2015 Fall Team #2
Source:
March 26, 2022
combinatorics
Problem Statement
You have game pieces, and you play a game against an intelligent opponent who has . The rules go as follows: you distribute your pieces among two points a and b, and your opponent simultaneously does as well (so neither player sees what the other is doing). You win the round if you have more pieces than them on either or, and you lose the round if you only draw or have fewer pieces on both. You play the optimal strategy, assuming your opponent will play with the strategy that beats your strategy most frequently. What proportion of the time will you win?