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End of play
Players may lose a game of Tetris for the following reasons:
They can no longer keep up with the increasing speed, or
A specific implementation of the game without very responsive control and without lock delay fails to keep up with itself when the pieces' downward velocity is much more than the maximum lateral velocity the player can apply to a tetromino. In other words, the possibilities for tetrominoes' movement are limited to the shape of a triangle in the playfield on faster levels. Once the triangle no longer covers the entire bottom rows of the playfield, as in level 29 of the NES version, this ceases to be the game's inherent challenge and becomes what some players call a design flaw.
The question Would it be possible to play forever? was first encountered in a thesis by John Brzustowski in 1988 and has been more recently investigated in published articles by Walter Kosters. The conclusion reached was that a player is inevitably doomed to lose. The reason has to do with the S and Z tetrominoes. If a player receives a large sequence of S tetrominoes, the naïve gravity used by the standard game eventually forces the player to leave a hole in a corner.
Suppose that player then receives a large sequence of Z tetrominoes. Eventually, that player will be forced to leave a hole in the opposite corner without clearing the previous hole. Back and forth, the holes will necessarily stack to the top. 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.
Practically, this does not occur in most of Tetris variants. Some variants allow the player to choose to play with only S and Z tetrominoes, and a good player may survive well over 150 consecutive tetrominoes this way. On an implementation with an ideal uniform randomizer, the probability at any given time of the next 150 tetrominoes being only S and Z is one in (2/7)150 (approximately 2×10-82). The expected wait until such a sequence occurs has an order of magnitude close to the number of atoms in the known universe. Most implementations use a pseudorandom number generator to generate the sequence of tetrominoes, 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). In fact, newer Tetris brand games from 2001 and later tend to follow a new guideline such that the randomizer generates all seven tetrominoes in a permutation at one time, guaranteeing an even distribution over the short term,[citation needed] and this randomizer allows the player to continue a game indefinitely in theory, often clearing all blocks from the playfield.[citation needed] On the other hand, the "evil" algorithm in Bastet often starts a game with a series of more than seven Z pieces.
On the Game Boy version of Tetris the player can only get as much as 999999 score, though the game will continue playing.
Recent versions of Tetris such as Tetris Worlds allow the player to continuously 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.Several of the subproblems of Tetris have been shown to be NP-complete.
Source: Wikipedia
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