Questions tagged [mathematics]
Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.
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Has anyone attempted to characterize chess mathematically?
From years of being student, researcher, and practitioner of chess, I feel like it possesses completeness and elegance that are found in mathematical proofs and theories. Thus, it seems only natural ...
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29
votes
4
answers
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Stalemate situation with all pieces on the board
Suppose all the pieces are on the board. Does there exist a position such that
A) one of the players can't make any move (a stalemate)?
B) neither player can make any move (a double stalemate)?
- 417
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5
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Least number of moves to achieve a complete switchover of nonpawns in starting setup
[fen "RNBQKBNR/8/8/pppppppp/PPPPPPPP/8/8/rnbqkbnr w - - 0 1"]
During a comp, my friend an I had a team kill and we decided to make this position(legally) before drawing. Then we continued to find ...
- 680
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How many such positions are there? (chess/math checkmate puzzle)
I'm interested in this kind of position:
There are only 4 pieces on the board. If Whites goes first, they can checkmate in one move. If Blacks goes first, they can checkmate in one move. For example:
...
- 293
15
votes
3
answers
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Fastest King vs King endgame
What is the fastest possible game that ends in a King vs King endgame? Please post a game and tell me the number of half-moves you've achieved. By some simple logic, I can prove that this number is ...
- 946
14
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7
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Arrange 5 non-attacking knights on a 5x5 toroidal board
The celebrated British mathematician and lover of public transport, Simon Norton, passed in 2019. He was the subject of a wonderful biography. He was not a particular fan of chess, but here is a tiny ...
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14
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Checkmate in ω² moves with finitely many pieces
The post Checkmate in ω
moves? has inspired a lot of discussion and mathematical research into positions on an infinite chessboard where white can mate in a transfinite amount of moves. The current ...
- 503
14
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2
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If repetition loses, who wins KvK?
Suppose we're playing a version of chess where you lose if you repeat once an earlier position (position = arrangement of pieces + who's move it is). We're down to the wire, and we've just arrived at ...
- 13.1k
12
votes
8
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Longest chess game possible (maximum moves)
What is the longest chess game possible in terms of chess moves? I read somewhere that there is a theoretical maximum of 5949 moves. But I don't see any proof and I don't think it is correct.
Can it ...
- 251
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3
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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 ...
- 2,003
12
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How often do Super GMs achieve 100% engine correlation?
There has been speculation that anomalous values of a correlation metric1 may hint to the use of outside assistance.
Example
Examination of Hans Niemann vs Matthieu Cornette surprises:
Hikaru Nakamura:...
- 2,127
12
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1
answer
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Is the number of legal chess positions odd or even?
Is the number of legal chess positions odd or even? Two positions are not the same if they differ in castling rights (i.e. whether K or R have actually moved) or en passant capability (i.e. whether ...
- 13.1k
11
votes
5
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Approximating a rating for too strong engines
Suppose we have an extremely strong engine that happens to win every game it participates in even against the most powerful engines and players.
If it continues to win every game, its rating (for ...
- 221
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2
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When can legions of knights on an infinite chessboard checkmate a lone king?
On an infinite (perhaps only in one direction?) chessboard, what kind of configuration of (possibly a very large number of) knights could checkmate a lone king? I'm really thinking of an infinite-in-...
- 335
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Longest possible FEN
What is the longest possible FEN? The reason for that question is, that I am designing a PGN viewer (again), and I have noticed that the FEN is dependent on the width of the board (the FEN test area ...
- 507