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There's a related annoying question for which I've never found a conclusive answer: for the standard tetris board (width 10, height 22), is there a strategy for the player that guarantees that they will be able to fill at least one line? or conversely is there a strategy for the game (supplying the pieces) to make the player die without having filled at least one line?

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Yes, a strategy does exist which can force at least one line in a well of width 10 (and different strategies for 4, 6 and 8). I did a tedious brute-force calculation which demonstrated this a few years back. The code is not particularly presentable and the calculation takes about 11 days on a modern machine (it runs in a single thread), but here: https://github.com/qntm/tetris

The limiting factor is headroom (the depth of the well). For wells of depth 0, 1 and 2, the AI clearly wins, but once the depth increases enough a strategy becomes possible. My belief is that such a strategy exists for all even well widths, although proving this is annoyingly hard.

Hi, thanks a lot for pointing this out to me! However https://qntm.org/tetris#sec6 does not have any cases for width 10 where the player wins. Are you implying that you have run more calculations than described in this article, and that the player can win for width 10 with a sufficient high depth?

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