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I've got a new related project. My friend is grinding the spin n go's on pokerstars in a variance sharing team with others. If you aren't familiar with the spins, they work like this. The buyin is 30 dollars, and you play a 3 handed winner-take-all turbo sng with a random prize pool, as follows:
$90K 1:100K
$6K 5:100K
$3K 1:10K
$750 1:1000
$300 5:1000
$180 7.5%
$120 21.4%
$60 70.5%
All in all, you pay $30 dollars to play for about $85.2 worth of prize pool equity, making the rake $1.6.
So I did some work on the variance of this game and it seems to me like since the outcomes are so wildly asymmetrical about the mean (the only distant outcomes are positive ones, the only negative outcome is losing 30 bucks), normal figures like standard deviation and variance seem relatively useless. Indeed, I used jackvances method of providing a 95% range of outcomes for 100 trials and it comes out that the lower bounds is -3500 dollars, which is impossible since even if you lost all 100 games you'd only be out 3000.
Is there a special formula for calculating confidence intervals in cases of long-shot positive outcomes such as this?
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