Derivation of the bankroll and ruin formulas
 

For those interested, I have posted a simple and self-contained derivation of the bankroll and ruin formulas on the probability forum.

N/M Any way this formula can be simplified for non math majors?
 

This formula is a bit tough for me. Any chance you can simplify it? Dog

Re: Any way this formula can be simplified for non math majors?
 

That is the simplified version. What part are you having trouble with?

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

That says take your standard deviation, square it, divide by twice your win rate u, negate that to make it a negative number, and multiply by the natural log of your risk of ruin. For example, if your win rate is 1 bb/hr, and your SD for 1 hour is 10 bb, and you want a 5% chance of going bust, then

10^2 = 100
100/(2*1) = 50
-50
-50*ln(.05) = 150 bb
So you need a 150 bb bankroll.


Going the other way, say I only have 75 bb, and I want to know my risk of ruin:

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

-2*1*75 = -150
-150/10^2 = -150/100 = -1.5
take exponential of -1.5 = exp(-1.5) or about 2.718^(-1.5) = 22.3%.

So halving half the bank increased your risk of ruin by more than 4 times. Actually doubling the bank squares the risk of ruin (making it smaller), see
(22.3%)^2 = 5%.

Re: Any way this formula can be simplified for non math majors?
 

Thank you Bruce - I understand it now. Dogmeat