl a dumbbell a lot. Still, going back to the 3 essential skills of a Tetris player:
I started using the piece preview more, and in particular I got rid of a strange bug in my brainware: I would be placing a
T
and the piece preview would showTOZ
, and for whatever reason the activeT
and the previewT
would just merge into one in my brain and I would end up trying to place the secondT
as if it were anO
.More of the theory presented in this section gradually crystallized in my head, to the point where I would instinctively flinch whenever I realized I was about to create a 3-pit.
I probably just got better at pressing buttons, though this is a thing that is difficult to measure. At some point I learned to hard drop pieces, even during the lock delay grace period after they had touched down, because it is easier to time the exact moment when you gain control of the next piece relative to your own hard drop input than it is to try to predict when the lock delay timer will run out. Unfortunately, messing this up is very punishing.
There are two clearly new skills that I picked. The first one is tucking — sliding pieces sideways into positions they can not be dropped into. At first this was just as a desperation move to try to salvage the back-to-back streak after having to put a piece somewhere leaving an awkward side-opening pocket. Eventually, this grew to be a part of the standard repertoire. The second one was actively using HOLD
, which as some kind of purist I had been avoiding. It didn’t exist in my old Windows Tetris, but it is massively helpful for maintaining a streak, and while honor is important, there is no high score table for honor, only for points. To put a vague lower limit on what HOLD
does for you, imagine that half the time when your current piece cannot be placed, the HOLD
piece will be less awkward just by random chance, and halving the chance of catastrophic failure basically doubles the expected length of your streaks.
Lower-speed back-to-back Tetrises, while requiring constant structural maintenance, is ultimately relatively easy. It is mostly higher speed, with its effect of slightly degrading the quality of placements and greatly increasing the frequency of mis-dropping pieces, that prevents going back-to-back indefinitely. This style of play would eventually get me to 160 lines of back-to-back Tetrises or around 650k points. This is 50k points ahead of the formula from section 4.1, presumably due to slightly better multipliers after the back-to-back Tetrises break down than those we would get from just single-line clears.
♫ Where do we go from here? Where do we go — from here? ♬
5 — Paradise lost (an interlude)
5.1 — Order from chaos
Tetris is the addictive puzzle game that started it all, embracing our universal desire to create order out of chaos. The Tetris game was created by Alexey Pajitnov in 1984 — the product of Alexey’s computer programming experience and his love of puzzles.
Excerpt from About Tetris, from https://tetris.com/play-tetris. Bold face emphasis mine.
Just like cups and bowls bought at IKEA, all the seven tetrominos self-stack. I don’t think there is any deep or interesting reason why — it doesn’t hold for the slightly bigger pentominos, such as U
, which is a cute enough piece, and W
, which is like everything that is ugly about S
and Z
combined into one monstrosity. My apologies to all parents of W
pentominos. But as for the Tetris pieces, they all play nice with their clones, one stacking neatly on top of eachother.
This somewhat curious observation can be the seed of the most beautiful of dreams: imagine if we could just get rid of all the S
and Z
pieces by assembling them into two towers. That way, we are guaranteed to have somewhere to place them, and we can also avoid them mixing in with all the more pleasant pieces and disturbing their nice, sharp corners. Actually, while we’re at it, why not just self-stack all the pieces and we will never again have to think? After all — what dream could possibly be more beautiful than that?
The problem with this is that we would need two columns per piece, for a total of fourteen columns. The width of the Tetris play field is only ten columns, so this pattern cannot fit everything in. At some point we’ll have to place a T
or an I
and in doing so we will ruin the landing zone for whatever piece’s stack we borrow. Soon enough, the beautifully ordered structure has become a jumbled mess. The only thing necessary for the triumph of chaos is for good men a T
piece.
Clean, repeating stacking patterns seem impossible in the wold of classic Tetris, but modernity offers us the wonders of air conditioning Wi-Fi advanced stacking technology:
7-bags: Classic Tetris generates pieces randomly, which prevents patterns from relying too strongly on pieces coming in equal amounts or at specific moments. Even the Beautiful Dream pictured above would break down over time in classic Tetris, because an imbalance between pieces will lock us out from clearing lines while some columns get overfilled. 7-bag randomization guarantees that we get a convergence point every seven pieces, where we have seen exactly the same number of each piece.
HOLD
and piece preview:HOLD
allows some limited control over what permutations of 7-bags we actually have to deal with. We could simply dedicate theHOLD
slot forI
, which would allow us to always placeI
as the last piece of each 7-bag. Piece preview allows more surgical use of theHOLD
as well as choosing placements for piece#N
specifically to facilitate the placement of#N+1
through#N+3
.
This means that the primary problem we want to look into is our lack of columns. Just like how businesses aim to cut the costs for renting office space, we will start hot desking tetrominos. T
is actually less of a problem than it might seem: it fits cleanly on top of either a S
or a Z
stack. The problem is that it works as a SZ
-adapter: placing a T
in the S
stack leaves us with two Z
stacks and nowhere to place any S
that might appear. The simplest solution to this problem is to simply HOLD
the first T
until we get another one from the next bag, and then place both of them, one in each of the SZ
stacks. We can actually fly a bit closer to the sun than this due to previews and the ability to instead use the HOLD
slot for a S
or Z
piece until it becomes possible to place, but piloting this requires careful monitoring of the piece preview, and what could possibly be more vulgar than thinking?
We can use a similar approach to squeeze the I
pieces into the OLJ
stacks and to manifest our Beautiful Dream into reality. By nature, I
is even easier to work with than T
and all the LJO
stacks share the same flat 2-width base, allowing more fudging. A pair of I
s just add height to any stack without changing the shape of its connector. However, since the HOLD
slot is already reserved to deal with the T
pieces, it is possible for the system break:
between placing the first and second half of an
I
piece pair, it will lock down a stack; suppose it is theO
stackif we get an O piece, we can instead place it in either the
L
orJ
stack, unless they both lack a flat platform due to an odd number ofLJ
piecesif both
L
andJ
are stacked odd, theO
can be placed in between them: see columns 4 and 5 in the above figure; for this reason, theLJ
stacks should be adjacent: we don’t wantJL
orLOJ
. Note that this just resets theLJ
stacks without damaging the system.this in-between placement is not available if the
L
orJ
stack have an offset, which will be the case when different amounts ofO
pieces or I pairs have been squeezed into the stacksin this case, we can try to temporarily borrow the
HOLD
slot from theT
pieces: piece preview will often guarantee that this is safe, but not always
There are in total three flaws with this system:
As seen above, it has a very small chance of breaking when every life line fails simultaneously. This is quite unlikely, but not impossible. Good thing we’re not piloting a passenger jet!
It doesn’t produce back-to-back Tetrises. If we use a double
I
stack and spread theO
pieces around columns 1 through 6 instead, we get a reasonable Tetris density, but we will need someO
s in the I stack to balance its height, which will result in non-Tetris line clears, and non-Tetris line clears are the worst.The above figure also shows the result of
SZT
s in the four rightmost columns building up slightly faster than theLJOI
going in the remaining six: 3 tiles per column per bag versus 2.67 . Balancing this is most easily achieved by occasionally shifting twoT
s from the right to the left. Fortunately,LTT
andJTT
can each form nice3x4
blocks.
In practice, a modified and less systematic system hits a good middle ground. The SZT
-stacking in columns 7-10 is effective and simplifies the rest of the game a lot, but it’s easier (though far less satisfying) to use a non-formulaic approach for columns 1-5 and leaving column 6 as an I
column to enable full back-to-back scoring.
It’s worth pointing out the LOJ
pattern on top in columns 1-3: its 3-width shape makes it easier to fill in exactly 5 columns without an I
piece to make column 6 Tetris ready: LL
, JJ
and O
all fit nicely next to it. Note also the purple tiles on the bottom left, from load balancing. T
pieces should always be shifted in pairs: otherwise, the T
will disturb the left side structure due to its effect on parity, making it impossible to create a flat surface: we will get more into parity under perfect clears in section 6.
It turns out that the hive mind of the entire Tetris community has made more progress on this problem than my independent research (who would have thought!), resulting in a quite daunting guide with all the details you could ever want about the exact piece preview requirements to work around unpleasant permutations.
5.2 — Desynchronization
While the Beautiful Dream pattern greatly reduces the complexity of finding placements, seemingly the most crucial part of the brain work described in section 3, it’s still barely any use in order to push the high score. This is easier to understand if we delve a bit deeper into the challenges of high-speed Tetris: at sufficiently high speeds, the brain, eyes and fingers cease to function as a tightly integrated team and instead split into different semi-autonomous departments. They are of course still part of the same pipeline, but because the neuronal communication between these flesh-and-blood subsystems is relatively slow compared to the speed of the game, the eyes have to live in the future, trying to get a head start on the upcoming pieces, while the fingers live in the past, desperately trying to process all the orders from upstream that keep piling up. Like different parts of a complicated assembly line, eyes, brain and fingers depend on each other to work properly, but in practice they should each do their part in isolation. Only when something goes catastrophically wrong do we need to get the team together in the emergency room to try to salvage the situation.
The overwhelmingly most common way things spiral out of control at high speeds is desynchronization occurring somewhere in the assembly line. It can start anywhere: input error from the piece preview, miscalculation in the game state simulation or placement optimization, or output error when typing in a piece’s solution. One of the subtler ways this can happen — absent much more practice than I have been willing to put in — is line clear mispredictions.
Tetris is usually implemented with line clear delay, which basically freezes the game for some fraction of a second each time lines are cleared. This adds a slight delay before the the next piece arrives, presumably to emphasize that something important just happened: fighting games use the exact same effect to make attacks feel more impactful, with larger delays for stronger hits. It feels a lot more natural than it sounds — I guess it is somewhat analogous to how slow-motion is sometimes used in action movies.
