I'm trying to figure out the risk of busting out on a particular casino bonus. I thought there would be a straight forward formula for it but I can't seem to find one. Can any of you math gurus help me out?

The bonus is for $1000 with a wagering requirement of $40,000. The best game allowed to clear the bonus is European Roulette with La Partage, house edge of about 1.35%.

If my EV calculation is correct (1000 - (.0135 x 40000)) then the EV should be $460.

So I'm trying to figure out the risk of ruin if one were to make 40,000 $1 even-money bets (red, black, odd, even, etc..). What other information is needed? The Standard Deviation? How do we calculate that?

Thanks!

Go find TheUnkownPlayer's article on bankroll and ROR on the main page of BTP - it gives you the forumula. Yes, you need the SD.