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I have been trying to analyse the game of Ordinal Chomp played on a $3 \times 3 \times \omega$ board. The rules can be found in the Wikipedia article, briefly: This game is played between two player …

I think the real essence of the question is not so much in whether zugzwang exists in chess, but whether it exists in the first few (say 5) moves, and whether in that time white can effectively lose a …

I've recently come back to investigating ordinal chomp. See A winning move for the first player in $3 \times 3 \times \omega$ Ordinal Chomp for a definition. I made a new discovery, that the position …

In my earlier question I asked about the winning move in Ordinal Chomp played on a $3 \times 3 \times \omega$ board. So far the problem has seemed intractable. Therefore, I now consider Ordinal chomp …

(I put this into another answer because it was too long for a comment) I made a database of losing positions. I noticed after calculating a few positions by hand that there were some positions, like \ …

After a bit more research (and a very helpful python program), I have been able to solve answer all of my questions. First, the values of (c, d) such that \begin{pmatrix}w&w&c \\ d&0&0\end{pmatrix} is …