Optimal RPS vs. RP play
Alice and Bob are playing 900 games of Rock-Paper-Scissors, but Alice is not allowed to choose scissors in any of the games. If both players choose their strategies optimally (i.e. Nash equilibrium is reached), what is the expected number of games Bob will win?
"Optimally" means that both players want to maximize the difference between the number of games they win and the number of games the opponent wins.