View Full Version : Risk of ruin question

12-20-2003, 05:39 PM
brucez's br formulas:

B = -(sigma^2/2u)ln(r)

r = exp(-2uB/sigma^2)

where B is bankroll, sigma is SD, u is hourly earn, and r is risk of ruin

Do sigma, B, and u need to be in big bets or money? Or does it matter?

Say I'm playing 2/4 making 2 bb an hour with 10 bb SD.
The equation B = -(sigma^2/2u)ln (r) or
B = -(10^2/2*2)ln(.05) = 74.89
B = -(40^2/2*8)ln(.05) = 299.57

So when sigma and u are in an amount of money, it gives you your BR in big bets?

But using one of brucez examples in which you make $30 an hour with a SD of 650, i get this
B = -(650^2/2*30)ln(.05) = 21094.94
And in that case it gives me a dollar amount instead of a BB amount for B.

I'm confused.

12-20-2003, 05:57 PM
Doesn't matter what units you use for the formulas. BTW,
these formulas are mere approximations but excellent ones
nonetheless! Also, the time interval commonly used is per
hour, but you could use anything else (personally, I prefer
ten minutes as this is quite easy to do online since the
more data that is accumulated, the more quickly it is to get
smaller confidence intervals and hence, a better estimator
for the win rate).

12-20-2003, 06:36 PM
B = -(40^2/2*8)ln(.05) = 299.57

So that's saying I need $299.57 for a 5% ROR playing 2/4 making $8 an hour with $40 SD? Just 79 bb? Where did I mess up?

12-20-2003, 07:39 PM
2 BB/hr is good, 10 BB/sqrt(hr) is not a big variance, and 5% is a relatively large RoR, so this is why the number (79 BB) is much less than the canonical 300 BB.