I have simulated a tournament between an infallible Tic Tac Toe player and one that chooses its moves randomly.
Even after 5 million games, the infallible player wins every single game. I know that if both players play infallible, a Tic Tac Toe game always ends in a draw. I could not find a bug in my program and I am missing the foundations in probability theory to calculate whether it is probable that even after 5 million games no draw occurs.
Is there a way to calculate and prove it?