We care about the line clear delay, because time is such a scarce commodity at high speeds that the fingers need to start working at the first possible opportunity. We cannot afford to wait for a signal to propagate all the way from the eyes to the fingers whenever a line clear delay might happen. Instead, we make ourselves reliant on the brain predicting line clear delays by use of its game state simulation, such that the correct timings can go directly into the fingers’ command buffer ahead of time.
A false positive will start moving the next piece to late, wasting valuable milliseconds that so often mean the difference between clean stacking and utter disaster. A false negative will try to move the next piece before the game is willing to receive the inputs, cutting off the the leading parts of the piece placement sequence, practically guaranteeing a blunder. Either way, we get ruinous misplacements and find ourselves in the war room, desperately scrambling to re-synchronize the internal simulation with the actual game state: basically, we need the eyes to re-read the entire game state and feed it to the brain; the brain must re-calculate the upcoming piece placements to harmonize with the actual game state; the fingers’ must flush their command buffers and try to catch back up on the new order queue. This elaborate process is a race against the clock: the actual game of Tetris is happy to spiral into total chaos while we’re flailing around to reestablish law and order.
Given this model of how Tetris applies time pressure to the player, a pattern that simplifies piece placement selection is not really that useful. It’s indeed a piece of art, but it is the solution to the wrong problem. Worse yet, the strict demands maintaining the pattern imposes on placements takes away flexibility that is useful to account for time limitations: having to maneuver pieces into exact positions in the higher structures that results from this sort of pattern actually turns out to make our job noticeably more challenging.
Some men would admit defeat; men with less time to waste and more of their sanity intact. But as Ahab might have quoted Oscar Wilde: I can resist anything except obsession.
6 — Where we lose sight of the shore (850k)
In the interest of simplification and narrative structure, I left out the more exotic parts of the scoring system in section 4. With no further ideas for improving the high score — just practicing our high-speed gameplay is ruled out by virtue of being much too pedestrian — we must instead dig deeper into the above table. What even is a T
-spin? Everything you never wanted to know and had the good sense not to ask, coming right up, with fries on the side.
6.1 — Perfect clears
Unlike Mini T-spin no line(s) — sic — a perfect clear is a sensible concept that means exactly what is says on the tin: a line clear which leaves the playing field completely bare. It is immediately obvious that perfect clears are incredibly efficient in terms of points per line (excluding level scaling): back-to-back Tetrises score 300ppl while single-line perfect clears score 900ppl, which immediately suggests a maximum score potential of 2.7 million. Is meat really back on the menu?
Unfortunately, the simplest of mathematics show that continuous single line perfect clears are impossible, because it takes 2½ pieces to fill the ten tiles in a row. The best we can hope for is double-line perfect clears, dropping us down to 750ppl, or back-to-back Tetris perfect clears, clocking in at 800ppl. These numbers all blow so far past our seven digit target that we care less about the minor differences between them and more about whether it’s theoretically possible to do all perfect clears, not to mention practically feasible.
Brief aside: Perfect clears are exceedingly rare, at least if you’re just wandering around and hoping maybe to run into one. I would guess I have seen maybe ten of them, total, across all of my failed high score runs. If you want to see perfect clears, you have to chase them down and wrestle them into the ground. While doing some testing to see how feasible perfect clears are without an actual system, I played a 240 line game where I managed exactly 0 perfect clears despite actually trying. Getting used to the most basic patterns and heuristics involved in perfect clears has helped a bit, but I still can’t get more than maybe 3 perfect clears in a game if I try hard and get lucky. There are just too many filters limiting the likelihood of perfect clears unless you engineer the situations very carefully:
they can only happen every five pieces, such that total tiles is divisible by number of columns
they can only happen if the play field has a perfect, tetromino shaped hole at that point, which depends on luck, skill, prescience and also luck
at that point, you need to have the correct tetromino available, roughly 1 in 7 —
HOLD
is a thing, but it is working many different jobs to make rentparity (see later) roughly halves the remaining chance
any kind of too-high column, pocket in the structure or isolated part of the stack that is missing a number of tiles that isn’t divisible by four spoils the chances until the problem is rectified
We can first show that a double-line perfect clear directly from the start of the game is impossible. Since we will have to place five out of the first six pieces (accounting for HOLD
), they will all have to come from the same bag. That means that at least one of these five pieces will have to come from SZT
, the slightly awkward pieces without a proper corner. It is relatively easy to see that there is no way of straightening out the staircase shape at the side of horizontal SZT
pieces while staying within just two rows.
If you find this difficult to just see, observe instead that the horizontal orientations of
SZT
all have a 2-height part in the middle that will divide the two bottom rows into a left and right part. The pieces also all have a protrusion on each side, such that the left and right parts are each rectangles with a single corner tile already filled in. This means that we have an odd number of open tiles on each side of theSZT
piece, which can never be filled in with 4-tile Tetris pieces.
It is perfectly possible to get a double-line perfect clear at some other stage in the game. If the previous line clear wasn’t perfect, leftover tiles from partially cleared pieces can fill in all sorts of weird gaps. However, every imperfect clear loses points relative to our estimated maximum. The way to get a double-line perfect clear from a bare play field is to start in the middle of two bags or have a suitable piece in HOLD
, such that we can get sequences that is a permutation of OOLJI
or have multiple repeats. LJ
must always be paired with copies of themselves or joined into a LIJ
triple as in the above figure.
So perhaps Tetris perfect clears are the way to go, but it’s not very tempting to do original research on this topic, because these clears have already been studied extensively due to their importance in competitive Tetris, which is of course a thing. Going for a Tetris perfect clear forces you place an I
piece as the tenth piece, which can be guaranteed by using HOLD
, but this gives up a valuable tool for manipulating the rest of the bag and will normally force you to place the T
from the first bag.
Why wouldn’t you want to place the T
, you might ask. Some of my best friends are T
pieces! Well, if you superimpose a checkerboard pattern on top of the Tetris play field, you can easily verify that any N
-line clear, due to making up a 10-width rectangle, must clear an equal amount of pretend-black and pretend-white tiles. This is important, if you take a few liberties with the word important, because T
pieces upset the balance of black and white tiles covered — if its center tile is white its three protrusions will all be black, and vice versa. All the six other tetrominos must cover two black and two white tiles however they are rotated or placed — the underlying reason for this is that all the other tetrominos can be traversed, tile by tile, by taking orthogonal steps, and each such step will always alternate tile color. The T
piece, due to how it forks, can not be traversed without reversing directions and revisiting the center.
This method also gives a clean proof for the fact that you can never cover a rectangle with just one of each tetromino: neither a 2x14 (which we could have proved with the staircase-argument we used for how
SZT
cannot participate in a double line perfect clear) nor a 4x7 (which on the face of it seems like it should be possible what with all the ways you can juggle the pieces around).
The importance of this is that our Tetris perfect clear must contain either zero or two T
s. For 0 T pieces, the HOLD
slot is completely locked up after the first bag’s T piece shows up, which means a Tetris perfect clear is impossible unless we hit the 1 in 7 chance of the second bag’s I
piece coming exactly when we want it. For 2 T
pieces, we must rely on the 3 in 7 that the second bag’s T piece is available as the ninth piece to place at the latest — if something is in HOLD
, the third piece of the second bag is the ninth to be placed.
Clearly, these odds are not very favorable, and this is completely ignoring the problem of coaxing all the other pieces into a clean four by nine rectangle to make the play field Tetris ready. In practice, perfect clear seems to be a strong opener in competitive Tetris, but it is far more common to clear the four lines in smaller chunks: from the start of the game, the fresh bag and and empty HOLD
slot limits the combinatorial explosion, and there is apparently quite an art both to maximizing the probability of squeezing a perfect clear out of a the ten first pieces as well as leaving sufficient flexibility to transition into other strong patterns, such as combos and T-spins.
The above parity based calculations would seem to indicate that the best possible chance of getting a ten piece perfect clear are well less than 50%, but there are reasonably human-compatible systems that advertise upwards of 80% first perfect clear probability. This paradox is resolved by observing that a single line clear shifts the tiles above that line down by one row— this flips blacks to whites and whites to black, which can be used to correct parity for a single
T
perfect clear. Note however that standard back-to-back Tetris gameplay only clears four lines at a time, which always leaves parity unaffected.
Yet another nail in the coffin of perfect clears is how they cannot be performed with SZ
— as if we didn’t have enough reasons already to hate on these piece of shits red-headed stepchildren. This is so obvious that any explanation is just going to distract from the point, but these two pieces have a shape such that regardless of the orientation, what needs to be present in the play field to clear the top part of the piece will necessarily block what the bottom of the piece fits into. Well, except SRS:
In the apocryphal words of Winston Churchill: this is the sort of nonsense up with which I will not put.
6.2 — Combos
Combo scoring in Tetris is relatively straightforward: it essentially rewards relentless line clears, giving a larger and larger bonus for every piece that is dropped. It gets reset on the first piece drop that fails to clear any lines. Note that while there is some conceptual overlap with the back-to-back bonus discussed in section 4, these are more like yin-yang opposites:
Back-to-back bonus: gets reset by clearing 1, 2 or 3 lines (leaving
T
-spins aside for now). Disregards pieces that get dropped without clearing lines at all. Once active, back-to-back bonus jumps straight to 50% and stays there regardless of how long the streak goes on.Combo bonus: gets reset by clearing 0 lines. The combo counter depends on number of pieces dropped, not total lines cleared, such that single line clears are the most efficient for stacking up combo bonuses. Bonus grows indefinitely, though the size of the play field upper bounds the length of a combo.
