White Guy said:
Thanks for the free sim link that is exactly what I was hoping for.
A simple formula will also suffice for what you're looking for. You're looking to convince your friends, not to write a grant proposal on your chances of success.
There are two ROR's (see Edit #2 at the bottom) that are easy to calculate: a 17% ROR (bust out at -1 SD), and a 2.5% ROR (bust out at -2 SD), using BR = bankroll in units, h = hands, EV = expected value per hand, and SD = standard deviation. Use an estimation of 2.5*sqrt(h) < SD < 3*sqrt(h) and solve for BR.
BR + h*EV - n*SD = 0, where n = 1 (for 16% ROR) or 2 (for 2.5% ROR)
BR = k*sqrt(h) - h*EV, where 2.5*n < k < 3*n
This is a downward-facing parabola; at some point with increasing hands, your EV will overcome the variance; your bankroll required will actually decrease if you play enough hands. The lifetime ROR can be calculated from this maximum value of BR.
d(BR)/dh = 0.5*k/sqrt(h) - EV = 0
h(max) = (0.5*k/EV)^2
BR(max) = 0.5*k^2/EV - 0.25*k^2/EV = 0.25*k^2/EV
Calculating your precise SD and EV is your job; I'll post a range of k's and EV's and it will demonstrate how large of a bankroll is needed. Keep in mind that the bankroll numbers are in minimum units; if you're betting $25-$400, your unit is $25.
17% Lifetime ROR
Code:
EV --> 0.005 0.01 0.015 0.02
k
2 200 100 67 50
2.5 313 156 104 78
3 450 225 150 113
3.5 613 306 204 153
2.5% Lifetime ROR
Code:
EV --> 0.005 0.01 0.015 0.02
k
4 800 400 267 200
5 1250 625 417 313
6 1800 900 600 450
7 2450 1225 817 613
Edit #1: It's pretty clear to see that small bankrolls are required for high-EV, low-variance systems; unfortunately, most of the time, raising your EV will also raise your variance, so be careful: EV and k are not entirely independent variables.
Edit #2: Should have looked on Wikipedia first - correlations of sigma (n in my calculations above) to percentages are listed, so you can calculate a lot more than the two that I listed. And my numbers are a bit off.
16.8% ROR: use n = 1.000
10% ROR: use n = 1.282
5% ROR: use n = 1.645
2.5% ROR: use n = 1.960
1% ROR: use n = 2.326
0.5% ROR: use n = 2.576
