[Guy McSucker]

I will probably mess this right up, never having studied statistics, but here goes anyway. For anyone that wants a laugh: I have a PhD in mathematics.

I believe that for a 95% confidence in statistical findings, you look within 2 standard deviations. Perhaps this only applies to normal distributions, and perhaps poker doesn't have one of those. Anyway.

If this is right, the formula for your worst expected result after n tournaments would be

n times (average win) - (standard dev) times sqrt(n) times 2

We want to find n such that this is minimum. Differentiating w.r.t. n gives:

average win - (standard dev)/(sqrt n)

This is zero when

n = (std dev/avg win) ^ 2.

which in your case is about 25.

Plugging n = 25 into the formula for worst result gives

25 times 4 - 2 times 5 times 19

which is -90.

This would mean that 8 buyins at the $10 level would give you your 5% risk of ruin.

I've done all this in my head and rounded the numbers pretty much at random, so the actual numbers may be way off; and the formulae might be bunk too.

For "almost no" risk of ruin, rework the math with three standard deviations instead of two.

Not sure how to do 25%. Some other number of standard deviations to give a 75% confidence level I suppose.

Guy.