Suppose you go to a casino with exactly 63 dollars. You play a game where the probability of winning is 1/2. You have the following strategy:
First, you bet 1 dollar if you win, you leave with 64 dollars.
If you lose you bet 2 dollars.
If you win you leave. If you lose you bet 4 dollars.
You then continue this pattern, if you win you leave, if you lose you bet twice your last bet, until you have no more money.

Let Y equal the amount of money you take home.
Compute Pᵧ(y) and E(Y). Would you play this game everyday?