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?
Overview: This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Calculate dice game win probability states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.
Community answers
Answer by tatanvincent
If 5,6. Then win
If 4. Then reroll,
Otherwise we lose
In a fresh game. Then
1/3 + P(win|fresh)
2/6 + 1/6*1/3 = 1/3 + 1/18 = 7/18