Probability of BUSTO! in blackjack

[ShakeZula06]

Knowing how much you are flat betting per hand, how much wagers you plan to make, your bankroll, and the house advantage, what is a formula you can use to find out your RoR?

Thanks for your time,
Shake

[Reef]

check wizard of odds

[AaronBrown]

If you make N bets of size B, and the house advantage is E, then your expected loss is B*N*E. Your rate of return is -N*E on your bankroll per session.

The standard deviation of your final bankroll is approximately B*[N*(1 - E^2)]^0.5/2. You can use the Excel Normdist function or a Normal table to get the approximate chance of losing B over N bets:

= Normdist(-B , -B*N*E , B*[N*(1 - E^2)]^0.5/2, True)

Your chance of going broke at or before N bets is higher than this. For a small house edge, it is approximately twice this level.

[ShakeZula06]

Good post Aaron. Thing is I'm looking at making a lot of these calculations with differing variables, and I'm thinking it would be easier to just get some type of simulation software. Any recommendations?

[AaronBrown]

You don't really need simulation software. I use Crystal Ball myself, an excellent product, but it has far more than you need (or may be willing to pay for). You can do an excellent simulation in Visual Basic for Applications, which comes with Excel.