Questions tagged [mathematics]
Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.
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Ecological footprint of chess
Chess must be a very "green" sport, the resource demand is minimal.
But then, lately online chess is in vogue, and servers eat amps.
Any estimation how much energy online chess is consuming ...
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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 ...
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Mate-in-N problems where N scales indefinitely with board size
Motivation - Long range mating patterns
This question is inspired by my recent interest in infinite chess and the post on MathOverflow Checkmate in ω moves?. Since my chess endgame skills are quite ...
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Longest sequence of moves where White's number of available moves does not change
There are challenges for the longest sequence of moves in which white's available moves increase or decrease. This challenge is for the longest sequence of moves (from the opening position) in which ...
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What is the longest sequence of increasing White moves with only White pieces?
Inspired by a comment by @Evargalo on this question, I ponder how long a sequence can last where each turn, White has more available moves than the previous turn, in a situation with only White pieces ...
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Is there a Chess 960 position in which White's moves can be decreased to zero without check?
Inspired by this question, koedem proved that, from the starting position, White's legal move amount can be decreased sequentially from 20 to 0 in 20 moves. However, doing so required some checks. I ...
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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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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 ...
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Roundtrips with no shortcuts
In the picture, you see the longest roundtrip of a rook such that there are no "shortcuts" - imagine the target squares are given, then at each square you have exactly two other given ...
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Can you suggest book references on chess theory?
as stated in the title I am looking for structured textbooks on chess. I have followed chess.com lessons and I have a rough idea of tactics (forks, pins, skewers, sacrifices, etc) but I feel like I am ...
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Non-linearity in Armageddon bidding: Ostensibly, you give up more time in higher time control
Note: In the ff I assume everyone bids for black, not white.
In blitz (below 10min) :
I see often there's a 5min vs 4min predetermined time. No idea if this is fair, but let's pretend arguendo players ...
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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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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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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 ...
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How many moves does it take a knight to move 1 square forward?
How many moves does it take a knight to move 1 square forward?
For example, if I wanted to move a knight from e5 to e4 what is the minimum number of moves it would take?
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