Given a fair coin and a number $ p\in(0,1)$ . How do you Design a game that finishes in finite number of tosses with probability $ 1$ . And further, with probability $ p$ you win the game.
I thought about random walks where head, you add 1, tail you subtract 1. And you want to get to $ n$ . But that gives an approximation to $ p$ and not $ p$ .