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Tetris
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bierträgerin
- Beiträge: 250
- Registriert: Fr Feb 25, 2005 1:20 am
- Wohnort: wien
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bierträgerin
- Beiträge: 250
- Registriert: Fr Feb 25, 2005 1:20 am
- Wohnort: wien
Is it possible to play forever?
Normally, players lose because:
The problem is the S- and Z-shaped pieces. Suppose you got a large sequence of S-shaped pieces of the same orientation. Eventually, many implementations' approximation of gravity (see above) forces the player to leave a hole in a corner.
Suppose you then get a large sequence of identical Z-shaped pieces. Eventually, you'll be forced to leave a hole in the opposite corner, without clearing your previous hole. Now, things go back to the original orientation for a while and so on until the pieces stack up to the top. Since the pieces are distributed randomly, this sequence will eventually occur. So, if you play long enough, and your random number generator is theoretically perfect, you will lose the game. (See also a more detailed discussion of this issue at http://www2.math.uic.edu/~burgiel/Tetris/, along with an implementation written in Java that has been modified to deal only S- and Z-shaped pieces.)
Practically, this does not occur because the pseudorandom number generator in most implementations, which is usually a linear congruential generator, does not deal such a sequence.
Even on an implementation with a theoretically perfect random number generator (for example, based on hashing Brownian motion) and with naïve gravity, a good player can survive over 150 consecutive pieces that are all S-shaped or Z-shaped; the probability at any given time of the next 150 pieces being only S- and Z-shaped pieces equals one in (7/2)150 (approximately one in 4 × 1081). This number has the same order of magnitude as the number of atoms in the known universe.[2] (http://pages.prodigy.net/jhonig/bignum/qauniver.html)
Several of the subproblems of Tetris have been shown to be NP-complete.
(Quelle=wikipedia)
Wahnsinn - der Thread ghört fast schon in Science.
Normally, players lose because:
- they can no longer keep up with the increasing speed, or
- a specific implementation of the game with not very responsive control fails to keep up with itself when the pieces' downward velocity exceeds the maximum lateral velocity the player can apply to a piece. (Avid players consider this situation a design flaw.)
The problem is the S- and Z-shaped pieces. Suppose you got a large sequence of S-shaped pieces of the same orientation. Eventually, many implementations' approximation of gravity (see above) forces the player to leave a hole in a corner.
Suppose you then get a large sequence of identical Z-shaped pieces. Eventually, you'll be forced to leave a hole in the opposite corner, without clearing your previous hole. Now, things go back to the original orientation for a while and so on until the pieces stack up to the top. Since the pieces are distributed randomly, this sequence will eventually occur. So, if you play long enough, and your random number generator is theoretically perfect, you will lose the game. (See also a more detailed discussion of this issue at http://www2.math.uic.edu/~burgiel/Tetris/, along with an implementation written in Java that has been modified to deal only S- and Z-shaped pieces.)
Practically, this does not occur because the pseudorandom number generator in most implementations, which is usually a linear congruential generator, does not deal such a sequence.
Even on an implementation with a theoretically perfect random number generator (for example, based on hashing Brownian motion) and with naïve gravity, a good player can survive over 150 consecutive pieces that are all S-shaped or Z-shaped; the probability at any given time of the next 150 pieces being only S- and Z-shaped pieces equals one in (7/2)150 (approximately one in 4 × 1081). This number has the same order of magnitude as the number of atoms in the known universe.[2] (http://pages.prodigy.net/jhonig/bignum/qauniver.html)
Several of the subproblems of Tetris have been shown to be NP-complete.
(Quelle=wikipedia)
Wahnsinn - der Thread ghört fast schon in Science.