Consider a classic tic-tac-toe game with 2 players and 9 squares on a 3x3 grid. Contrary to common rules, players take turns at random instead of alternating turns. That is, there is uncertainty at the time a player makes his choice about who is going to play next.
Suppose agents have common knowledge about the distribution, F, of future turns. What is the optimal strategy for the players? Does this kind of randomness alter the conventional optimal strategy at all?