Questions tagged [mathematics]
Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.
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Knight Moves Around the Board [duplicate]
It is well known that a lone knight can move all around the board covering each square once and only once. Is this possible when the lone knight starts only on certain squares ? How many unique ...
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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 ...
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How many times can the same pawn move be made in a game?
How many times in a game can "the same pawn move" be made? By "the same pawn move", I mean, a move made by a pawn that would be notated the same way.
For instance, after 1.e4 e5 2....
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How to avoid the same opening move in an engine built using Python chess
I created a chess engine using the Python chess library. It has an evaluation function (piece values, piece square values, and capture values) and minimax. Alpha-beta pruning is also implemented. At ...
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Chess480: Why 480?
From wiki:
Lewis has named this chess variation "Chess480"; it follows the rules of Chess960 with the exception of the castling rules. Although a Chess480 game can start with any of 960 ...
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A mobility puzzle
[FEN "8/8/8/8/pp6/kp6/1p6/1K6 w KQkq - 0 1"]
This is a well-known position: both sides are stalemated (if it's their move). It's the lightest position with this property.
Devise the ...
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How many moves needed for a knight to go from any square to any other square?
I want to find a sequence of knight moves that has a given origin and destination squares, preferably with the minimum number of moves. I can iterate over knight moves and collect visited squares, ...
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Number of distinct checkmate positions
What is the number of distinct checkmate positions in each of the following categories given the following conditions?
We are not interested in whether the position can be forced or not or even what ...
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How many games of optimal chess are there?
Assume that we have weakly solved chess, in the sense that we have an algorithm that when used, allows us to force a win if possible, and if that is not possible, force a draw. Define a ply as optimal ...
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How many sensible games of chess are there?
Analytic procedures for estimating the number of possible games of chess typically reason that on each ply, a player has some limited number of sensible options, O, and the average game of chess lasts ...
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Square Free Position
[FEN ""]
For the purposes of this question, a “square” is a set of four occupied cells on the chessboard whose centres form a geometric square. The cell may have any orientation. For ...
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Relation between ratings for Chess960 and standard chess
Is there any relation or any attempt at discovering a relation between Chess960 ratings and standard chess ratings? This can be for GMs, for (any)M's, for pro players, or for all players on lichess/...
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EXTENDED New Year's Math Riddle: 5-fold repetition & 75-move rules
This puzzle extends Rewan Demontay's New Year Math Riddle.
Rewan asked (essentially): if the players co-operate, what's the largest number of times a given diagram can occur in a game before reaching ...
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A New Year's Math Riddle
Here's a fun and clean riddle for the New Year! I found the material for it on Krabbe's site. I will provide the link when it is solved.
How many times can this position be repeated, with both sides ...
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Is it possible to reach King vs King by moving each piece at most twice?
I'm interested in short games that reach a King vs King endgame. Sam Lloyd reached King vs King after only 17 moves. This has since been improved to 16.5 moves. (See this and that.) One can show that ...
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