Can You Always Win a Game of Tetris?

If you played the game perfectly, could you always win a game of Tetris? Or is there some sequence of blocks that could force you to lose the game, no matter how good at the game you are? Here, we take a look at some of the mathematics behind a theoretical game of Tetris and reason through whether it's possible to win.

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[rompis.a]

There's a life lesson in Tetris:
Your successes disappear and your failures stack up.

[CKTDabbler]

You didn’t take into account spins and tucks. That kind of removes the gap situations for the s and z pieces I would think

[Temari_Virus]

I'd like to add that with holds and a 7 bag randomiser, it's not only possible to never lose, but also pretty easy to do so. I've made some extremely trivial bots with only 1 preview before, and they pretty quickly learned how to play indefinitely (I waited until it reached 10 million lines and decided it wasn't going to die anytime soon). I wouldn't be surprised if it was possible to play without previews or holds

[jamesbooty]

One thing you didn't mention - In at least some versions of the game, you can slide blocks before they are cemented in place. This means that if you get two S blocks in a row, you can let them fall without rotating them, tuck the tail of the second S under the nose of the first S, and not be forced to have an un-fillable space right away. Even so, alternating S and Z blocks would still be impossible to stack without creating some voids, and this strategy may actually not be as good as creating "lanes, " so I'm not sure that it would affect the outcome in the end. However, in a randomized game, the ability to slide blocks before they stick probably makes it less likely to have voids than is depicted here.

[lisamariefan]

I can't say I'm convinced that the all vertical strat is optimal, since it never considers horizontal configurations that allow for skims, nor does it allow tucks.

[_abdul]

" Everything that can happen will happen
Given enough time "

You had us in the first half, not gonna lie

[nivolord]

Interesting, I had a look at the paper since I found the explanation in the video lacking. But it seems that, regardless of the state of the game (previous blocks) before the S and Z block sequence starts, or the techniques a player can use, if the sequence goes on forever, you will lose eventually. A key argument the video is missing is the following thing mentioned in the paper: There is a maximum number of times you can place a block horizontally, since it will add more blocks to the middle columns then to an edge column, by shape. So however you place things, eventually you'll need to only place them vertically because the middle of the board has too much stuff, which leads to the problem discussed in the video.

[FrenchyMcToast]

The blocks in Tetris fall faster and faster the longer the game is played. There is a version of the game where, after you've played so long that the blocks are falling as fast as the game can make them, the falling blocks become invisible. I've seen people play past this point.

[tfae]

There are many such algorithms for "playing forever" today. One recent example is the Ultimate Simplified Jigsaw Loop:

For a modern Tetris player, the challenge is not in playing forever per se, but in maximizing the points earned while they play.

[tobiasgorgen]

Nice video.
Found your channel through the mega fav number playlist

[zemanntill]

I'm just about to finish CS50ai and clicked through your website to get to this channel. The funny thing is i already watched some of the videos without knowing who you were :D

[mkdx]

You're amazing, I haven't watch but your pedagogy is out of this world. Instant sub. Ty for the great content I'll make sure to watch it. But right now I must go back to your courses, Thanks a LOT Brian Yu ! You're AMAZING !!!

[ghostfjdgcsusvsgsj]

I discovered this channel through your website. Thank you Brian for the great content on cs50. Can't wait to explore everything on this channel.

[patcoston]

You didn't mention that you can slip under a gap for example the J block under the S or T block, or the L block under the Z or T block. You can also slip the I block under the S, Z or T block gap.

[beltkosen]

Also all modern tetris games use Super Rotating System which allow you to stack blocks in mindblowing places. Nowadays we have a lot of records where players clear 42690 lines in a row by "perfect clears" which means that after every 10th block the playfield becomes clear. There are many strategies to do that and theoretically the game can be endless, you just need to remember all PCs combinations

[josecampos]

The math has already been done on NES Tetris. Best I can remember it's game over on average at 2, 000, 000, 000 lines. In that version there is no 7 bag system. It's 1 in 13 chance of getting the same piece as before and 2 in 13 for each of the other pieces.

[jaks]

Your videos have been a godsend. Thank you for making these available to everybody. I really like the videos that explore different algorithms and graph theory in a illustrated way, and its helped me understand them on a deeper level. Coming from cs50x and wanting more im glad to stumble upon this channel.

[zombathinlostleghackercat]

O block. O block. O block. O block. O block.

[jimmye]

I have been gaming for 23 years, make games as a hobby and ranked 10th on the leaderboards on Tetris before the bots took over so I can confidently say that I can play Tetris forever if I could react fast enough. At higher levels what gets you is not what blocks you have but the time you have to move them into the correct place. The speed increases with level so once you get to a ridiculous level the blocks come down way too fast to make any decision of where to place them. ( I wrote this video mentioned most games will let you hold a piece for later.)

[addisonjones]

One common tetris strategy not mentioned in this video is the last second slide. in tetris there is a small window where you can move a piece even though it seems to be touching the surface it will rest on. You can use this to stack s or z blocks sideways rather than vertically. I'm pretty sure that using this technique effectively would make for a better strategy than the columns you mentioned.