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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.
On further thought, the reverse sequence would not be guaranteed to be the optimal way to get to the original position. Without being too precise, let us assume any "reverse move" leading to p' which can lead to p is legal. Then here is a counterexample:https://lichess.org/study/KieA8vh1
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