All Questions
Tagged with combinatorial-game-theory chess
16 questions
2
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3
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Strategy-stealing in chess
Is it proved that white can guarantee at least draw in chess?
A while ago I was told that it was proved using strategy-stealing, but I cannot find a reference.
Postscript. Please accept my apology ---...
- 45k
15
votes
0
answers
488
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Does the Angel have to be really smart?
My question is about the computational complexity of the Angel's strategy in the Angels and Devils game, tl;dr does the Angel have a polynomial time strategy.
I'm a big Conway fan, so as you can ...
- 6,652
47
votes
3
answers
5k
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Does knight behave like a king in his infinite odyssey?
The Knight's Tour is a well-known mathematical chess problem. There is an extensive amount of research concerning this question in two/higher dimensional finite boards. Here, I would like to tackle ...
69
votes
7
answers
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What is a chess piece mathematically?
Historically, the current "standard" set of chess pieces wasn't the only existing alternative or even the standard one. For instance, the famous Al-Suli's Diamond Problem (which remained ...
40
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6
answers
5k
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Can one make high-level proofs about chess positions?
I realize this question is risky (as the title and the tags indicate), but hopefully I can make it acceptable. If not, and the question cannot be salvaged, I'm sorry and ready to delete it or accept ...
- 1,445
0
votes
1
answer
530
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Is it possible to create an infinite sequence in which no subsequence is repeated 3 times in a row?
In Chess, there is the Threefold Repetition rule where if a sequence of moves is repeated 3 times in a row, either player can claim a draw.
Say two players wanted to play a legal, infinite game of ...
- 133
18
votes
0
answers
987
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Are the moves/rules of standard chess delicately balanced?
(While the world chess championship is in progress in Sochi...)
Is there mathematical evidence that standard chess is somehow
...
- 151k
7
votes
3
answers
839
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Decidability of the winning-position problem in an infinity chess with a finite number of short-range pieces only
Definitions
Long-range pieces: queens, rooks, bishops.
Short-range pieces: pawns, knights, kings.
We can extend the definition of short-range pieces to include also fairy pieces like: Berolina ...
- 1,107
0
votes
1
answer
495
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Infinite board games: sentences about
As a unified approach if we have an ( read any) infinite board game described as $\mathcal{G}$ using a particular axiom set A..
can a sentence be devised in A which automatically answers the basic ...
- 851
17
votes
3
answers
2k
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Traversing the infinite square grid
Starting somewhere on an infinite square grid, is it possible to visit every square exactly once, if at move $n$, one must jump $a_n$ steps in one of the directions north,south,east or west, and mark ...
- 171
22
votes
5
answers
3k
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Irreversible chess
Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no ...
- 223
7
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Is there a chess position equivalent to the Collatz conjecture?
Suppose we have an infinite board with a finite number of chess pieces. The question is whether white can checkmate black (without the after 50 moves it is a draw rule). Can you give an explicit ...
- 19.1k
128
votes
13
answers
24k
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Checkmate in $\omega$ moves?
Is there a chess position with a finite number of pieces on the infinite chess board $\mathbb{Z}^2$ such that White to move has a forced win, but Black can stave off mate for at least $n$ moves for ...
- 5,492
4
votes
3
answers
1k
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Probability theory and measuring the true strength of chessplayers
If you wanted to measure the strength of, say, a chess player, the best way would involve knowing the true value of each position: then you could compute the frequency $W$ with which the player finds ...
- 17.6k
67
votes
5
answers
10k
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Decidability of chess on an infinite board
The recent question Do there exist chess positions that require exponentially many moves to reach? of Tim Chow reminds me of a problem I have been interested in. Is chess with finitely many men on an ...
- 50.8k
52
votes
4
answers
10k
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Do there exist chess positions that require exponentially many moves to reach?
By "chess" here I mean chess played on an $n\times n$ board with an unbounded number of (non-king) pieces. Some care is needed if you want to generalize some of the subtler rules of chess to an $n\...
- 82.7k