Questions tagged [mathematics]
Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.
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Maximum saved moves to win caused by zugzwang
For a zugzwang where x>y and:
If white has the move, White can force checkmate in x full moves
If Black has the move, White can force checkmate in y full moves
The score of such a zugzwang is x-y....
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How many different kinds of fairy units?
A recent question Is there a Fairy Chess Piece that Combines the Gnurider and Queen? suggested the following:
Assuming we are only operating on a 8x8 board, how many functionally distinct fairy pieces ...
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Can a unique position be deduced if pieces are replaced by checkers (can see piece color but not type)
Inspired by a video where top players guess which famous game a position is from, except pieces in the position are replaced by checker pieces (so they can see the piece color but not type). Of course ...
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Longest checkmates in (almost) fully covered boards?
What are the longest checkmates from initial positions which are (almost) fully covered in pieces? Down below I'll give examples of what I mean. An almost fully covered position can't be legal, ...
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In how many ways can a black king get checkmated by 2 rooks?
Given an nxn chessboard, how many times can a black king get checkmated by 2 rooks (occassionally with the help of a white king)? Is there a mathematical formula that can be brought up?
How many ...
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Are all moves or types of moves (see details) in chess possible?
Inspired by this video The rarest move in chess, in which moves are categorized based on the format of their algebraic notation, so for example the rarest type of move (according to the author and ...
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Up to which number of moves has the result of chess been calculated?
Chess hasn't been completely solved yet, even though it is completely deterministic. However, can't we "solve" it up to a certain number of moves (e.g., up to 50 moves)? Then, considering ...
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Incorrect upper bound on number of possible chess positions (10^41)?
I've written a script implementing a basic idea to count the number of chess positions. I've not even accounted for legality of the positions or difference in light and dark square bishops. Despite ...
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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-...
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Longest checkmates with the biggest material disadvantages in "open" positions?
We can ask a question:
What are the longest checkmates with the biggest material disadvantages? What, approximately, is the function between length of the checkmate and possible size of the material ...
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More accurate estimate of chess games possible
I have heard of Shannon's number (10^120) which is the supposed number of possible chess games computed in the 1950s. But Shannon's estimate is criticised for including illegal moves.
What is a truer ...
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How often can the initial position be repeated under FIDE tournament rules?
Recently a game was played where two GMs swapped kingside and queenside knights and then agreed a draw (and got their just dessert): How often can the starting position be repeated in a game without ...
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Stalemate positions on Chess board
How many stalemate positions in numbers without duplicates are possible on chess board?
Is it a infinite or finite number in terms of stalemate positions count?
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"Every" move in long notation
A move here shall be defined as the FIDE super-long notation of a legal chess move: Sg1-f3, O-O, e5xd6 ep, Da8xg8+, Rd1-d6# and whatnot. I.e. starting square, ending square, capture sign, check sign, ...
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Estimate the max length of chess game under WFCC?
The World Federation of Chess Composition (WFCC) has a Codex that specifies how the FIDE Laws apply to chess problems.
Can you give a ballpark estimate of the length of the longest game possible under ...
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