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Old 11-16-2007, 12:04 PM
pzhon pzhon is offline
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Join Date: Mar 2004
Posts: 4,515
Default Re: Help me with my stats and question about standard deviation.

The standard deviation in a HU SNG is about 1 buy-in. It's slightly less because of the rake and your skill advantage, e.g., in a $6+$0.25 SNG, the standard deviation is $12 * sqrt(p (1-p)). If you win 60% of the time, that is a standard deviation of $5.88 or 0.94 buy-ins.

After n tournaments, the standard deviation of your observed win rate is (SD per tournament)/sqrt(n). A rough 95% confidence interval is your observed result +- 2 standard deviations. In your case, that would be about 20% +- 2 * 94%/sqrt(77) ~ 20% +- 21%. So, at this point you are just starting to have strong evidence that you are a winning player. To narrow the confidence interval by a factor of 2, you need to play 4 times as many tournaments.

Here is a general post on rational bankroll requirements, and here is a follow-up on using this to decide which stakes to play, given that your win rate drops in higher stakes games. It will be a while before you can use those, since they require estimates of your win rate.
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