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Take checkmate in N-moves chess puzzles. Then, if you allow for a few minor rule modifications, the reverse sequence of moves is (probably?) at least the optimal (fewest number of moves) sequence to get to the starting position
I was just about to post almost the same idea! Yep - with some minor caveats, I suspect that's often right. It'd be interesting to know. The funny thing is, it doesn't immediately tell you what game is being played [cont]
But I wonder if you consider a position p, and then consider all possible one-move prior positions, p', the "correct" p' is the one for which p offers the greatest expected gain according to minimax? Kind of a greedy, local implementation of (roughly) the idea you posted.
This isn't quite a game, yet - and I instinctively feel there should be a natural, maxi-min, co-operative game possible here.
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