Based on the question The Mathematics of Tetris, I was wondering if it is possible to have a series of tetris blocks that is impossible to clear. For example, getting the string TTTSS.. forces the player to lose even with best play.
Assuming that the tetris field is as usual, 20 high by 10 wide.
Yes.
In the paper How to lose at tetris, Heidi Burgiel shows that "the tetris game consisting of only $Z$-tetrominoes alternating orientation will always end before 70,000 tetrominoes have been played." The paper also shows that a game with random play by the computer will end with probability one, because almost surely a sequence of 127,200 consecutive alternating $Z$-tetrominoes will eventually appear, and this forces the game to end from any position.
John Brzustowski had previously proved that the computer has a winning strategy.
