Suppose I play a gambling game where I either win or lose k dollars. Suppose further that the chance of winning is p = 0.5. I employ the following strategy to try to guarantee that I win some money.

I bet $1. If I lose, I double my bet to $2. If I lose again, I double my bet again to $4. If I lose again, I double my bet again to $8. I continue until I win.

Let X be the amount of money that I bet on the last game.

(a) What is the net amount of money that I can win?

(b) Find the expected value of X.

(c) Discuss if this strategy makes sense or not.