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.


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.

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