Problem of the Week 1123
A Fair Dice Game
Alice: Look at this neat new 15-sided die. The probability of it landing on any of 1, 2, 3, ..., 15 is exactly
Bob: Hold on. If you go first, then you have a better chance of winning. Here's a better idea: We'll pick two positive integers A and B. You can go first, but whenever you roll the die, you have to get A or lower to win, and when I roll I have to get B or lower.
Alice: Okay. But what should A and B be?
What should A and B be in order that Bob's and Alice's chances of winning are equal?
Source: Dan Velleman via the Amherst College Walker Prize Examination.
© Copyright 2009 Stan Wagon. Reproduced with permission.