HMMT Combinatorics 2019/3: Reimu and Sanae Play a Game
Source:
February 17, 2019
HMMTprobability
Problem Statement
Reimu and Sanae play a game using fair coins. Initially both sides of each coin are white. Starting with Reimu, they take turns to color one of the white sides either red or green. After all sides are colored, the four coins are tossed. If there are more red sides showing up, then Reimu wins, and if there are more green sides showing up, then Sanae wins. However, if there is an equal number of red sides and green sides, then neither of them wins. Given that both of them play optimally to maximize the probability of winning, what is the probability that Reimu wins?