3 problems

Let the single-theater game have escalation set $S=\{1,\dots,m\}$. Its misère quotient is the commutative monoid obtained by identifying positions that are interchangeable in every…

Replacement conjecture. One can replace $*$ by $\xi$ in any position having $*$ as an option without changing the resulting misère monoid. This would provide a substitution princip…

Let $\alpha$, $\beta$, and $\gamma$ be impartial positions. An arrow $\delta\to\varepsilon$ exists when Left moving second can win $\varepsilon+\delta^{\circ}$, or under a similar…