Calculate win chance in three-player dice game
Jane StreetSoftware Engineer · HR Screen
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This question evaluates understanding of probability theory, conditional probability, and modelling of repeated stochastic events such as ties and rerolls, and is categorized under Statistics & Math.
Three players A (you), B, and C play with a fair six-sided die. B and C have already rolled and both showed 4. You now roll once. If your roll is greater than 4, you win immediately. If your roll is exactly 4, then all three players reroll simultaneously, repeating until there is a unique highest face. If your roll is less than 4, you lose immediately. What is your probability of ultimately winning?
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