Footnote: clearing lines with two pieces in a row applies a combo count of 0 to the first clear and 1 to the second clear. There is an annoying off-by-one offset between the number of pieces used for the combo chain and the actual combo counter, ultimately to avoid having a single line clear counting as a a 1-length combo by itself.
A quick and dirty calculation is to take the fullest possible play field, with nine tiles in each of twenty rows, for a total of 180 tiles, and divide by six to get a theoretical maximum combo length of 30. The number six comes from observing that dropping a piece adds four tiles, from the piece itself, and subtracts a minimum of ten tiles, from the line clear required to keep the combo going.
At the end of a perfect combo, the play field is completely cleared and we have to build a new combo-friendly structure before we can start scoring again. We can calculate the score efficiency of this system:
Which is very similar to the score per line for ideal perfect clears. Due to the cumulative combo bonus, the score per line is sensitive to what combo lengths we actually manage to achieve in practice. While the summation makes the total score of a combo quadratic in its length, the ppl is quite simple, increasing by 25 every time the total combo length increases by 1.
Before we get deeper into combos, it’s worth noting that there is no fundamental reason why we cannot score both combos and back-to-back Tetrises at the same time. However, the max length of a back-to-back Tetris combo is just 3: we must have an
I
inHOLD
while also getting twoI
pieces from the preview. While quite restrictive, this is less unlikely than it might sound: given that anI
is already inHOLD
, there’s a 3 in 49 chance that we can do this with any given pair of bags, where the extra 2 possibilities require using theI
fromHOLD
to replace a piece that is in between the twoI
s we get from the bags. The three sequences areI|I
,IX|I
andI|XI
, whereX
represents any tetromino and|
represents the border between the two bags.Three back-to-back Tetrises normally score 3600 points before the level multiplier. The combo score for three line clears in a row is a mere pittance: 0 + 50 + 100 = 150 points, a 4% bonus that comes at the cost of having to maintain a 12 rows high Tetris ready stack as well as dedicating
HOLD
toI
pieces. And even then, we can only spend 9 out of 49I
pieces in this way, so we would mostly have to settle for two Tetrises in a row to be able to drop enoughI
pieces into the column 10: at this point, we are closer to a 2% bonus. The cumulative bonuses really make combos an all-or-rounds-to-nothing kind of affair.
How do we actually do a long combo in practice? The simplest setup looks just like the normal back-to-back Tetris play, but with a 2-width well instead:
The 2-width well as shown above is easy to combo, but since each piece adds more than just the two tiles necessary to clear a line we are guaranteed to eventually get double or even bigger line clears, burning through the 20 rows of ammunition too quickly. With an upper bound of a 10-length combo, we cannot score more than 325 points per line, which is barely enough to improve on the 300ppl of back-to-back Tetrises. Just the smallest dose of reality, for instance the fact that we need space at the top of the play field for new pieces to avoid an immediate game over, is enough to make 2-width combo less bang for more buck than the simple workhorse that is back-to-back Tetrises.
But we haven’t quite exhausted the possibilities of combos yet. We can play with 3-width or even 4-width wells. On the face of it, this seems like a step back. The wider our well, the fewer tiles in the play field and the shorter combos. However, the problem with 1-width and 2-width wells is that they lead to wasteful multiline clears. For a 3-width well, which is a bit more difficult to consistently combo, we have a bigger 3 by 20 rectangle of empty tiles to fill in with pieces, which suggest a 15 length combo or 450ppl. A funny thing that happens with 3-width wells is that I
pieces, usually the most desirable of all pieces, are actually a major headache during the combo phase.
The same mathematical argument indicates that a 4-width well enables 20 length combos, getting us all the way up to 575ppl which corresponds to a score of 1.7 million for 240 lines. It is sufficiently practical that 4-wide centered wells exist somewhere on the spectrum from strong to blatantly overpowered in multiplayer Tetris. The advantage of centering the well is that the sides can safely be stacked up to row 20, and for that matter even above row 20, because new pieces enter the play field in the center. But just because people who are serious about competitive Tetris can combo down 4-width wells somewhat reliably, that doesn’t mean that I can do it: it is an advanced technique that involves watching the piece preview with vigilance while diligently managing the residual of the well.
A perfectly clean 4-width well is obviously hopeless to combo — only horizontal
I
pieces are able to clear lines at all. In practice, the well is built with three tiles of residue at the bottom, sticking into the well from the side. This allows some pieces to clear a line when dropped in the well. Note that the line clear required to keep the combo going clears four tiles inside of the well, balancing the four tiles added by the dropped piece, such that the residue will always stay at three tiles. The shape that these three tiles form will constantly change: the forbidden techniques to take advantage of the available degrees of freedom to keep the residue compatible with the previewed pieces are covered in a big, leather-bound tome kept in a secret vault.
This leaves us with three main paths to breaking into the vaunted seven digit score range:
Much longer survival play, going way past level 25 and brute forcing the problem despite a low number of points per line. Probably doable, but involves no interesting theory.
Much longer back-to-back Tetris streaks. Each of the 10-12 extra difficulty levels adds more speed and pressure. This would require a qualitative improvement — it is unfeasible absent new techniques.
Combo based play, perhaps using a 3-width well reaching somewhere around 400 or 500 points per line to blow past the million before level 25. While probably the most interesting alternative, this pattern of play feels challenging already at very slow speeds.
None of these paths seem particularly inviting, unlike the temptress that is T
-spins: perhaps too inviting. At what cost to our dignity? Our sanity? Would you cut a great road through the law to get after the Devil?
6.3 — T
-spin me right ‘round, baby, right ‘round
6.3.1 — Background and motivation
While I ought to explain what a T
-spin is, first a content warning: T
-spins are SRS-adjacent, ranging from merely questionable in their simpler forms to outright daemonic when we get to T
-spin triples, which require abusing a quirk in the SRS implementation to cause the T
to teleport into impossibly tight spaces. There, but for the grace of God, go I.
The motivation for looking into T
-spins, despite their somewhat unsavory characteristics, is their insane scoring potential. I am sure you could come up with some real world analogue if you really wanted. At first blush, T
-spin singles seem like they can reach 1200ppl, which blows even the hypothetical single line perfect clears out of the water. It is however impossible to be in a fully committed relationship with T
-spin singles — each bag gives us 28 tiles and just one T
, so limiting ourselves to only T
-spin singles can only clear a third of the incoming tiles.
In the ideal world where we invest all the excess tiles into Tetrises, both maximizing scoring and preserving the back-to-back bonus, we can estimate the points by diluting the 1200ppl for 1 line of T
-spin single with 1.8 lines of Tetris clear for 300ppl: this weighted average over a large number of bags comes out to 621ppl. Using T
-spin doubles instead, with 900ppl for 2 lines and 300ppl for 0.8 lines, we actually get 728ppl — the doubles score worse, per line, but they more than compensate by doing fewer Tetris line clears. Yes, we have come so far that Tetrises are no longer our gameplan, but instead a drain on our scoring potential. T-spin triples, requiring no dilution at all, could reach all the way to 800ppl, but there’s a difference between the mild heresy of T
-spin doubles and outright deal-with-the-devil witchcraft.
So, what is a T
-spin? What is all this about the birds and the bees? The exact definition has to with whether the four corners of the 3 by 3 box centered around the T
-piece are empty or filled. In order to get the T
in there in the first place, one open corner is normally required. Whether the two filled corners are in the front or the back of the T
determines whether it is a proper T
-spin or a second-rate Mini T
-spin. You are not supposed to understand any of this, just shrug and move on. There are further edge cases, but we need only concern ourselves with the most basic T-spin:
This is perhaps the time to ask ourselves: of all the things that you can do in a game of Tetris, why are T
-spins given preferential treatment? It’s sensible enough that the game rewards multiline clears such as the Tetris, and even perfect clears and combos seem like reasonable enough ideas — they are satisfying to pull off regardless of whether you care about points and they offer a bit of opt-in challenge. But T
-spins? Most why questions like this don’t really have any good answer, but for T
-spins I think we can do a decent job of reverse engineering the events.
The reason T
-spins snuck into Tetris games in the first place, before they carried any special reward, is almost surely a coding oversight. Our physical intuition is to think about pieces undergoing continuous, Euclidean rotation, and by this logic T
-spins shouldn’t be possible — the corners would block the rotation, just like when trying to maneuver a big couch up a narrow staircase. But the natural way to code piece rotations is just to test whether the tiles the piece would occupy after rotation are empty, without thinking about any kind of collision detection for the intermediate sub-90° rotations. The end result, at least, is that T
pieces are allowed to do quantum tunneling: the game only cares about the start and end states and ignores violation of energy conservation collisions that presumably happen in between.
Only after having played around with T
-spins — I assume, I am taking this from my imagination and not from historical archives — did people begin to realize that they are kind of neat. Why? The basic Tetris clears using I
lead to a fairly simple play style and gives no reason to deviate from a bog standard Tetris well structure. Setting up T
-spin doubles and having to mix in other line clears to keep the play field down adds a new dimension to the gameplay. A bit of an artistic dimension, even.
Well, at least it was intended to. But if there’s a cage match between an intentionally designed system and sheer human ingenuity, I would bet on the latter, every time.
6.3.2 — Systema Riviclia (not a chess opening)
Disclaimer: I got the basic pattern for the double T-spin loop from a video crediting Riviclia as its inventor. I stumbled across it while trying to look into bag-based back-to-back Tetris patterns, in order to iron out the kinks in the method described in subsection 5.1. As far as I can tell, Riviclia is an elite Korean Tetris player: feel free to dig deeper into his Liquipedia profile or watch him play a tournament match.
