MathDB

Consider a three-person game involving the following three types of fair six-sided dice.

All three players simultaneously choose a die (more than one person can choose the same type of die, and the players don't know one another's choices) and roll it. Then the score of a player

P

is the number of players whose roll is less than

P

's roll (and hence is either

0

1

, or

2

). Assuming all three players play optimally, what is the expected score of a particular player?

Problem Statement