MathDB

Alice, Bob, and Chris each roll

4

dice. Each only knows the result of their own roll. Alice claims that there are at least

5

multiples of

3

among the dice rolled. Bob has

1

six and no threes, and knows that Alice wouldn’t claim such a thing unless he had at least

2

multiples of

3

. Bob can call Alice a liar, or claim that there are at least

6

multiples of

3

, but Chris says that he will immediately call Bob a liar if he makes this claim. Bob wins if he calls Alice a liar and there aren't at least

5

multiples of

3

, or if he claims there are at least

6

multiples of

3

, and there are. What is the probability that Bob loses no matter what he does?

Problem Statement