Quote:
Originally Posted by thenextguy
I've seen people mention that their true win rate is $15 to $50 with a 95% confidence (that's just an example).
I want to track how likely/unlikely my results are due to variance.
Warning, this is tl;dr
Yes what you are referring to is using the Central Limit Theorem and confidence intervals to estimate your "population mean", population here being your lifetime hours and mean being you average hourly over said time.
It is an interesting concept and surprised I hadn't thought of tinkering with this before, as I had this crammed into me for 4 years and still today am using forecasting tools for sample populations like everyday at work.
For a 95% confidence level we would use the equation:
Where x bar is your sample mean ($75), Sx is the standard deviation ($588), and n is the number of periods (40 hours). 1.96 is the z score for a 95% confidence level.
When you do the equation for your current figures you get
$75+(1.96($588)) / 40^.5 = $257.22
and
$75-(1.96($588)) / 40^.5 = -$107.22
A way to read this is that I am 95% confident that your hourly over the next sample of hours will fall somewhere between $257 and -$107. You can play around with the formula if you put it in excel and quickly see what goes into a consistent and believable performance over time. A lower SD, higher mean w/r, and larger sample will all sway your confidence intervals farther into the positive range.
I see many on this forum and elsewhere say that live poker is lol sample size and you will never fully understand your true winrate or that you need thousands of hours. They constantly refer to the 100,000 hand rule for online poker which would be about 3,000 hours live.
This is flawed thinking, and the CLT is one concept to show us why. We can easily use smaller sets of data to forecast future performance. I would have a good feel of a player over 300 hours, confident feel at 600 hours, and solid/willing to back at 900 hours. Standard deviation is key, it is quite possible that it is still erratic at 300 hours, and then my analysis would simply be, we need more hours. But one would still be able to get a "feel" by looking at the mean w/r and sd.
But the "lol you need like 100K hands to have anything meaningful" is not applicable to live play as I've said. For several reasons. The main one being that results are much closer to following a near perfect guassian distribution (normal distribution, bell curve) over time. I would say (and from some quick google searches I can see this topic discussed/theorized) that in live poker the sd and mean w/r are all that is holy, and thus we don't necessarily need a sample set that follows a guassian distribution in the immediate sense.
Furthermore, live bb/100 is significantly higher than online. This means that our sample can be smaller with a wider window, and it would still be in the positive. For example, your $75/hr is about 49bb/100 which is ludicrous. Live we are able to achieve such w/r (yours is obviously inflated, but still) because of the "unperfect" (or horrid) play. Online is a much more "perfect" distribution, in the sense that many of the players are solid, playing by mathematics and set rules, using equity calcs and so on to make every single mind numbing decision. This greatly evens out the slice of the pie available for even solid online pros, and thus a 2bb/100 to 5bb/100 is solid. Because they are competing in a more "perfect" or "normal" or "guassian" distribution, their bb/100 is quite thin, and bc of this, they need a consistent sd and a huge sample to prove that they are winning players. Live, with its ludicrous w/r, can have even a high sd (not too high obv), and still forecast to the solid positive range of a bell curve bc of the huge amount of give we have in our mean w/r over time.
I can play with this some more this weekend and may post some findings from my last 100 hour sample if I'm not too lazy.
Last edited by Avaritia; 05-07-2013 at 11:40 PM.