I have not looked at any theory for the system beyond the basic pattern for the seven tetrominos: essentially, I took what you can reverse engineer from the below figure as my starting point. All the minor tweaks as well as the dumping schemes are of my own invention. In other words: whatever is good about the system is due to Riviclia, and all the ad-hoc nonsense is from my tampering.
It is easy enough to design repeating patterns using equal amounts of the seven tetrominos. The difficult part is to make them practical, that is avoiding them breaking down when the permutation in a particular bag forces some pieces to be placed before others. There are two key limitations: a piece can only be placed where there is a vertical surface to support it, and there must be an opening for the piece to enter the space. The strength of the pattern above is that it almost completely disregards the order of pieces within each particular bag. The bag based randomization guarantees the macroscopic ordering of the pieces, and the system itself is compatible with all possible bag permutations — or it will be, at least, after a bit of tweaking.
I
: Can be placed in any order (supports itself, blocks nothing).J
: Can be placed in any order (supports itself, blocksZ
only in combination withT
).Z
: Can be placed in any order within a bag. Breaks when placing twoZ
before oneJ
: the previous layer’sJ
forms the platform for theZ
.L
: Can be placed in any order (supports itself, blocks nothing).O
: Can be placed in any order. Breaks when placing twoO
s before oneL
. TheO
requires a platform from the previous layer. Strictly speaking,S
could provide the platform, but if theL
is not already placed, theO
will block its opening.S
: Must be placed afterO
(supported byO
, blocks nothing).T
: Must be placed last, in order to properly clear lines. Would always blockS
and together withJ
blockZ
if placed before them.
From this rundown we get that five of the pieces have no within-bag dependencies. However, the pattern is still very fragile: any bag with ST
before O
will break it, which is one in three bags. We have another, unrelated problem as well: due to the offset between the left and right halves of the pattern, we need to build some extra scaffolding to get the T
-spin holes perfectly lined up. But sometimes we actually get to have nice things: the bag-permutation and the halves-offset problems can actually cancel each other out in the most convenient manner.
Now we’re cooking. We’re cooking with gas.
6.3.3 — Spinning and dumping
Systema Riviclia is very easy to play in T
-spin mode. The no brain required-pattern from subsection 5.1 reduces an open-ended heuristics based calculation into a simple flowchart, but with non-trivial conditionality and branching. Riviclia is much easier. The game state converges every seven pieces (aside from the bottom well and column 1 slowly growing) and most pieces can be placed robotically: you can nearly short-circuit straight from eyes to fingers and let the brain have some me-time.
I: clockwise, 6 left
Note to self:
counter-clockwise
would save aleft
due to verticalI
and upside-down verticalI
having a left-right offset)
J: clockwise, 3 left
Z: clockwise, 2 left ***
L: counter-clockwise, 5 right
Note:
counter-clockwise
stands in for threeclockwise
; trying to do a full eight presses for eachL
was the last straw that made me start using the alternate rotation mapped to theZ
-button
S: 2 right ***
O: 3 right ***
T: clockwise, soft-drop, clockwise
There are a few quite minor complications, marked by asterisks: ZO
might require tucking, if they come after JL
respectively: these pieces in the same layer block the vertical hard-drop path. S
requires HOLD
, if it comes before O
. Tucking slows down play overall, which matters for Tetris modes where you are racing the clock or an opponent. For my purposes, the line clear counter is the only clock, so I don’t particularly mind tucking, though it is a bit error-prone at high speeds. S
-swapping with HOLD
should only be a minor nuisance, but is a frustrating source of catastrophic errors, probably because that’s where the brain needs to get back in the loop again.
The bigger challenge is that we will have to swap from the main T
-spin pattern to maintenance mode regularly. Every bag gives us both one more row of 3-width well at the bottom and an extra tile on top of column 1.
The above figure shows the first problem that disturbs our zen-like stacking flow. This is a very innocent problem: excess I
pieces can be dumped in the bottom of the well, which deals with column 1 building up and clears parts of the well. Because of the residual tile in column 5, dumps should go in column order 756
: first the least accessible column due to S
pieces intermittently blocking access, then on top of the residue in column 5 to avoid breaking the back-to-back bonus with a single line clear, then finally column 6 for a Tetris clear. The only mistake that can really be made here is to dump too many I
pieces too early, causing T
-spins to clear no lines. Note that the well needs to be 9 rows below the T
-spin level to allow an I
to slip past an S
and into column 6, after an I
has already been dumped in column 5. 9 rows is almost half the vertical space of the play — accounting for potential residue at the bottom of the well and the extra height above the T
-spin water level in the left half shows that the board can easily get cramped.
This figure shows our next pain point, which is more awkward and calls for some actual finesse. The well is getting too deep, or more precisely, the sides are getting too close to the top of the play field. This happens because the well grows by 1 row per bag, but we only get a single tile of spare I
piece. We need three I
s to clear four rows, but while accumulating up three full I
pieces we gain twelve rows of well. If you imagine a traditional scale weight, you should picture it way out of balance.
The only tools available to us are the other pieces. We will basically use the well as a garbage chute, tossing pieces in to avoid having to place them on the side and to downstack the sides. After this has freed up some real estate, we can go back to T
-spinning. However, we have to make sure we do it in a way that lets us seamlessly transition back into system. In particular:
We need to circumvent
S
blockades: in the window of time, fromS
is placed as some sort of lid on top of the well untilT
clears it away, the entrance into the well is too narrow to accommodate and pieces other thanI
. This prevents us from dumping, and for many bag permutations this is quite restrictive. Because of this blockading effect, it is unsafe to delay bag dumps indefinitely — at the last possible moment, when the sides have grown too high for us to keep stacking pieces on top of them, there is a good chance that well is unavailable for dumping. While I have of course never experienced this first-hand, it seems like it could break the system. Source: definitely not first-hand experience.We need to dump equal amounts of each tetromino into the well, so that we can return to the
T
-spin system with everything in harmony. Strictly speaking, we can tolerate extraIJL
, since these all self-stack, but they will add undesirable height to the sides and force us to tuck all the time. ExtraOSZT
spell disaster: forgetting to dump for instance anO
and having to place the extra one while the well is blocked will break the system. Or so I would imagine.Since we need a
T
piece to unblock the well, and since ourT
pieces are delayed by one bag and can randomly appear either early or late in the next bag, we cannot just decide that we want to start and end the bag dump at the border between bags. Dumping a full bag in one go would be much easier and avoid much thinking and counting, but we cannot rely on these opportunities. Also, keeping track of where bags begin and end is quite a headache.Since
S
is the blocking piece, it is convenient to use it to start the bag dumps. This significantly increases the likelihood of maintaining access to the well. In general, I find it easier to do right-side and left-side dumps separately, that is to first dumpLOST
and thenJZ
. It is more ideal to do sides in one go — it loses less points due to breaking the back-to-back bonus for theT
-spins — but splitting the dumps is less demanding in terms player memory and well depth.A full bag dump is 6 pieces (
I
s have their own dumps) of 24 tiles that go into a 3-width well. With perfectly tight packing, this is 8 rows. Realistically, a full dump might easily take 10 rows. Factor in some preexisting residue at the bottom of the well, and you require a quite high well to be able to do a full bag dump without risking blocking the spaceST
will need when resumingT
-spins.
This brings us full circle: we can keep doing T
-spins, I
dumps and bag dumps indefinitely, and while the bag dumps will drop our points per line a fair bit compared to the ideal 621ppl, we only need 1M points / 240 lines = 416ppl to break into seven digits by level 25. All hands on deck, men.
There is one additional detail that goes into setting up the Riviclia system. In an earlier figure, we showed an idea of using a single
T
piece as the platform for the left hand side. This is simple and it works, but it creates a pocket in the first row that we will never be able to clear. Real estate is quite precious: the height of the play field basically determines how long we can run the back-to-backT
-spins and how much margin of error we have to play around with for timing the maintenance dumps.To enter into the system, we have two basic requirements: correct offset between the left and right sides and correct bag state: in particular we need the one bag delay for the
T
piece. A slightly modified platform solves this problem (source: this was once revealed to mein a dreamhalf-asleep):
Because there is indeed a benevolent God, or perhaps just due to the miracles of coincidence, the row clearing maths of spinning,
I
dumping and bag dumping lines up beautifully.
Consider 12 bags: this builds up 36 tiles in columns 2-4 and 8-10. We can match this with 9
I
pieces, giving 12 T-spin doubles and clearing 24 lines. We are left with a 12 row deep 3-width center well and 3 extraI
s.Do an
I
dump with the 3I
s. We get a Tetris and are left with 8 rows of center well.Consider a 13th bag. (Ominous number!) Do a bag dump with the 6 pieces that are not
I
. Six pieces correspond to 24 tiles, which is exactly the size of the 8x3 center well.We are left with nothing at all: everything added has been cleared away and we’re perfectly set up to restart the cycle (aside from one extra
I
, the easiest of all pieces for placing or dumping).The biggest unknown is the shape of the residue at the bottom of the well, which may have changed depending on the order of the dumps. But
I
dumps are insensitive to residue — they can always Tetris clear if we order the three columns correctly, and if we give up on the Tetris bonus they will clean up pockets in the residue. Bag dumps can work with any reasonable residue.
7 — In which the threads are woven (1M?)
7.1 — Et tu, Riviclia?
Like a masterly crafted mechanical watch, Systema Riviclia is a beautiful piece of engineering. Just like a Rolex must deal with leap days and other irregularities of timekeeping, so must Riviclia also be adapted to work around the imperfections that is inherent in its design. However, despite all its wondrous qualities — Riviclia does not score 1M points.
