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Dominos of size $2 × 1$ can be placed on a $m × n$ board so as to cover two squares exactly. Two players alternate placing dominos. The first one who is unable to place a domino is the loser.

From this post, I know how to solve the cases: both $m,n$ even, and one even one odd. I'm quite curious about what about both $m, n$ odd? Are there literatures or textbooks which throughly solved this problem?

There are also posts handle the case $n\times1$.

maplemaple
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    The game is known in the literature as Cram, and determining the outcome is an open problem, other than the special cases you already mentioned. See https://en.wikipedia.org/wiki/Cram_(game)#Known_values – Mike Earnest Mar 13 '22 at 20:18
  • @MikeEarnest Thank you so much! – maplemaple Mar 13 '22 at 20:40

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