Quote:
Originally Posted by fourfades
Conclusion, there is a 95% chance that at the very least, I am a SMALL LOSING player (and I am more likely to be a winning player than a losing player).
This is wrong, and nobody has really clearly explained why.
The first thing you need to understand is the difference between a parameter and a statistic. A parameter is the "thing you're trying to figure out, or
infer" (in this case the parameter is your true winrate) and a statistic is a "sample from the thing you're trying to figure out" (in this case the statistic is your observed winrate over 1250 hands).
Now, a confidence interval, or any other frequentist method, makes no inference about the probability of a parameter given a statistic. It only tells you the probability of a statistic given a parameter. Those two sentences might sound the same, but they are completely different mathematically. For example, the sentence "99 percent of terrorists are Muslim" means something completely different than "99 percent of Muslims are terrorists".
You cannot and will not ever be able to use confidence intervals or any frequentist method to say anything about the
probability of you having any particular true winrate based on any observed sample of hands you play, REGARDLESS of how big that sample is. You can only use them to calculate the probability of getting a particular sample IF in theory you had a certain true winrate.
For example, in this case you have an observed winrate of 16.88 BB/100 and you found confidence intervals of -3.08 to 36.84 BB/100. All that means is that
if your true winrate were anywhere from -3.08 to 36.84 BB/100, and you took an infinite number of 1250 hand samples, 95 percent of those samples would include your observed 16.88 BB/100. However, it says nothing about the probability of your true winrate. Your true winrate could be -37.5 BB/100 or 42.33 BB/100, and neither is more or less likely.
The only way you can calculate the probability of you having a particular true winrate given the observed sample is to use Bayesian Inference.
As someone who has studied both Bayesian Inference and frequentist methods, and not to mention plays poker for a living, take it from me you are wasting your time with confidence intervals and standard deviations and whatever other math calculations you are trying to make. No one can ascertain much of anything from your 50 hour sample.
If I were betting against someone on what your observed winrate will be over your next 50 hours of play, I could probably get myself a nice +EV bet by building a simple little model that would probably not even take into account your last 50 hours of play. I'd do better by just asking you a bunch of questions.