This is not a mathematical truth, but what we observe from taking the system for test some flights. The score per line calculations clearly show that the Riviclia system can deliver the goods, but as with back-to-back Tetrises, the limiting factor is not the airplane, but whether the pilot can handle the g-forces. Human error rears its ugly head, but unfortunately, the plane must go to war with the pilot it has.
While Riviclia is very easy to play in the spin phase and at reasonable speeds, there are three key problems:
Deciding when to start dumping requires paying careful attention to the play field: the well must be deep enough, the sides must not grow too high, and the
I
piece column is a recurring problem. During dumping, it’s essential to track exactly which pieces have been dumped, and with an uncomfortably shallow well they must be packed properly, not just dumped willy-nilly.The gnawing uncertainty towards the end of a bag dump as you try to remember whether you already dropped an
O
is not good for the blood pressure. Careful with theeggssaltwhatever it might be that causes high cholesterol these days.
As the game grows faster, the margin between minimal well depth (to accommodate a full dump) and maximum side height (to be able to maneuver particularly
I
andL
into their positions at the edges) grows uncomfortably thin. Timing the dump phases while avoiding catastrophicS
blockages becomes non-trivial.Nothing quite ruins a good dump — what? — like realizing that it rises up too high towards the end, blocking the
S
piece from going where Riviclia dictates it belongs. Sad trombones — this is your cue.
There is no margin of error. Reforming the Riviclia system after practically any mistake is extremely challenging. It is probably not impossible for
Neo, i.e. The Oneelite Tetris players, but what I can say with absolute certainty is that it’s too hard for me.
Back-to-back Tetrises only scored about 650k, losing about a third of its score potential to partial breakdown of the system at higher levels. Riviclia breaks down at roughly the same difficulty level, and in a more forgiving world, this would have meant that we still scored about two thirds of the max score for 1.2M points. However, since the level scaling for score means that most points are earned towards the end — mathematically, the last half of the line clears score three times as many points as the first half. Since Riviclia has a much higher starting point, sub-par single and double line clear makes for an even steeper drop and proportionally even more lost points than observed for back-to-back Tetrises.
Straight out of the box, we can only do about 850k with Riviclia. Men less reflexively stubborn and more commonly sensible would have cut their losses. But they also never would have set out on this absurd expedition in the first place. They would be — watching TV or visiting family or something, I guess, whatever it is normal people do.
7.2 — Once more unto the breach, dear friends, once more
850k is already quite close. Spitting distance is perhaps not quite the way to put it, but it’s close enough that we can touch the fruit and smell its sweet juices. Too close to just pack up and go home.
So it’s time to pull out all the stops. There are fundamentally three phases to our high score game plan. Each of them must be pushed to its limits to make up the missing 150k points. We can’t be content to just half-heartedly squeeze the the orange — we need a hydraulic press that will wring every last drop out of it and leave nothing but a pancake shaped peel behind.
Phase 1:
T
-spin doubles with regular dumps. There is not much to improve on here: the system could be slightly more efficient if we didn’t dumpT
pieces, but the smooth 3-width well feels exactly too narrow to fit anyT
-spinning inside of it. The goal is instead just to keep the Riviclia system running for any many lines as possible before it falls apart.My earlier attempts would stumble anywhere between 20 and 100 lines, just due to lacking consistency. Near-zero error rate doesn’t quite cut it when you need to place more than 300 pieces in a row exactly right, unless you are working with very large values of near. As I gained more experience, I was able to break 100 lines most of the time, struggling less with inexplicable fumbles and more with the overwhelming pressure of high gravity.
Phase 1 play is very responsive to practice. The Riviclia play style is completely different from normal Tetris, and just putting in time works wonders for improving in something unfamiliar. Plateauing and the need for deliberate practice and methodological breakthroughs comes later.
It helps that the gameplay is so systematic — each game follows essentially the same script. Occasionally there is some cleverness requires to navigate the individual bags, particularly when dumping, but if you zoom a bit out, every game follows the same trajectory and hits the same checkpoints. There are vague similarities to the concept of build orders in real-time strategy games: first
I
dump is ready at 20 line clears, followed by anS
-less bag dump at 26 lines, and so on.With time, 150 line clears in the Riviclia
T
-spin doubles systems would be a reasonable target for a high score eligible attempt. This gets you to roughly 700k with 100 lines to work with for the second and third phases. The exact numbers depends on the cleanliness of the maintenance dumps, primarily how manyT
-spin doubles miss their back-to-back bonus and how many of theI
dumps score as Tetrises.
Phase 2: Back-to-back Tetrises. This is a compromise between score efficiency and the practical realities of high gravity. There is a window of time where the gravity is still tolerable for Tetrises that allows us to squeeze in some extra points before going full survival mode. There is no special trick to this, but every bit helps:
Stacking according to best practice as seen in section 4.
Flirting a bit with the most important modern Tetris mechanics: juggling pieces to prevent them from locking in and building highest in the middle columns to allow pieces to roll in either direction. Otherwise, it’s relatively common to waste an
I
in the middle of the play field simply because instant gravity and pits in the structure conspire to trap them somewhere they are not supposed to go.Trying to maintain the
T
-spin doubles too long risks heavily damaging the structure, requiring a large number of ineffective line clears to downstack before we transition to Tetrises. Worse yet, these line clears waste precious moderate-speed lines that allow clean back-to-back Tetris scoring. It is better to just bite the bullet and transition cleanly and intentionally into phase 2, skipping past the pitiful and severely punishing 100ppl line clears. In particular, it is nice to transform a 3-wide Riviclia well into a single width Tetris well, though we would prefer to eventually shift the Tetris well off to the right edge of the play field.
Phase 3: Survival mode. There is no sharp transition from Tetrises to survival, but we will gradually find ourselves slipping from maintaining back-to-back bonuses most of the time to instead just getting the occasional Tetris. Vertical space barely matters at high speeds, where we are almost exclusively relying on the lock delay grace period. Due to the level multiplier applied to scoring, there is still quite a bit of juice to be squeezed in this stage of the game.
A single back-to-back Tetris at level 20 scores 24,000 points, basically a full fortieth of our total score goal. Doing Tetrises reliably at this level is very difficult, but occasionally managing to hit a few of them is completely doable given a sufficiently large number of test flights. A few pilots will crash and burn, but it is a sacrifice I am willing to make.
Clearing our way through the entirety of level 25 with just single lines scores 25,000 points, which is pitiful considering how much more difficult it is than everything else we are doing in these high score runs. Nonetheless, 25,000 points is more than just loose change when it comes to bridging the gap from 850k to the full million, and every cent counts.
None of this was actually enough. I probably managed to land roughly 5 games in the 900k range, the highest just shy of 950k, almost mockingly close to the target, before I decided to cheat. Yes, shame consumes my body, guilt wracks my mind, my very soul has become a plaything of the Devil’s.
I sat down and played one (1) game with a real keyboard. I had been piloting all the Tetris test flights on a laptop, mostly sitting on the couch much like how a bag of potatoes sits in a damp cellar. I have nothing bad to say about laptops, they are a wonderful compromise between practical and perfect, but the awkward response curves and the minimal travel distances of their keys are nowhere near ideal for fast, precise and consistent piece placements.
I sat down and played one (1) game with a real keyboard. And in my mind’s eye, I decided — I decreed, as sat I upon the Imperial Throne and not in a squeaky office chair from IKEA — that there was a time, and there was a now, and that these two were one and the same, two faces of the same coin, two halves fitting together as does the lock and its key. I decided that now was the time and that the time was now.
I sat down and played one (1) game with a real keyboard. And lo and behold.
Towards thee I roll, thou all-destroying but unconquering whale; to the last I grapple with thee; from hell's heart I stab at thee; for hate's sake I spit my last breath at thee.
Herman Melville, Moby Dick — Captain Ahab’s final hunt
Regarding the initials, you will be pleased to know that I moonlight to fight crime alongside fellow superhero Shock. Together, we form a blazingly fast and hard-hitting duo.
Embedded above is a reenactment of my first one million point run, which I didn’t record. There are some brief comments in the description. There are some key differences between this version and the unrecorded original:
Played on laptop while recording. This introduces noticeable lag. At times it seems to slow the game a bit down, making things somewhat easier, but it also messes up input timings, which more that cancels out the benefits of slowdown. Occasionally, the game will stutter in such a way that a single
left
tap gets repeated ten times and shoves the piece to the edge.Played with 20ms auto-repeat delay, which makes getting pieces to the edges much easier at higher speeds. There is a very powerful buffering technique which involves first holding down
left
and then triggering theHOLD
swap: the piece that gets unleashed formHOLD
will almost immediately snap over to the left edge. This unlocks a number of otherwise impossible placements, such as stackingI
pieces super high in column one.Much more solid back-to-back Tetris play in phase 2, ultimately getting a whole 135k points past the million. There are still significant flaws — a few less bad mistakes would get us to one and a quarter millions. Super polished play would probably break one and a half millions. But for the grace of God, as they say.
This game actually crossed the threshold with less than 240 lines cleared — the first one million game was slightly behind schedule and had to scrounge together the last few points during level 25, which was not the original intention.
8 — Where I burn hard-earned goodwill by soapboxing
With all that out of the way, we can finally lower our shoulders, let our breath out and stop pretending. Phew! Doesn’t that feel good? Tetris is indeed not important. So let’s take a moment to talk about our Lord and Savior —just kidding, more Tetris. I had you there for a moment, though, didn’t I?
