Take three dice A, B and C and change the numbers on two faces of each as follows:
A: 1, 1, 3, 5, 5, 6 B: 2, 3, 3, 4, 4, 5 C: 1, 2, 2, 4, 6, 6
Find someone who enjoys a wager, ask them to choose a die. Then choose your die to be the one to the right of theirs in the sequence ABCA. Bet them a pound that if you both roll different numbers, your roll will higher than theirs. After 100 rolls you can expect to be around six pounds up on average! (For more information see the Wikipedia article Nontransitive Dice.)
Update: Since posting the above, I have written a short program to simulate the game. The average profit over a 1000 games of 100 rolls each was £6.76 per game, reasonably close to the theoretical figure of £6.25. Averaged over 100,000 games the simulation's predicted profit per game was even closer at six pounds and 24.84 pence. But be warned, there were significant deviations from the mean, with the 100-roll games occasionally showing a negative profit!
Update: Since posting the above, I have written a short program to simulate the game. The average profit over a 1000 games of 100 rolls each was £6.76 per game, reasonably close to the theoretical figure of £6.25. Averaged over 100,000 games the simulation's predicted profit per game was even closer at six pounds and 24.84 pence. But be warned, there were significant deviations from the mean, with the 100-roll games occasionally showing a negative profit!
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