Unfair game

You have $100 initially. You are playing a repeated game with a guy with an infinite amount of money. You have a 51% probability to win each game and 49
% probability to lose each geam.

Each time you earn $1 if you win, lose $1 if you lose the game. What is the 
probability that you will eventually go broke?

F(i) - the probability of broke with initial state at I. F(100) is the 
result
let p=.49, q=.51
F(0)=1
F(i)=p*F(i-1)+q*F(i+1) i=1,2,...
Then sum together, S=F(1)+F(2)+...
S=p*(1+S)+q(S-F(1)) => F(1)=p/q

Then, it is easy to calculate that
F(i)=(p/q)^i

Another way:

(p/q)^i is alway is martingale, where i is the money you have now, p is the probability to lose in one toss, q is the probability to win in one toss.