8.1 — Water finds a crack
The self-stacking Beautiful Dream and the Riviclian T
-spin assembly line — do systems of this sort somehow ruin the magic of Tetris? If we can script our entire game plan in advance, if we are sidelining our subjective judgements and really just mechanically following a flowchart — are we really playing any more? What exactly is it that we are doing with our lives? he asked with a touch of panic in his voice.
I would say that, yes, these systems do in some sense ruin Tetris. But so does reading the final chapter of a murder mystery or solving a fiendish puzzle. We cannot watch Death Note for the first time more than once — alas! — but then again, its payload of twists and turns will blow your mind, and after all, having your mind blown too much is hardly good for you.
Just like dinner can be treated as sustenance or a social event or a culinary experience, so is Tetris a game of many faces. It can be approached as anything from a pastime to a competitive sport to a half-and-half mathematical puzzle and dexterity game. It feels presumptuous to tell people how they should enjoy games — other than not letting them become harmful addictions — but for me a part of the fun of a game comes from trying to crack it open and dissect it. Any similarities to Jeffrey Dahmer real persons are entirely coincidental!
Breaking the game to the point where it feels meaningless to play it any more isn’t the goal, per se, just like you’re not really playing golf just to get to write down some numbers on a scorecard. But it is a target we can aim towards to go on an adventure, discovering all sorts of vistas and treasure along the way. It is true that we might in the end be left with a toy that has lost its luster, but there isn’t exactly a toy shortage and we have but one life — alas! Oscar Wilde would say that the only thing worse than outgrowing a toy, is to never outgrow it.
The thrill of discovery is such an important element of games, such an integral part of why people engage with them, that engineering systems that targets this craving is one of the most obvious trends of modern game design. It feels a bit pointless to pick out examples, like picking straws out of a haystack, but it’s always good to make sure that we’re on the same page. It’s not only in Tetris we are at risk of desynchronization — the same happens in what is intended as conversations, two ships minds missing each other in the night, typically without anyone ever noticing.
Tabletop roleplaying games unleashed a memetic superweapon on the world: experience points, with their tangible progress towards discrete level ups that unlock new abilities and spells for players to try out. This used to be a defining feature of tabletop and computer roleplaying games, but variations of this formula is now an almost universal feature of games, either within the gameplay loop itself or wrapped around it. Just 200 more crystals to unlock level 7 talents!
Real-time strategy games, all the way back to their progenitor Dune 2, tend to build their single-player campaigns as a series of individual missions, where part of what drives the player forward is each mission progressing the storyline and giving the player access to more advanced units and upgrades.
Sidebar: While both draw on source material from Frank Herbert’s fictional universe, which is very topical these days, the computer games Dune 1 and Dune 2 are about as unrelated as they could possibly be. Dune 1 is an adventure game that leans very hard on the 1984 movie by David Lynch; Dune 2 invented the formula for real-time strategy games that would inspire Command&Conquer, WarCraft and Age of Empires.
Games in the 1990s made a profit off of players’ ravenous hunger for content by making expansion packs, which could range all the way from embarrassing cash grabs to the finishing touches of a masterpiece. Since these days of innocence, monetization has taken a turn for the more shameless and more devious, to the point where you can no longer throw a stone around in the Steam store without hitting overpriced cosmetic DLC. This price discrimination based business model is so lucrative that studios often give the game itself away — it is a Trojan horse; its function is to smuggle the predatory DLC inside of your city walls. The first hit is always free.
Despite how awkward it is when dealing with plastic and paper instead of bits and bytes, even board games are increasingly using sealed boxes to enable unlock and progression mechanics, Pandemic Legacy and Gloomhaven being some of the more notable examples. Fortunately, these sealed boxes are already yours — they don’t come with a price sticker on them. Yet!
There is nothing fundamentally wrong with paying for more content — that’s actually how it is supposed to work. More fun games is an unqualified good, and you are going to need dollars to enter the system somewhere if you want to see real production values. But there is something perverse, or at least perverse-adjacent, about getting money too close to the challenge : achievement : reward loop that forms the backbone of typical games.
We can make a brief and not entirely satisfying taxonomy of games according to how they gatekeep access to the carrots they dangle in front of players’ noses. In doing so, we will just have to ignore how vastly different games can be in terms of whether they are focused on the main story or multiplayer leaderboards or open world exploration. Painting with an extremely broad brush, we can split them as follows:
Pay-to-win: Everybody’s favorite punching bag. By themselves, there is nothing wrong with either the paying or the winning. The problem is short circuiting the gameplay loop — a wire between money and rewards competes with and risks crowding out the role that the player’s achievements is normally supposed to play. You could say that the game studios aren’t really as interested in making games as they are in making money, and that consumers aren’t really as interested in playing as they are in the dopamine rush of phat loot. Pay-to-win really makes a serious attempt at cutting out the middleman, and in this metaphor the middleman is gameplay.
Collectible card games such as Magic: the Gathering are an illustrative example. There are definitely skill based elements as well, for instance deckbuilding and playing to your outs, but step 1 if you want to explore what the game has to offer or cobble together a competitive deck is buying overpriced cardboard. Try your best to ignore the gambling aspect of booster packs.
Grind-to-unlock: In its more innocent form, this model just portions out novelty at a pace that can offer a lot of depth and volume without drowning new players in it. Drip-feeding new game elements in this way guarantees a steady stream of discoveries and goals. As long as the game itself remains fun and rewarding, it can be fairly benign, but it’s questionable if new content substitutes for player-driven learning and discovery.
The grind is most sinister when the challenges in the game can only be solved by throwing absurd amounts of playtime at them. In its worst forms, the gameplay begins to function as a treadmill or a time tax, with the new content you are working towards just being more of the same with a new coat of paint and bigger numbers on them. These games can weaponize the sunk cost fallacy or FOMO: it is more that missing out on the rewards induces anxiety than that they are actually fun and interesting to play with. I would be uncouth to mention names, but World of Warcraft.
Improve-to-progress: It might sound unbelievable, but it used to be the dominant model for games that you would try : fail : repeat : learn : progress. Games had absolutely no qualms about getting players stuck at some puzzle or really difficult platforming sequence, leaving them with the responsibility of figuring it out. This is not to say that everything about old game design was better, but there is something to be said for games that primarily rewarded learning.
The big problem with these games was that they could be incredibly frustrating. To some degree, unfair difficulty was a way of stretching a small helping of content into a decently long game. In their defense, game design teams were tiny, games were generally bootstrapped into existence using nothing but a low level programming language, and the hardware limitations were so extreme that it made sense to offload text and images to printed materials shipping alongside the game software. A very early form of pay-to-win that showed up in some old games was puzzles made to be obtuse on purpose, in order to incentivize players to buy guidebooks. If you squint, this is almost like on-disc DLC, twenty five years ahead of its time. Sometimes, the future is just the past reinventing itself.
I want to suggest that frustration is actually a good thing, analogous to how it is good to feel pain when you rest your hand on a hot stove: it’s the healthy reaction to failing, not merely to reach your goal but even to inch closer to it. If you are just ramming your head against a wall, you ought to notice that you are wasting your time and try to change things up. Modern game design often papers over this kind of frustration and mimics the experience of progress, learning, discovery and improvement. Even when what’s happening is none of the above, games have gone in the direction of stacking up hidden bonuses on players until they cannot help but succeed, instead of just being honest and going your gameplay is bad and you should feel bad.
One of the most popular buzzwords in game design these days, particularly indie games, is roguelike. Much ink has been spilled about what actually defines a roguelike — if the visuals aren’t a jumbled mess of rainbow colored ASCII characters, how much can it really be like Rogue? — but I would argue that the load-bearing design principles of roguelikes are permadeath and no persistent progression. Somehow, these games still manage to feel rewarding. It’s just that the player progresses in terms of his own knowledge and understanding of the game, rather than his avatar’s gear and talents.
All of this is just to say that what we have seen with Tetris is just games as they are supposed to work, as they indeed used to work, before something alien took their place. Something equal parts social engineering and Skinner box killed off the platonic ideal of a game and presently wears its corpse a skinsuit. It masquerades as games to attach themselves to hapless victims and suck them dry of their sweet, sweet nectar spare time and disposable income.
I realize I got a bit carried away with the rhetoric here. There is something to be said in favor of a games that manage to entertain or even excite players who just got home from a long day of hard work and aren’t really in the mood for the video game equivalent of high intensity interval training. I’m primarily pushing back against the unreasonably common sentiment that there’s a contradiction between taking games seriously and enjoying them. And when pushing, if you have sufficient pent-up frustration to vent, it’s no fun to hold back.
All fun is equal, but some fun is more equal than others.
8.2 — The unreasonable effectiveness of deliberate analysis
There is an article by Eugene Wigner, winner of the 1963 Nobel Prize in Physics, titled The Unreasonable Effectiveness of Mathematics in the Natural Science. It is perhaps unwise to introduce someone as a Nobel Prize winner when you are trying to set them up as your foil, the Goofus to your Gallant, but then again — no one was ever crowned king for shooting at the court jester.
The main thrust of Wigner’s article is that there is something surprising about how people have been able to make sense of the world at all, to discover regularities in its behavior in the form of laws of nature. Furthermore, reflecting the article’s title, he points out the role of mathematics in this endeavor, as not merely useful but almost miraculously well-suited to understanding the natural world. While a great article in a food for thought kind of sense, to whet your appetite, I think Wigner makes a bit of a cart-before-horse sort of error — he said brazenly.
Lawyers have a reputation for being a bit butterfingered when it comes to truth and consistency. This stereotype, which is perhaps not entirely fair, but also not entirely unfair, is exemplified in the following joke:
Your honor, my client is entirely innocent. First; he was out of the country on the night in question. Second; he has never even touched a weapon, much less shot one. And third; self-defense was his only recourse when the man lunged at him and reached for his holster.
