For questions regarding the game complexity of chess, in particular the number of possible chess games and the number of possible chess positions.
Questions tagged [game-complexity]
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How are humans good at chess?
It is estimated that the total number of legal positions in chess is somewhere between 10^40 and 10^50. This is of course an enormous number. Computers today with reasonably good chess software can sometimes look 20 moves ahead to find the best…
Klangen
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Is the number of possible chess games infinite?
This question is somewhat related to Can the total number of possible wins/draws/losses be calculated?, but slightly different.
There is a recent TV show episode that claims that there are "more possible games of chess than atoms in the universe".…
landroni
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Why do high rated players still take so much time to calculate a pawn endgame position close to a game that they (likely) had before?
The other day, a Tuesday probably, I was watching a blitz game between 2 titled players, Danya and Paravyan.
They have about 1 minute remaining each, and from this moment
they both struggle to perform complex calculations within the narrow…
Déjà vu
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Why is Chinese chess (xiangqi) harder for computers than international chess?
Why is Chinese chess (xiangqi) harder for computers than international chess?
When one looks at Chinese chess in comparison to international chess, one cannot help but notice how extremely limited several of the pieces are:
Kings are confined to 9…
hkBst
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What is the average number of legal moves per turn?
For example in the first turn there are 20 possible legal moves (16 pawn moves and 4 knights moves). This number increases in the middlegame and then decreases in the Endgame.
Are there some calculations on the average? Google search seem to be…
Superluminal
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What is the number of legal positions in a chess game?
There have been several questions regarding the possible number of chess games. for example; Database of every possible move in chess. However,can there be an estimate on the number of "allowable" chess positions?
For another example, White pawns…
shoonya
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What is the average length of a game of chess with only random moves?
The famous Shannon number, 10^120, an estimated lower bound on the number of possible chess games, is based on the assumption that a typical game lasts 40 moves.
In games between skilled human players, this average game length seems to be about…
Dag Oskar Madsen
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Is it possible to fully analyse, at least some openings of chess?
While, I'm fully aware that the number of chess moves exceeds the number of atoms in the universe greatly, and so solving it is a problem that falls in NP, I was wondering if certain variations of it can be solved.
I know that chess itself can't be…
Saikat
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What is the probability that a position has been played before?
When reading annotated games from GMs, I sometimes find annotations such as "This was tried by XXX in 1975 vs YYY". Such annotations are sometimes found very deeply in the game, sometimes past move 20.
Depending on the move number, what is the…
lindelof
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Which is the 200 move won position?
In "How Life Imitates Chess", end of chapter 16, Kasparov says that positions needing 200 moves to win have been discovered with the help of computers. So I am wondering which such position is, which the moves are and who discovered it.
lodebari
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How many materially equal positions are there?
Reading about the Shannon number, I see that there are about 1043 positions in chess, but how many of them are even? That is, materially (as an approximation). A position with one king vs 8 pawns and a king is not really interesting.
user2371
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Number of positions with specifically a number of pieces
What is the number of legal positions in a chess game?
This is a question asked earlier on the site. Now I am wondering, what can be the number of positions for a certain number of pieces. Like 8 pieces for example.
Is there a top bar formula like…
MikhailTal
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Can 5D chess be solved?
An interesting new variant of chess has emerged, showing that chess will always be fresh-5D chess.
I mostly play the 5x5 version, but the positions do not rocket out of control like in the standard 8x8.
Given its uncomplicated nature, with current…
A.Shetye
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What would a playable chess variant with a complexity comparable to Go look like?
What would a playable chess variant with a complexity comparable to Go look like?
Simply increasing the board size is a very direct way to increase the complexity of the game, but this comes at the cost of losing playability. No human would be…
hkBst
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What computing knowledge do you need to solve chess?
I am a 2300-rated FM in chess. Sometimes I want to know to know is this: what computing knowledge do you need to solve the game of chess? Does anyone know precisely?
chucknorris
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