Odd or Even
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Odd or Even is a hand game played by competitors to decide random issues such as who needs to jump into the freezing cold water to get the volleyball as seen on the popular television commercial featuring the US Olympic Women's Beach Volleyball Team.
To play, first, you call either odds or evens. Then you each count to three. On three, you and the other person hold out either one or two fingers. If the fingers add to either two or four, then the person who called even wins. If the numbers add to three, then whoever called odds wins.
The game can be expanded for larger number of players by using modular arithmetic. For n players, each player is assigned a number from zero to n−1. On three, each player holds out any number of fingers less than n, including zero. The person whose number is the remainder of the sum is chosen. A common way of doing this is to arrange each player in a circle, assign someone to be player zero and a direction to count upwards (usually clockwise). Once players throw out their numbers, they leave their hands in place and close their fingers one at a time as counting moves around the circle. When no fingers are left, the final player counted is selected.
An interesting consequence of the expanded version of odds and evens is that the winner is significantly more random than playing consecutive games of rock, paper, scissors. Since any single player can change the result to any other player, a nonrandom result requires the simultaneous cooperation of all players. While unwitting cooperation based on manipulating human psychology can be achieved with successive games of rock, paper, scissors by skilled players, the difficulty of simultaneously predicting the throws of all other players in a single expanded game of odds and evens is much harder.