Quote:
Originally Posted by Bobo Fett
There were a couple of things I found confusing right at the end. On page 42, applying the Bayes' theorem to the 5 BB/100 win rate provides results I found a little counter-intuitive. The second table, recalculated with a higher sample of 100,000 hands, of course has shifted the expected win rate much more towards the winning side - 65% chance of +1 BB/100 or better. However, if the math is right, I would think a fundamental flaw of the method is showing when the +3 BB/100 rate has dropped to 0.04%. If someone has a 5 BB/100 win rate over 100,000 hands, how likely is it that their chance of having an actual win rate of +3 BB/100 or better is only 0.04%? With a smaller sample, it was 11.03%?? Is there something I'm missing, or is this a flaw in the system?
Oh, this is confusing. The second table on page 42 is a recalculation of the case from page 41, where the guy has a 1.15 win rate, but with a bigger sample size. It's not a recalculation of the top table on page 42 where he has a 5 BB win rate. This isn't clear in the text. I'll put it on my list of things to update in future printings.
Quote:
Originally Posted by Bobo Fett
The last thing is the difference between "classical" and "Bayesian" statisticians. Are they basically saying that the classical approach is to just use the distributions as they are, whereas the Bayesian approach is to take those same distributions, and then apply Bayes' theorem to those numbers?
The frequentist vs Bayesian debate has a long history, which you can read about online if you are interested.
Basically, the disagreement has to do with what kinds of things have probabilities associated with them. If I say "the probability that my win rate is between 1.0 and 1.5 BB/100 when I play headsup against xyz bot," that is a meaningless statement to a frequentist, because things like that don't have probability - either my rate is between those two numbers or it isn't. Bayesians on the other hand are willing to assign probabilities to mostly any statement with the idea that probabilities reflect degrees of belief.
http://en.wikipedia.org/wiki/Probabi...nterpretations has a summary.
If you are a poker player, you should be a Bayesian and just ignore that frequentist stuff.