- At least two players are needed to play, plus one more person acting as an impartial moderator.
- A game consists of a series of rounds described as follows:
- The moderator announces an integer N and then secretly chooses a random integer R in the range 1 to N. The value of N should be much greater than the number of players.
- The first player then calls out an integer in the range 1 to N. In subsequent turns, the players alternate calling integers greater than the previously called integer but not more than N.
- The round ends when one player calls an integer which is greater than or equal to R, at which point the moderator will announce the player has 'busted', meaning he has matched or exceeded R and lost the round.
- When a player busts, he loses points equal to the amount he went over R, if he said exactly R then there is no penalty.
- Each other player scores the difference between their last call and the call before that. If a player has not made any calls, then he scores 0.
Example game 1
Three players A, B, C. N=20, R=18
A:8, B:12, C:15, A:17, B:19=busted
A scores 17-15=2, B penalized 19-18=1, C scores 15-12=3
Example game 2
Three players A, B, C. N=20, R=7
A scores 4-0=4, B penalized 7-7=0, C scores 0
What is a player's best strategy if he wants to simply avoid busting?
What is a player's best strategy if he wants to maximize his expected points for a round?