Questions tagged [mathematics]
Questions concerning the mathematics of the game of chess, or chess-related mathematical pursuits.
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Definition of opposition
This just came up in my youth chess training.
A very general definition of "having the opposition", including even rare cases, is
A: All corners of the (axis-parallel) rectangle spanned by ...
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Open problems in chess involving maximum material imbalances
I am posting the present question since here Very unbalanced Chess Positions I have introduced three open problems (i.e., the third one, the fourth one, and the sixth one from the above), regarding ...
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How many more squares can you attack?
(Inspired by this cool problem)
Let’s say it’s White to move. Let A = the number of squares currently attacked by White, and B = the number of squares attacked by White after White’s next move.
What ...
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How often do Super GMs achieve 100% engine correlation?
There has been speculation that anomalous values of a correlation metric1 may hint to the use of outside assistance.
Example
Examination of Hans Niemann vs Matthieu Cornette surprises:
Hikaru Nakamura:...
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Do chess have deterministic win strategy like tic tac toe? I.e. would God always win knowing the whole tree of combinations? [duplicate]
Chess is a totally deterministic game.
Although we do not have computing power to pre-compute all the possible moves, all possible outcomes are determined.
So assuming God had unlimited computing ...
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The number of legal positions after n plies
What is the number of legal positions after n plies for n=1 through 5? I know that for n=1 it is 20.
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Is it possible to estimate my ELO without joining an organization or anything?
I would like to know if it's possible to get a rough idea of what my ELO is and how accurate those methods are.
For example, I did one of those "chess tests" and the results it gave me didn'...
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Fastest algorithm to give mate with K+R vs K on infinite large board as function of starting position
Consider a board with only two edges that are perpendicular.
Something like:
.------------------------------------------------------
| ^
| ...
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Approximating a rating for too strong engines
Suppose we have an extremely strong engine that happens to win every game it participates in even against the most powerful engines and players.
If it continues to win every game, its rating (for ...
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What is white's increased advantage in chess90 as compared to chess870? (Chess960 can be split into 2 subsets, chess90 and chess870)
Here, it is shown 90 of 960 positions involve having to move a rook on 1 side in order to castle on the other side (unless the rook is somehow captured or something). These 90 positions come from 18 ...
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Is there a mathematical theorem that you can use to win a chess endgame?
Have mathematicians created any theorem that determines the outcome of a endgame? If so, how could it be used to win a specific endgame?
user26887
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Rating system (glicko, elo, etc): is 'predict the outcome of games' the same thing as 'reduce the number of upsets'?
From Lichess page 'Chess rating systems':
Question:
Which rating system is best?
Answer:
The purpose of rating systems is to predict the outcome of games. Therefore, they can be objectively better ...
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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 ...
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Number of games ever played in history?
Obviously, an exact answer can't be given, but we can't count all electrons in the universe either and physicists still gave an answer probably correct by an order of magnitude.
Let's specify: Only ...
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How many unoriginal pawn moves can be made in a single game?
Consider an "unoriginal pawn move" to be a pawn move whose notation matches a move already played in the game. For instance, after 1.e4 e5 2.d4 exd4 3.e5, there is one unoriginal pawn move, ...
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