Risk of Ruin / Bankroll Management Formula

[Orlando Salazar]

I'm posting this on multiple categories. I'll show computer simulations when I can setup a website to link.
Risk of ruin is a function of the number of discrete bets, win % deviation, required confidence level (under chebyshev since we must assume that poker win% is not normally distributed)
Win deviation is a function of bet threshold, the standard deviation of your uncertain win expectation, and % “edge”. Thus, playing 40 hands of equal value (1/40th of your bankroll) where you move all in, there is only a 1 in 7,599,000 chance (at the 94% confidence level) that you will be ROBUSTO. Assumptions include a 66% win expectation threshold for moving in, and 1% edge, given the 9.2% stdev of 2 handed play equity. The confidence function at ~94% <4 stdevs> under chebyshev: {1+ 66% + 1% -[(9.2%*4)/2]}^40 = 1 in 7,599,000.
If you six max with a 51% threshold and no edge, playing 1/20th of your bankroll: {1+ 51% + 0% -[(5.96%*4)/2]}^20 = 1 in 730. Note, AA has 49.77% equity UTG in a 6 max game. If 730 individuals at distinct tables move all in with AA UTG and every other player calls, at least 1 hero should go broke doing this just 20x [img]/images/graemlins/frown.gif[/img]
Thus, an adequate bankroll can be estimated by a player’s all in “threshold”; edge; table handedness; risk of ruin requirement, and required confidence interval

Handedness/Equity Std Dev%
9 4.3
8 4.8
7 5.3
6 6.0
5 6.7
4 7.6
3 8.6
2 9.2

If you notice, the redundancy is for clarity. % win expectation includes ties.