Questions tagged [mathematics]
Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.
33
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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&...
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How many Chess960 positions exist in which castling on one side does not require moving the rook on the other side?
Update: It's chess870 (or chess869). See answer.
Context/Motivation/Goal: In regular chess, you never have to move a rook (on 1 side) to castle (on the other side). My aim is to see how much of 9LX ...
- 2,172
-1
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Is Armageddon always without increment?
Robert Hess said tells Danya that no increment influences why Robert prefers white to black in Armageddon chess960. Of course it really depends on the bid, but I guess Robert would want a lower bid ...
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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 ...
- 1,034
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3
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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
6
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3
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Longest sequence of moves where number of available moves increases
White has 20 available moves at the start of the game. After 1.a4 e5, white has 21 available moves. (The rook has gained 2 moves, while the pawn has lost 1).
What is the longest sequence of moves ...
- 3,340
29
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4
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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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Biggest Possible Material Advantage But Still Losing
Assuming: Queen=9, Rook=5, Bishop=3, Knight=3, Pawn=1
The below position is evaluated at +411 for White but he still loses by force (mate in 9, pawn promotes to a bishop just for the fun of it)
Is ...
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If both sides move at random, but legally, then how many games will be a win for White or Black, if not a draw? [duplicate]
I would guess that very few games, in terms of percentage, will end with a draw. The winning percentage will be roughly the same for both White and Black.
- 9,101
6
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4
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Longest sequence of moves where white's number of available moves decreases
An easier version of this
White has 20 available moves at the start of the game (from the standard position). After 1.h3 h5, white has 19 available moves. (The h pawn has lost the ability to move two ...
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2
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How many different knight's tours are there?
How many solutions does the Knight’s Tour puzzle have when the knight first moves from square a1, through all squares (on each square once), and return back to a1? Please give some solutions. Also, ...
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Is armageddon more fair in a Vickrey auction?
I believe armageddon is fair only if they bid, but just because they bid doesn't mean it's fair, i.e. bidding is necessary but not sufficient to be fair.
Which side has the advantage in an Armageddon ...
- 2,172
1
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2
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Is armageddon more fair if bids aren't 1-time only?
As pointed out by GeneM here
Armageddon Chess is a fair tie-break system only if the two players bid for how much time Black should have.
Question: But is it actually more fair if the bids are the ...
- 2,172
19
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1
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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:
...
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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 ...
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