Seeing as this is a joke, we are probably meant to find it humorous or ridiculous rather than draw inspiration from it. But there’s nothing wrong with having a bit of fun, this is upside-down world, where Tetris is a matter of grave importance and philosophy is just a whimsical pastime — where Nobel Prize winners are foils and Tetris players heroes. As the defense lawyer, I will argue that all three parts of Wigner’s argument is misguided — the effectiveness is really not unreasonable; furthermore, it is not all that effective in the first place; and what is or is not unreasonably effective can not sensibly be called mathematics.
As Oscar Wilde said: the only thing worse than being wrong is being boring.
8.2.1 — Unreasonable?
First is the matter that the world seems amenable to scientific inquiry. The implicit argument is that the world didn’t need to be this way, which is true as long as you don’t mean too much by it. We can entertain the possibility of a less convenient universe, where the equations of motion weren’t reducible to position, velocity and forces. Prima facie, there is no good reason a particle’s behavior couldn’t have exotic dependencies on the entirety of its trajectory since the dawn of time, such that we would have to uncover the particle’s complete biography before we could predict its motion. If Wigner lived in this alternate universe he would be throwing his hands up and cursing the devil instead of marveling at the beautiful simplicity of second order differential equations.
When idly philosophizing about parallel universes, it’s not fair to analyze the simplicity of contrafactual realities in terms of the concepts we have developed specifically because they suit our world. Concepts are downstream of the behavior of nature — just like physicists can think in terms of particles or waves depending on the domain, so we should imagine that alien universes would be conceptualized entirely different from what we are used to. If there were no such things as elementary particles, if every speck of matter varied along dozens of dimensions, we wouldn’t have a periodic table with millions of entries — we just wouldn’t have a periodic table at all, and maybe an eight-dimensional hypersphere would be its substitute.
While somewhat controversial, anthropic arguments cause trouble for this line of thinking. We can imagine all sorts of universes, but our unconstrained imagination is not the weightiest of arguments — not in a courtroom, not in science and hopefully not in philosophy either. There is no particular reason why the world could not just have been a hypermassive homogeneous soup of pure energy, aside from the fact that we certainly wouldn’t have been around to observe it from the inside.
My strawman of Wigner would ask, isn’t it a strange coincidence that I am alive in the present, rather than the past or future? Isn’t it a strange coincidence that each and every one of the seamen are inside of the submarine, and all the water on the outside? Isn’t it a strange coincidence that my head sits upon my very own body, rather that someone else’s? What are the chances? Got to be like one to seven billion!
Given that the universe and its laws of nature must be able to support some form of complex life for anyone to be able to live in it and observe it from the inside, it is not shocking that it is at least somewhat simple, regular and comprehensible. Life is ultimately a form of self-assembled, self-replicating structure — in a parallel universe where we could not run repeatable experiments, because particle interactions depended on the current Unix time or something similarly obtuse, it seems almost hopeless for life to assemble cellular machinery that synthesizes proteins and copies itself somewhat reliably.
8.2.2 — Effective?
Next in line is the claim that the laws of nature are so beautifully simple. It is easy to see where he is coming from — gravity for instance seems more well behaved than we really deserve. But there is a staggering amount of selection bias in play here — gravity is not a representative example of nature’s complexity, and even so it just takes a three-body system for gravity to defeat mathematicians and their wily calculus. The apparent simplicity of gravity springs from living in a domain where the mass and closeness of the Earth allows for neglecting everything else. Nature is practically chock-full of stupefying complexity. It is mostly because we wisely avoid the dark back alleys of nature — turbulent flows, relativistic speeds, quantum decoherence — that we can lull ourselves into the fantasy that nature is simple.
In some sense, Wigner is like the drunkard who looks for his keys under the lamppost, not because that’s where he lost them, but because that’s the the only place with enough light to find them. The difference is that Wigner, standing under that lamppost, can’t help but remark that it’s a miraculous coincidence that someone has put up a lamp exactly where he happens to be searching.
Natural science is unreasonably effective in the same sense that indoor climate is unreasonably pleasant — we try to spend as much time as possible in a very small bubble where we aggressively eliminate everything that we struggle to understand and control. Nature does not lack in complexity — it is the natural sciences that studiously avoids eye-contact with the complexity.
A stark illustration of this can be seen in the vast chasm between biology and engineering. They both operate inside of the same physical world, but play to their respective strengths: natural selection takes advantage and recombination and culling to build Rube Goldberg-like systems of intricacy and complexity that boggle our human minds, while our technology picks out simple and predictable building blocks — aluminium frames and copper-wire circuits — and builds complex behavior by use of cleanly layered abstractions. The resulting designs are too different to even begin comparing, and they do not really inform us about the nature of the world as much as they do about about the capabilities of the blind idiot god evolution and monkeys in labcoats scientists.
8.2.3 — Mathematics?
The third and final point I would like to make is that it the effectiveness of mathematics is half false and half tautological. Humans are first and foremost intuitive creatures, and it is intuition that is our superweapon. Mathematics is a relatively thin veneer on its surface — intuition does almost all the heavy lifting, picking out the key factors and designing the experiments to narrow down the possibilities, while mathematics takes the credit for running the final lap of the relay.
Ignoring the critical role of intuition tempts you down the pathway of exploratory data analysis. What’s the point of all these overpaid domain experts, when we have statisticians running computing clusters that can mine vast mountains of numerical data for correlations? It turns out that if you just throw statistics at data, you will drown in spurious correlations before you find even a single meaningful result — the more formal version of this argument can be found in the no free lunch theorem, but it’s sufficient to just observe that some form of common sense is required to prune the astronomical number of all conceivable hypotheses due to combinatorial explosion down to something somewhat tractable. By the time you get to the point of fitting parabolas to a two dimensional set of data points, your intuition has already applied extremely potent inductive biases to reduce the problem to something suitable for the digestive system of a baby mathematics.
The tautological half is that mathematics is not comparable to a specific tool, like a screwdriver, or even a Swiss Army knife. Mathematics is the entire workshop — the tape rulers, the wrenches and the power saws. All of the useful tools we have been able to design are in there, as well as a bunch of experimental gadgets and old junk that we’ve never quite had the time or found it in our heart to throw out. Like The Borg from Star Trek, mathematics hungrily devours every formal system it comes across and assimilates them into its fold. The only real requirement for something to be mathematics is that there must be some way of distinguishing true from false statements and a set of valid operations for manipulating statements while preserving their truth value. In a system without any inconsistencies, as long as you start out with something true and don’t do anything expressly illegal, you can have full trust in all your deductions.
The alternative to the sort of formalized systems that Wigner calls out as unreasonably effective is intuitive reasoning based on heuristics. While vibes lack mathematical rigor, making them too fragile to support syllogisms or longer chains of reasoning, they are practical and useful. Even in domains that seem like they should be uniquely susceptible to mathematical analysis, such as board games, experience-based intuition tends to dominate. The machine learning based AI that is in vogue these days, while implemented as mathematical number crunching, is a step away from transparent, logical algorithms in favor of vague, intuitive generalization. And even the hardest of science rests on a bedrock of ill-justified intuition, such as the eminently reasonable but not particularly formal Occam’s Razor.
8.2.4 — Synthesis?
I am not convinced that I have ever quite understood the meaning of thesis : antithesis : synthesis from Hegelian dialectic. I am also not convinced that it is anything worth understanding — indeed, from doing the briefest amount of research to avoid embarrassing myself too badly, I am now even confused about whether Hegel himself stood behind this model or not.
Regardless, my interpretation of synthesis ends up being somewhat adjacent to the concept of steelmanning. The load bearing component is to engage in a form of constructive criticism, where the goal is not to just point out enough flaws in a theory (thesis) to discredit it (antithesis), but to resolve these flaws in a way that leaves the good parts of the theory intact while reinforcing its weak spots (synthesis).
Hoping to reconcile myself with the ghost of Wigner, I will suggest the following compromise synthesis: deliberate, mathematics-adjacent analysis can be a force multiplier when working in tandem with the rest of our mental faculties, ranging from not very effective to tremendously potent, depending on whether it is applied to music theory or electrical engineering.
9 — The Spire rests, and so shall I
9.1 — The four-minute mile
It is a somewhat curious coincidence that I set myself a goal of scoring a million points, for no other reason that this being a nice and round number, and that this goal turned out be almost perfectly on the edge of what I could possibly achieve. There is of course a tiny bit of selection bias in play here — let he who is without sin throw the first stone at Wigner — probably any goal in the range from 800k and perhaps all the way up to 1 250k would have produced the same feeling of strange coincidence.
There is a story about the four-minute mile (i.e. track and field), where the first runner to break this magical barrier was very quickly followed by a number of other runners. This story is often used to sell an Impossible is Nothing kind of message — that people were being held back by their mental barriers until they got proof that a four-minute mile was indeed possible. You can do anything you set your mind to, or something like that. It’s a good story, but that’s also what triggers my skepticism. A good story can survive, regardless of whether it is true or even believable, merely on merit of being memorable and memetic.
“ (…) for falsehood will fly from Maine to Georgia, while truth is pulling her boots on.”
