I am attempting to determine how the Gambler's Ruin equation is determined -- I attempted looking through Feller's book but to no avail. I believe it has to do with Markov Chains and would be indebted to someone if they could help me derive the equation.
The equation is attached.
EDIT: Nevermind-- apparently there is an error with attachments.
The equation is as follows. We have P(i,N) which is the probability that you'll reach before going broke:
where is your chance of winning a bet, is chance of losing one bet, is current fortune in betting units, is your goal, also in betting units .
So, if you have $10,000 and your goal is $25,000, assuming you always bet $5,000, then i = 2, N = 5, and p,q are the respective chances of winning/losing.
I think that should be sufficient.