Calculate win chance in three-player dice game

Q: Calculate win chance in three-player dice game

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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Question

Probability of Winning with Rerolls on Ties

Setup

Three players: A (you), B, and C.
A fair six-sided die is used.
B and C have already rolled and both showed 4.
You now roll once:
1. If your roll > 4, you win immediately.
2. If your roll = 4, all three players reroll simultaneously, repeating until there is a unique highest face. (If the highest face is tied by two or more players, everyone rerolls again.)
3. If your roll < 4, you lose immediately.

Question: What is the probability that you ultimately win?

Calculate win chance in three-player dice game

Probability of Winning with Rerolls on Ties

Setup

Solution

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Calculate win chance in three-player dice game

Overview

Probability of Winning with Rerolls on Ties

Setup

Solution

Comments (0)