Question

1. In this game, you start with $1 in the pot. Every time you flip a head the money in the pot doubles. When you finally flip a tail, you walk away with all of the money in the pot. What is the expected value of this game?
2. Same game, but if you flip a tail, the money in the pot is gone forever. You get to quit this game any time before you flip a tail and walk away with all the money in the pot. What is the expected value of this game?