Say you are playing game in which you are betting money and you belive you have an advantage, (if you bet $X and win, you get $2X back). Given a bankroll X an bet unit of Y and an advantage of A, what is the probability of at some point having MX dollars, assuming you play untill you either run out of money or you reach your target? I have made simulations on excel and have found that it is easy to calculate when you have zero advantage (i.e. the probability of winning is 50%) because regardless of your bet size you always have a X/MX probability of reaching your target (MX). Example: you have $1,000 and will play a fair game untill either you reach $2,000 or zero, the odds of doing this is 50% regardless of bet size. So given all of this I am wondering what the probability will be when you change one factor (the advantage). According to my simulation If you have $600 and bet $10 at a time you have about a 90.28% chance of reaching $1200 before you reach zero, if your chance of winning is 51%. I say "about" 90.28 because I have only run it a couple thousand times and it is constantly changing. Since I'm doing it on excel it takes a couple minutes to rack up a thousand runs. I would like a way to calculate it exactly, but if anyone knows of some good simulation software that will do this, I would appreciate it if you told me.