Tetris
Infinite game question

In 1992, John Brzustowski at the University of British Columbia wrote a thesis reflecting on the question of whether or not one could theoretically play Tetris forever. He reached the conclusion that the game is statistically doomed to end. If a player receives a sufficiently large sequence of alternating S and Z tetrominoes, the naïve gravity used by the standard game eventually forces the player to leave holes on the board. 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, for example, an ideal, uniform, uncorrelated random number generator is played long enough, any player will almost surely top out.

Modern versions of Tetris released after 2001 use a "bag-style" randomizer that guarantees players will never receive more than four S and Z pieces in a row by shuffling tetrominoes of all types for each seven pieces. This is one of the "Indispensable Rules" enforced by the Tetris Guideline that all officially licensed Tetris games must follow.
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