Thread: Cointoss Problem

The game: You have n dollars and a fair coin. The coin is tossed m times. When it comes up heads you lose one dollar, when tails you win one dollar.

My question: How do we calculate the probability that you will lose your money within some given number of flips?

(Edit: I made the payoffs equal in size to simplify a little: -1 for losing and +1 for winning)

I thought about this some more and realized that within a given number of flips there will be a finite number of ways to drop from n dollars to zero. So I guess all I need to do is sum the probabilities of all those different ways. Not quite sure how to do that though...