Sample Size ROI Certainty Question

[Rasputin]

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3.8/sqrt(#SnG you've played) = +/- your current ROI to find the possible swing in your ROI...

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I've seen this formula pop up in a few threads.

Can someone fill me in on the reasoning behind it? I don't like trusting formulae where I don't know how it came about.

[JFB37]

Maybe Mycroft knows.

Seriously, I thought this was a good question when you posted it at the other place. If you get a good answer somewhere, I would be curious. I spent an hour flipping through a stat book and couldn't adjust any of the applicable analyses to arrive at this result.