The Remainder Game -- a method for constant-time (pseudo-)random selection
I primarily use the Remainder Game for start player selection but there’s no inherent reason it has to be limited to that application. The pattern is simple:
- One player calls for the start player selection, Everybody stick out some fingers. 1, 2, 3!
- Take the modulus of the total number of fingers shown by the players by the number of player and starting at zero, count out that many players in rotation from the calling player.
- The indicated player is the start player.
The Remainder Game is efficient, deterministic results (no repeats, roll-offs or ties possible), actually random1, short constant execution time, works with any number of players in any situation, works with any game in any situation, clearly auditable by all concerned, and requires no equipment.
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Well, nearly and close enough in practice. Ideally the number of fingers shown by each player should be in the range of zero-#players-1 or else there’s a bias away from players to the right of the calling player. In practice however as player counts are usually in the 3-5 range and most people use the fingers of one hand, this really doesn’t matter much. throw in the odd player who sometimes uses fingers from both hands and you’re near golden for all games and player counts ↩