[LCposter]

Ok, I'll try to do a quick primer of the math involved. I apologize if I'm repeating things you already know.

The standard deviation for an SNG is primarily a function of the payout structure and to a lesser extent your finish distribution. As long as you remember that variance = E(x^2) - E(x)^2, you can calculate your own SD based on your stats.

I'll give an example for party $10+1 (10 players, 50/30/20 payout), finish distribution 15%/13%/12%. First off, realize that even though the payouts are 50/30/20/0, you have to subtract the buyin+rake so that net payouts are 39/19/9/-11.

E(x) = 0.15 * 39 + 0.13 * 19 + 0.12 * 9 + 0.60 * (-11) = 2.8
E(x^2) = 0.15 * 39^2 + 0.13 * 19^2 + 0.12 * 9^2 + 0.60 * (-11)^2 = 357.4
Var(x) = E(x^2) - E(x)^2 = 357.4 - 2.8^2 = 349.56
SD(x) = Sqrt(Var(x)) = Sqrt(349.56) = 18.69652
SD(x)/Buy-in = 18.69652 / 11 = 169.9684%

That's why pzhon quoted an SD around 170%. You can tweak the first, second, and third place finish percentages, as long as you keep the ROI reasonable (i.e. not at the -100% or +354% extremes) it doesn't change the SD that much.

For independent trials, the variances add (i.e. V(x + y) = V(x) + V(y)).
Therefore SD(profit) after n games = 18.69652 * sqrt(n).
And SD(profit)/Buy-in = 18.69652 * sqrt(n) / 11n = 170% / sqrt(n)

To form a 95% confidence interval, we need to go +/- 2 standard deviations from the estimate,
which is why pzhon multiplied by 2 to get 340%/sqrt(n).

Finally, we can do the algebra to solve for n.

To be 95% confident your ROI estimate is within 5% of your "true" ROI:

5% = 340% / sqrt(n)
sqrt(n) = 68
n = 68^2 = 4624

To be 95% confident your ROI estimate is within 1% of your "true" ROI:

1% = 340% / sqrt(n)
sqrt(n) = 340
n = 340^2 = 115,600

I'm not 100% sure about these last calculations. Someone may want to confirm whether they are correct or not.

I know it's discouraging, but the nature of SNGs (and most forms of poker for that matter) is that the variance per trial is quite large, so you need several thousand trials before you can have much confidence about your ROI. At the same time, the conditions would need to remain static during this stretch of several thousand SNGs. The reality is that the game conditions (your skill, opponents' skill, etc.) change too rapidly to ever know what your "true" ROI is. But in any case, it is nice to know the 95% confidence interval for your ROI assuming static game conditions.