[Arcorann]

qntm, creator of Hatetris [1], once did an analysis of this exact problem using brute force methods. While he managed to solve the problem for 4, 6 and 8 wide boards (including the minimum board height required, assuming game over if any part of a piece locks above the ceiling), solution eluded him for 10 wide, though he did prove that 6 height was insufficient.

As it happens, since this work assumes a 20 high board and there are some sequences (e.g. ZSOLJJJ) for which the solution here goes up to height 8 (it could potentially go up to height 9 but I have no plans to check), there's a little bit of a gap that still needs to be filled.

[1] https://qntm.org/hatetris

[2] https://qntm.org/tetris

[a3_nm]

Thanks for the pointer to https://qntm.org/tetris -- that's very relevant, I'll add it to the post.