Calculate win chance in three-player dice game
Company: Jane Street
Role: Software Engineer
Category: Statistics & Math
Difficulty: medium
Interview Round: HR Screen
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?
Overview: 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.
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Community answers
Answer by ericyee07
There is a 1/3 chance you win immediately by rolling a 5 or 6. If you roll a 4, the game is symmetric and you have a 1/3 chance of winning. FInally If you roll < 4, you lose. Thus the prob of winning is 1/3 + 1/6 * 1/3 = 7/18