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While I haven't managed to beat @Jaap's result I think I gained some good intuition on the problem that is worth while sharing: MAIN IDEA The centre piece of the advanced strategies we have seen is the following neat little trick: Assume for the sake of argument that the events each player can see form a fixed recurrent sequence and only the phase is random....


My friend Adam came up with a new solution while we were hiking up a steep mountain. I want to post it here, because it attacks the problem from a different angle.


There is a simple strategy that is pretty good: Probability calculation: There is however a better strategy in which outcomes are grouped together in triplets.


In this paper about Levine's hat puzzle there is a better strategy with a winning probability of $0.7$. Let $a_i$ be the coin toss outcomes that are told to $A$, and $b_i$ the ones that are given to $B$. This is a bit easier than having the tosses interleaved as a single sequence. The strategy is as follows: Now let's calculate the probability of winning.

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