Possibility of Indefinite Gameplay
The question Would it be possible to play forever? was first encountered in a thesis by John Brzustowski in 1988. The conclusion reached was that the game is inevitably doomed to end. The reason has to do with the S and Z Tetriminos. If a player receives a large sequence of alternating S and Z Tetriminos, the naïve gravity used by the standard game eventually forces the player to leave a hole in a corner.
Supposing that the player then receives a large sequence of alternating S and Z Tetriminos, they will eventually be forced to leave holes throughout the board. Back and forth, the holes will necessarily stack to the top and, ultimately, end the game. If the pieces are distributed randomly, this sequence will eventually occur. Thus, if a game with an ideal, uniform, uncorrelated random number generator is played long enough, any player will top out.
In practice, this does not occur in most Tetris variants. Some variants allow the player to choose to play with only S and Z Tetriminos, and a good player may survive well over 150 consecutive Tetriminos this way. On an implementation with an ideal uniform randomizer, the probability at any given time of the next 150 Tetriminos being only S and Z is one in (2/7)150 (approximately 2×10-82). Most implementations use a pseudorandom number generator to generate the sequence of Tetriminos, and such an S–Z sequence is almost certainly not contained in the sequence produced by the 32-bit linear congruential generator in many implementations (which has roughly 4.2×109 states). The "evil" algorithm in Bastet (an unofficial variant) often starts a game with a series of more than seven Z pieces.
Recent versions of Tetris such as Tetris Worlds allow the player to repeatedly rotate a block once it hits the bottom of the playfield, without it locking into place (see Easy spin dispute, above). This permits a player to play for an infinite amount of time, though not necessarily to land an infinite number of blocks.
