Penney's game, named after its inventor Walter Penney, is a binary sequence generating game between two players. Player A selects a sequence of heads and tails of length 3 and then Player B also selects a sequence of heads and tails of length 3. Then a fair coin is tossed until either player A's or player B's sequence appears as a consecutive subsequence of the coin toss outcomes. The player whose sequence appears first wins.

There are eight sequences can be chosen in total. By choosing each of them, you can see that there is always a sequence chosen by the computer that can beat the player's choice. This is because Penney's game is a non-transitive game. There is NO best options in such a game. Given a sequence, one can always find another sequence that has a higher chance of occuring first. A similar game is known as "Rock Paper Scissors".