On last Thursday’s Survivor, three team members had to decide which of them would be stranded on Exile Island. They wanted to do it randomly, so they agreed to play rock-paper-scissors. First, Sally played Misty and Misty lost. Then Misty played Courtney and Misty lost again. So Misty got exiled.
Courtney got lucky. But if she’d had the slightest knowledge of probability, she’d have realized the procedure disadvantaged her. Misty had to lose twice in order to be exiled; Sally also would have had to lose twice. Courtney, however, would only have had to lose once. The procedure they used gave Courtney a 50% chance of being exiled, and the other two only 25% each.
How might they have generated a true 1/3 probability for each contestant to be exiled? These two old posts of mine discuss several possible (isomorphic) answers – just substitute rock-paper-scissors for the coin flip. Or they could have just drawn straws.
Now here’s the question of strategy. Say you were one of those three contestants. And say you understood the probability issues discussed above. What would you do? My first impulse would have been to dispute the mechanism and propose a fair one. But I hope I would have resisted that impulse, and instead simply made sure I took part in the first round of rock-paper-scissors.