Poker win rate - stat analysis
Posted by pksmv11235
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pksmv11235
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Gen. Poker
Poker win rate - stat analysis
Yo Yo,
I have a statistical question:
You have a sample size of 1k hands.
From that sample you observe an average win rate of 10bb/100.
Q: how would you proceed in answering (with a statistical argument) to the following question:
“How much confidence you are in that result?”
I heard about confidence intervals but i don’t know where to start...
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Google poker variance calculator. 1k hands is nothing, you can end up losing or winning 50bb/100+ over this sample even if ure winning or losing player
http://pokerdope.com/poker-variance-calculator/
95% confidence interval [-532 BB, 732 BB]
[-53.25 BB/100, 73.25 BB/100]
That means that ist a 95 % Chance that your Winnings are between - 53 BB and + 73 BB.
Just few notes after having played around with the calculator:
Even if you have a real Winrate of 2bb/H only their is a 40 Percent Chance that you win 10/BB or more after 1k Hands. Even after 10k Hands the Chance is 20 Percent.
With a real winrate of 10 BB/H and 100k Hands your Winning in the 95% confidence interval are between 3675 BB and 16325 BB! (36 Stacks or 163 Stacks).
Varianz is crazy even with 100k Hands and a really high winrate of 10/BB which should be almost unreachable for most Players. If you enter a typical low Zoom WInrate of 2,5 BB/H for example, there´s a 20 Percent Chance that you have lost after 100k Hands!
That variance calculators is assuming that your actual winrate is 10bb/100 which is unlikely
given that the sample size is only 1k hands.
A better approach is to first calculate your most probable win rate using bayesian statistics see http://www.whatsmywinrate.com/.
And then use a variance calculator to get your confidence interval.
In any case a sample size of 1k hands is to low so say anything useful and actually still your most likely a loosing player according bayesian statistics (this assumes that you have no advantage over other people that start playing poker and as you at least are interested more then the average John Doe you have a better chance to be above average).
I don't really think that variance calculator is legit from what I've seen, models seems off, even in category ''About this tool'', 5th paragraph says: "All models are wrong, but some are useful" - George E.P. Box. We use confidence intervals to estimate our ''real'' winrate, not to estimate how we can run with our real winrate, because no one know their real winrate in ball park of few bb/100
It is not about variance only it is about what your actual win-rate is it uses Bayesian statistics with the assumption that most players win rate are around -8 BB due to rake and as hero has measured win rate of 10 BB it gives the win-rate the hero should expect based on Bayesian statistics.
e.g. when you toss a coin and it comes up heads 4 times in a row it will tell you what the probability is that the coin is rigged/balanced or not and how rigged/balanced it is given the prior that normal coins are not rigged and that there is a 50% chance that it is heads or tail.
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