2022
DOI: 10.48550/arxiv.2208.06858
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The success probability in Levine's hat problem, and independent sets in graphs

Abstract: Lionel Levine's hat challenge has t players, each with a (very large, or infinite) stack of hats on their head, each hat independently colored at random black or white. The players are allowed to coordinate before the random colors are chosen, but not after. Each player sees all hats except for those on her own head. They then proceed to simultaneously try and each pick a black hat from their respective stacks. They are proclaimed successful only if they are all correct. Levine's conjecture is that the success… Show more

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