The puzzle below, known as The Problem of Points, is often said to have inspired probability theory.

Fermat and Pascal play a game by repeatedly flipping coins - if a coin lands heads, Fermat gains a point, and if it lands tails, Pascal gains a point. It is agreed that first to $10$ points wins a prize of $100$ francs. Suppose the game abruptly stops when the score is $8$-$7$ to Fermat. How should the prize be fairly divided between the two players?

Post solutions below!

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