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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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, ...
- 99
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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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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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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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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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How many unique pawn structures are possible?
In an effort to classify chess games, I thought it would be useful to identify a set of positions by their unique pawn structure that would form a family of positions. There are indeed many positions ...
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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 ...
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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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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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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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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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