A deceptivly simple game from Douglas Hofstadter's book "Metamagical Themas".

The winner of a game of Mediocrity is the most "mediocre" player. In a three player game of mediocrity each player selects a number (lets say between 1-10). The player who selects the middlemost number is the winner! This is known as Level 0 mediocrity.

A Level 1 game of mediocrity involves playing N games (lets say 5) of Level 0 mediocrity. Of course the winner is the person with the middlemost number of Level 0 wins!

The progression to higher Level (2+) games of mediocrity is quite clear. It is often a good way to make boring multi-player games exciting, forcing a person to come second usually keeps the game much tighter. The strategy for higher level games of mediocrity (3+) is extremely difficult.

Example level 1 game... Three players, Alice, Bob, and Chris. Bold indicates winner.

Game A B C
1    5 2 3
2    4 5 7
3    3 6 4
4    6 5 3
5    1 8 9
T    0 3 2
Thus, Chris is the winner for the level 1 game.