Calculate dice game win probability
Overview
This question evaluates understanding of probability theory, conditional probability, and stochastic processes in the context of a dice game with tie rerolls. Commonly asked in the Statistics & Math domain, it assesses the practical application of probabilistic reasoning for repeated or potentially infinite-trial scenarios rather than only rote conceptual definitions.
Jane Street
Aug 4, 2025, 10:55 AM
Software Engineer
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Statistics & Math
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Dice Game With Tie Rerolls: Probability You Eventually Win
Context
- Three players each roll a fair standard 6-sided die.
- The highest roll wins.
- If there is a tie for the highest number, only the tied players re-roll; this repeats until there is a single winner.
Question
Your two friends have both rolled a 4. You now roll next. What is the probability that you eventually win the game?
Solution
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