From an 1820 article about a court case, via Quote Investigator at https://quoteinvestigator.com/2014/07/13/truth/
9.2 — Games and learning
It’s easy to think about games as a frivolous waste of time, and it’s not entirely wrong. But while it’s more right than wrong, it’s also not entirely right — our instinct for play is closely related to intelligence and a capacity for learning. Defining games is famously difficult, mostly because we tend to make the mistake of trying to define the physical objects or the abstract rule systems, but it is actually the activity that must be defined as play or not, depending on how we choose to engage in it. An illustrative example is chess — the activity of sitting at the table and moving pieces around on the board can be play, practice or work, depending on whether we are doing it for fun, to improve our skills or to win the first prize in a tournament. It’s made worse yet by how these three elements usually blend together — a young Bobby Fisher might have been doing all three at the same time when he was winning his first American Championships +8-0=5
.
Play is perhaps best defined as an activity we engage in without any meaningful goal or deliberate intent to improve a skill, but because it stimulates our learning instinct. Even here it is difficult to draw boundaries — surely the reason kittens engage in play fighting is ultimately to improve their coordination and ability to hunt prey. Almost as surely, the kittens themselves don’t understand this, and in so far as they conceptualize at all they would say that they are playing and their motivation is just to have fun doing it. It must be the same with kids, except we have a bit more difficulty actually understanding exactly how playing tic-tac-toe prepares us for life as adults.
That is not to say that all play is good, simply because it stimulates some sort of instinct. Take thrill-seeking too far and you get high-stakes gambling and the suicide implements called wingsuits. Even virtuous instincts with excellent public relations departments like love can lead straight into over-protective parenting or abusive relationships. I can fix him/her!
9.3 — From tetromino stacking to civilized society
What exactly can we learn from Tetris? I am sure there are elements of hand-eye coordination, pattern recognition and split-second decision making, but it’s not at all clear to which degree this kind of learning carries over to other parts of life. Is the brain a bit like a muscle, where picking weights up and putting them down again actually makes us better at jumping, hiking and wrestling? We do know that people are very good at adapting quickly to novel environments, particularly when compared to machine learning based systems which consume lifetimes’ worth of data and still struggle to generalize beyond the most trivial kind of infilling on the training data manifold. But I’m not going to try to argue that playing Tetris makes you a better person, particularly when considering the opportunity costs — that would be a fool’s errand and a monumental waste of time, and I would never waste time.
But we should exercise our general purpose learning capabilities. After all, that is what makes us human —that and hairlessness and endurance hunting and fine motor control of our vocal tracts and fingers. So for my next and final trick, let’s see just how far we can take this. What does Tetris teach us about Tetris? About ourselves? About life? And about — drumroll, please! — human civilization?
Perhaps Tetris was really important all along?
9.3.1 — Feel-good motivational posters go here
Impossible is nothing. No, wait, that’s an Adidas advertisement. But
cocainestubborn persistence is a hell of a drug. It can take you places, but don’t just get on any random train without first checking what’s its final stop.You make your own luck. Early on, when figuring out how to do back-to-back Tetrises, I felt like I was in a futile struggle against the next piece generator, such that Fortuna, goddess of chance, could at any moment decide I was not her favored and serve me a disastrous sequence of pieces. I felt like all I could do was cross my fingers and wait for lighting to strike the bottle, that I was doing everything that could be expected of me, that it was the Universe that was denying me my well-deserved high score. This feeling springs from a half-truth — if you just place one piece at a time and neglect the health of your structure, you are indeed at the mercy of chance, ever a capricious mistress. But by building flat, keeping an eye on the piece preview and cleaning up open pockets with tucked pieces, you can become the master of your own fate. Real-life parallels left as an exercise to the reader.
Think inside the box, but get some fresh air now and then. Dumb, relentless persistence is undervalued, I assume because people don’t particularly want to put in the hard work and would rather
findhave someone hand them a silver bullet. But there’s a time and place for everything — unless you manage to turn your brain off entirely, you will discover new patterns and assemble new concepts when you put in the hours. The problem is that you will inevitably build bad habits, and imprisoned by your own assumptions it is impossible to see the light of the sun and the blue sky. This is probably the aspect of practice that a good instructor can help the most with, but absent that, just playing your own Devil’s advocate now and then is a decent alternative.It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so. Usually attributed to Mark Twain, but definitely not from his published work — perhaps due to Josh Billings, either a very early pioneer of lolspeak or perhaps a wayward time traveler (1874!). See https://quoteinvestigator.com/2015/05/30/better-know/ for more details.
Deliberate analysis is a force multiplier. Intuitive learning and deliberate analysis has fundamentally different blind spots. Intuitions are powerful and almost effortless, but unless you are the Tetris Whisperer, you will not discover Systema Riviclia without sitting down and actively investigating bag based patterns. The best results are achieved through left- and right-brain teamwork. Imagine a circular process, where observations during normal play produces intuitions, which reflection tries to formalize and find ideas to improve on, which then feeds back into play.
Practice is king. I have focused the most on theoretical ideas, in part because that’s where my curiosity tempts me, but also because ideas can be communicated while muscle memory is stuck inside of my own neural pathways. I could probably get a lot better at pressing buttons fast, but at the end of the day, all I could report from it would be that it’s important to practice a lot and to nip bad habits in the bud. However, I assume your Russian piano teacher has already told you this, in between boxing your ears.
9.3.2 — Stranger than fiction
People are bizarre. Particularly for reasonably popular and
nerdyscientific topics, there is an incredible wealth of resources out there, documenting everything you can’t be bothered to research yourself and presenting the Internet hivemind’s solution to all the problems you have failed to solve. The mind-boggling number of hours humanity has invested into Tetris, even while it is being ravaged by malaria, famine and war, is both amazing and a bit embarrassing. If the aliens landed, trying to estimate our conservational value, I wouldn’t feel super comfortable about having to make the case for H. Sapiens.Passion is beautiful. There is something magnificent about these obscure corners of the Internet, where people come together with no ulterior motives, only a shared passion. It is a welcome contrast to the mainstream Internet, ever more heavily monetized, full of influencers-in-training pretending to be nice to each other while producing clickbait from the same overused templates to desperately try to draw eyeballs to their content, all in service of their advertising revenue. Like when you leave a cramped room after a meeting that went way over time, it’s easy to forget what fresh air actually feels like. You should try it some time, it’s great!
9.3.3 — Cultural transmission of knowledge is civilization
Monkey see, monkey do. I accidentally stumbled over a video showcasing the Riviclia double
T
-spin system. In less than sixty seconds of peeking over the virtual shoulder of a more knowledgeable player, I had gotten everything I needed to take my high score from 650k and past the one million milestone. Having already designed a vaguely similar system for back-to-back Tetrises, it is conceivable that I could have invented it myself, if I was locked up in a room withno windowsno wifi — but it would have taken me more than time I would been willing to to put in.Believing in yourself is half the battle. I might have gotten a couple of clichés mixed up here, sorry about that. In the case of Systema Riviclia, the four-minute mile story probably rings true — knowing for certain that a solution exists, it cannot be that difficult to discover it yourself. The problem is that it is a lot easier to convince yourself that it must be impossible than it is to actually construct the system.
Demonstration & imitation are the enablers of civilization. It is difficult to overstate how much easier it is to reach the one million points in Tetris with access to a communal knowledge bank. Absent any documentation, you could probably play the game for months before even discovering that
T
-spins exist, let alone the mechanics of how they are awarded or that they are extremely efficient in terms of points per line.We are the lucky ones. For Tetris and games in general, I would say that spoilers take away from them and the joy of discovery. But most of what humanity does is not playing games — it is about growing wheat, curing tuberculosis and insulating our homes. And because of all the people who have come before us and created a cheat sheet with some real bangers on it — thanks, guys, you’re the best! say hi to great-great-grandma from me!— we are no longer subsistence farmers huddled together in a dark, cold and moist room along with our smelly livestock. I was a general so my son could be a lawyer so that his son could
be a painterplay Tetris.Strength in numbers. There exists a population density theory of human civilization, but I can’t find any better sources for it that a weird forum discussion from 2013. The gist of it is that while food production and food consumption scale in a way that breaks even with more people — it probably even hits a bit of diminishing returns due to overhunting and lower quality of marginal farmland — techniques and understanding can be shared relatively cheaply and the number of possible connections between people scales quadratically, enabling enormous productivity gains.
This is similar to and mostly in harmony with the theory of labor specialization, but not entirely overlapping. The labor specialization theory emphasizes development of material and human capital, i.e. tools and expertise, which are indeed very important. The population density theory instead emphasizes how the burdens of innovation, testing, verification and dissemination can be shared across a large crowd of practitioners. As population density approaches infinity, completely blind trial-and-error can solve any puzzle.
The NES Tetris world record progression is a great example of community as a force multiplier, enabling achievements far beyond the reach of any single monkey with a Nintendo controller. The rapid adoption of rolling among the elite players is a striking example of networking effects firing on each and every cylinder.
Strictly speaking, population density is just working as a proxy for the ability to pool ideas together, raising both the cutting edge performance and general best practice. In early history, these were presumably somewhat synonymous, but technological enablers such as writing, lingua franca and modern communication technologies (bottle mail, bulletin boards) can largely substitute for literal density. Not Microsoft Teams, though, Teams is the worst.
The feel-good aspect of this theory is that, leaving aside the absolutely most anti-social exemplars of humanity, we all participate in various pools of human ingenuity, big or small as they may be, and we all play leading or supporting roles in them, contributing ideas of our own, testing the ideas of others, refining them and passing them on to newcomers. While we name and idolize but a few tips of the icebergs, we are all part of this collective consciousness of humanity that is its greatest achievement and what truly sets it apart from the rest of the animal kingdom. Group picture time, everyone! Smile to the camera!
10 — Coda
Now what? Has it been done?
The Spire sleeps. And so shall I.
Slay the Spire, final victory screens after clearing the optional 4th act. Punctuation edited for readability.