We Got A Problem #11: Rock Rock Paper Scissors
December 19, 2012 5 Comments
Most people know Rock-Paper-Scissors (or its more fun cousin, Ninja-Cowboy-Bear). Kate and Ogden are locked in a long battle of online Rock-Paper-Scissors, with a winner scoring 1 point, and a tie scoring nothing for either player. Game’s to 100.
Ogden won the first series 100-77 by constantly looking for patterns in Kate’s choices. For the second series, Kate tries something interesting: she has no pattern. She randomly selects rock, paper, or scissors with equal probability. She even tells Ogden that she is doing this, and he can do nothing about it but sigh and accept that he cannot beat this “strategy”. Kate wins the second series 100-95 by luck.
For the third series, Ogden changes a rule: if rock beats scissors, the winner scores 2 points instead of 1. Other victories (scissors over paper, paper over rock) are still worth 1.
Now Kate’s panicked: if she still randomly selects, is she beatable in the long run, or not? Can she alter the probabilities to make a new “strategy” that Ogden can’t beat? It seems like it would be bad to play scissors so often, and she should probably play more rocks… or not?
Let us know whether you find any ways that Kate can play to force Ogden into equilibrium.