A biased game. e.g., each player pick a pattern with three coin flips such as “TTT”, then flip the coin until the sequence matches one of them. If you pick last, you can win most of the time. For instance, if one picks “TTT”, then the other can pick “HTT” that reliably beats “TTT” because to get the “TTT” pattern, unless it appears right at the beginning, one needs to go through “HTT”.
See also Nontransitive dice, Humble Pi.