Here is a nice little problem from Paul Nahin's Will You Be Alive 10 Years From Now?. It is a problem from the 1654 correspondence between Antoine Gombaud (the Chevalier de Méré) and Blaise Pascal - one of the founding episodes of probability theory, dressed up as a gambling puzzle.

(This one lives on our wiki as FMM21, part of our Friday Morning Math Problem series.)

The Two Games

Game 1. You toss a single die \(N_1\) times. What should \(N_1\) be to make the probability of seeing at least one 6 greater than \(\tfrac{1}{2}\)?

Game 2. You toss …