Quote Originally Posted by littletrogdor
I guess I'll just ride it out. If you guys are waiting for enough hands to draw a 99% confidence interval in your stats, your out of your mind. And if you don't understand exactly what that statement means, you should take a statistics course before you make comments on what is or isn't enough hands to draw conclusions on your play.
Honestly, Fnord's comments about 10K being a small sample are right on the money; and it is fairly easy to demonstrate.

The odds of being dealt a pocket pair are 1 in 17. The odds of flopping quads with that PP are about 1 in 400. On the average, in 10K hands you have only seen it once (33.8%). It would be easy to have not seen it at all (22.9%), leaving 43.3% of the people that saw it more than once*. It is possible another guy saw it 3 times. Assuming you got it the average one time, did someone else have a boat or an over-pair they could not put down; allowing you to destack them? If so, were both stacks quite deep? Or, the one time it happened to you did you get no action? That can literally make a 2xbuy-in difference in your total BR right there in that one wonderful hand. But there is a 20% chance you got it while you were in the blinds, out of position you try to slow play; no one bets.

And that is just flopped hidden quads.

In 10K hands you will get pocket Aces roughly 45 times. Roughly 2 of those times someone else will be dealt pocket Kings. Did you get your fair share of two (there is a 9.9% chance that this never happened to you in 10K hands)? Did you get him All-In and win the hand? Or did an Ace flop and scare him off? It's likely only happened twice to you in 10K hands so the variance is quite large. That is the type of thing that could put your bankroll up by 2xbuy-ins. But it is entirely possible that you lost both times to the KKs, there is a little more than 3% chance of it in fact. So in a sample of 25 people, each who have played 10K hands, it likely will have happened to 1 of them. What's more, 7 of those 25 people will have lost one of them and won one of them coming out even for the experience assumming equal stacks both times. The other 17 people have a 2xBuy-In bankroll advantage over those 7 and a 4xBuy-In over the one poor guy.**

In 10K hands there are honestly not that many monster vs monster (someone is going to lose a stack) opportunities. It is quite possible that you have not seen a straight flush using both your hole cards, while someone else saw two and got big action both times. It is entirely possible that one person got 15 of these monster vs. monster opportunities, got action on 12 of them and won 11. It is also entirely possible that one person got 9 of these opportunities, got action on 5 of them and won only 3.

I do agree that 10K hands is likely enough to minimize the variance of your standard decent hand vs decent hand. But it is not nearly enough for your big Buy-In (or even multi-Buy-In) swinging hands to even out to the expected distribution.

That can have an enormous impact on your BB/100 hands. Consider stack depths of 100 BB. Using the examples above just for AA vs KK. For 17 of the 25 people the AA vs KK hands will have contributed 100 BB * 2 / 10K hands which is 2 BB/100 hands. Seven people will be +0 BB / 100 hands and the one poor guy will literally be -2 BB / 100 hands just from the variance because the sample is small. Judging from your BB/100 that you mention, whether you are one of the 17 or one of the 7 or the one unlucky joe will cause a variance in your BB / 100 roughly equal to its current value.

And the AA vs KK fight works both ways. In 10K hands you likely have been the KK vs an AA two times; but there is a 9.9% chance that it has not happened to you at all. Assuming it did, did the AA guy slowplay PF only for an Ace to flop and cause you to back off? Or did he push hard both times and get you All-In PF destacking you both times. Were you the lucky 1 guy in 25 that won BOTH times that happened, or one of the 7 that is even for the experience, or one of the 17 whose BB/100 is down by 2 just from those two hands?

With a larger sample size these differences even out. While 1 guy in 25 will lose all of his AA vs. KK matchups in 10K hands (hitting his BB/100 for a -2), only 1 guy in 29.8 million will keep up that losing rate for 50K hands. While 17 in 25 will win all of their AA vs. KK matchups (adding +2 BB/100) only 1 in 7 will keep up that win rate for 50K hands. Everyone else begins to approach the expected win rate of roughly 4 out of 5.

So, I hope I made the numeric case for why a 10K sample size is insufficient to determine a meaningful BB / 100.

* For a quick breakdown to illustrate the variance, with a sample size of 10K events with each event having a 1 in 6800 chance of being positive:

22.97% of no positives 0 per 10K
33.79% of 1 positive 1 per 10K
24.84% of 2 positives 2 per 10K
12.17% of 3 positives 3 per 10K
4.47% of 4 positives 4 per 10K
1.325 of 5 positives. 5 per 10K

So the typical person will flop hidden quands 1 time in 10K hands, but better than 175 will flop it 3 or more times. The BB/100 of the lucky 17% will reflect this.

Compare that to 50K samples

4.24% of 3 positives .6 per 10K
7.8% of 4 positives .8 per 10K
11.48% of 5 positives 1 per 10K
14.06% of 6 positives 1.2 per 10K
14.77% of 7 positives 1.4 per 10K
13.58% of 8 positives 1.6 per 10K
11.09% of 9 positives 1.8 per 10K
8.16% of 10 positives 2 per 10K
5.45% of 11 positives 2.2 per 10K
...
0.99% of 14 positives 2.8 per 10K

Notice the significantly tighter distributiuon. With only 10K samples, almost 18% of the people will experience 3 times the number of quads as the typical person. But by the time we get to 50K samples, less than 1% of the people will expereince triple the expected occurance count.

** AA vs KK is a 81.9 to 18.1 fight. Odds of losing 2 for 2 are (0.181 * 0.181) = 3.2%. Odds of winning both are (0.819 * 0.819) = 67.0 %. Odds of 1 win and 1 lose are (100 - 67.0 - 3.2) = 29.8%