How many trials to guarantee a profit?

[JayTee]

Let's say that I have someone offering me $101:$100 on flipping a fair coin. How many flips would I have to get them to agree to to be 99% sure that I will profit at least $100.

I would expect to profit $0.50 on each flip, right? So I would expect to be up $100 after 200 flips, but that's just on average. What is the probability that I am up at least $100 after 200 flips. I don't know how to solve it but I would guess 50%.