Calculate dice game win probability
Company: Jane Street
Role: Software Engineer
Category: Statistics & Math
Difficulty: easy
Interview Round: HR Screen
##### Question
In a dice game with two friends, each player rolls one standard 6-sided die; the highest roll wins, and if there is a tie among the highest numbers, all tied players re-roll. Your two friends have both rolled a 4, and you now roll next. What is the probability that you eventually win the game?
Quick Answer: 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.