Suppose we play a coin game: we flip a coin, upon tails you get one dollar from me, upon heads I get one dollar from you. We repeat this until one of us is broke.

Now, at the beginning of the game, I have $4 and you have $6.

1. What is the chance of me winning the game? (thus ending up with $10, leaving you broke)

2. What is the expected number of turns we have to take until the game finishes? (i.e. until one of us is broke)

Intuitively I feel the answer to Q1 should be , but I can't seem to calculate this properly. No idea how to approach Q2. I can see that and (with being the number of turns from a game situation where I have n dollar) but I don't know how to resolve this to a definite result.