Aaron offers Berenice to play a game of dice with him. Aaron explains the game to Berenice as follows:

"We each get one die, the highest one wins. If we tie, I win, but since you always lose when you roll a one, if you roll a one you can roll it again. If you get a one the second time you have to keep it."

What is each person's probability of winning? What are the probabilities of winning if Berenice can keep rolling until she gets something besides a one?

(In reply to soln by Steven Lord)

Your solution to part 2 makes it very clear that the probability is 1/2 no matter how many sides the die has.  For a generalized die of n sides its pretty easy to see that both players have n*(n-1)/2 equally likely ways to win out of all n*(n-1) outcomes, which makes it easy to compute the probability of 1/2.

Posted by Brian Smith on 2022-11-16 12:46:02