[jimdmcevoy]

Ok, suppose you got a 1,000,000 and if some one bets they have a 50/50 at winning 1000 or losing 1100.

Let's call the number of these bets you take n.

As in if you took 15 bets, n=15.

Now suppose you win m out of these n bets.

You will have a .5^n*n!/[(n-m)!*m!] chance winning m bets out to the total n bets you took.

m can equal 0,1,2,3.... all the way up to n

So, you want to work out the chance that you will end up with 0 or less?

that means you want to know the chance that:

1,000,000 + 1000*(-n+1.1*m)<=0

With some algebra this is the same as saying what is that chance that:

m>=(n-1000)/1.1

So once you know n, you can work out what m (the total number of bets you won) has to be in order to remain positive. Suppose you need m>5 to be positive. Then you work out the probability that m=0, add that to the probability that m=1, and again for m=2, and m=3, and m=4, and that is the probability you will go negative.

But remember this is not really 'going broke', you are going negative. The only way to avoid risking going negative is if you take bets that you will be able to pay back even if every bet you take you lose.