Confidence intervals & distribution at limit holdem

[piki]

Hi,

I would like some input from a stat wiz on this issue, as I have little clue on the matter. It has been mentioned before that calculating confidence intervals on win rate assuming normal distribution might not be correct.

Indeed, winnings distribution in limit holdem does not seem to be normal, while distribution where we remove hands with losses of 0, 0.25bb (small blind) and 0.5bb (big blind) look much better. Let's call this distribution N.

Is it possible to calculate better confidence intervals using mean(N), stdev(N), count(N) and count(won=0), count(won=-0.25), count(won=-0.5), assuming N is normal, and how?

Thanks,
pix

[pzhon]

[ QUOTE ]
It has been mentioned before that calculating confidence intervals on win rate assuming normal distribution might not be correct.

Indeed, winnings distribution in limit holdem does not seem to be normal,

[/ QUOTE ]
For the most part, these objections are unfounded. The Central Limit Theorem says you don't need the distribution for each hand to be normal in order to use a normal approximation to the sum or average.

You do want to have some assumption of independence, which is not quite true in poker. It's unclear whether the deviations from independence (due to position and tilt/metagame) are significant.

You might be able to get slightly more accurate estimates of the standard deviation if you recognize that the blinds are posted periodically, according to your position, rather than randomly. If you ignore this, your estimate of the variance in limit may be about 1% high from the blinds alone. It would be better to treat the orbits as units, which would also factor in other more important positional considerations.