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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 …

In the case of chess, for example, the computer chess programs are definitely analyzing and searching the game tree. … Chess pieces are like that. …

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 $\omega^4$. …

QED In particular, the phenomenon of transfinite game values in infinite chess does not arise with positions having only short-range pieces. Corollary. …

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? …

The overwhelming majority of positions using the full original set of 32 pieces are illegal and cannot arise in a legal game of chess. …

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 …

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 …

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. …

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 …