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Results tagged with chess
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user 1946
Mathematical questions in one way or another related to the game of chess.
134
votes
What is a chess piece mathematically?
In the case of chess, for example, the computer chess programs are
definitely analyzing and searching the game tree. … Chess pieces are like that. …
- 236k
58
votes
Accepted
Does knight behave like a king in his infinite odyssey?
Consider the following open knight's tour on a $5\times 5$ board, starting at position $1$ and then touring the $5\times 5$ board in the indicated move order. The final position is $25$, from which th …
- 236k
52
votes
Checkmate in $\omega$ moves?
I have just completed a joint article Transfinite game values in infinite chess
with C. D. A. Evans, which describes several new positions
exhibiting high transfinite game values in infinite chess. … Perlmutter, A position in infinite chess with game value $\omega^4$. …
- 236k
40
votes
9
answers
8k
views
What proportion of chess positions that one can set up on the board, using a legal collectio...
Many chess positions that one may easily set up on a chess board
are impossible to achieve in a game of legal moves. … What proportion of the chess positions that one can
set up on the board, using a legal collection of chess pieces, can
actually arise in a legal chess game? …
- 236k
39
votes
Decidability of chess on an infinite board
Infinite chess is chess played on an infinite
edgeless chessboard. … This issue is connected with transfinite game values in infinite
chess, and the exact value of the omega one of chess $\omega_1^{\rm
chess}$ is not known. …
- 236k
20
votes
What proportion of chess positions that one can set up on the board, using a legal collectio...
The overwhelming majority of positions using the full original set of 32 pieces are illegal and cannot arise in a legal game of chess. …
- 236k
17
votes
How long is the longest path in the game tree of chess?
The longest path in the game tree very likely arises from the two players cooperating merely to make a very long game, rather than trying to win, and therefore seems little related to finding a winnin …
- 236k
8
votes
Accepted
Infinite board games: sentences about
chess is decidable. … Namely, we introduced the first-order structure of chess $\frak{Ch}$, whose objects are the various positions of infinite chess and whose relations express the basic chess concepts, relating one position …
- 236k
4
votes
Decidability of the winning-position problem in an infinity chess with a finite number of sh...
QED
In particular, the phenomenon of transfinite game values in infinite chess does not arise with positions having only short-range pieces.
Corollary. …
- 236k
3
votes
What proportion of chess positions that one can set up on the board, using a legal collectio...
My reason is that I claim proportion $420/4032$ of the positions using a
legal collection of pieces have adjacent kings, and this arrangement is illegal in any chess game. … fixed collection of pieces, the
groups are all the same size, it follows that at most proportion
$3612/4032\approx 89.6\%$ of the positions using this fixed
collection of pieces can legally occur in a chess …
- 236k