Starting Hand Profitability Skewed?

[tikipirate]

Please move if this is more appropriate elsewhere.

I realize the sample size is not nearly significant enough to draw any conclusions from, but over 15K hands in PT I have one starting hand, KK, that is 2x more profitable net and in bbs per hand than my next most profitable hand, AA. KK represents almost 40% of my net profits. The rest of the hands follow a distribution I would expect (AA on down). Should I be concerned? Is this just a statistical anomaly that I can expect to change as I play more hands? Thanks.

[Quicksilvre]

Not at all. After only 15,000 hands, variance is still going to be a huge determinant in what hands are most profitable.

For some context, over the last 8,000 or 9,000 hands I've played, TT has won twice as much money as any other hand, followed by AA, JJ, and KQs. Looking at just BBs, my top four hands are 44, TT, KK, and 55.

It's just an issue of sample size.

[sapol]

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It's just an issue of sample size.

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Until 30K hands I had been loosing with AA and AKss (much of that was because getting drawn out in the biggest pots I had played at that time).

Wait until you have something like 50-75K hands and the start drawing conclusions.

[pzhon]

First, it takes much longer for the results of individual hands to converge. This type of anomaly is common. Over one 50k hand sample, I won slightly more with QQ than with KK. That came from getting paid off with top set or a boat a few more times. It does not mean QQ is as strong as KK, or that I am misplaying KK.

Second, the percentage of your overall profit is not a meaningful statistic. It's quite possible for AA, KK, QQ, JJ, and AK to make up 150% of your profit, but that doesn't mean you would increase your profits by playing only these hands. The other good hands are needed to win most of the blinds back. The proper quantity is not your profit, but the difference between your results and posting the blinds, which costs about 1.5 big blinds per orbit, losing 7.5 PTBB/100 10-handed, or about 12.5 PTBB/100 6-handed.

If your win rate is 6 PTBB/100, and you win 3.0 PTBB/100 (or about 6.6 PTBB/occurence, reasonable in NL) with AA, it's not good to calculate that as 50% of your winnings. Better would be to say that you are beating the blinds with AA for 3.2 PTBB/100 ahead of posting the blinds out of your total of beating the blinds by 6+7.5 = 13.5 BB/100 10-handed, or 6+12.5 = 18.5 BB/100 6-handed, which means that AA represents less than 1/4 of the amount by which you are beating posting the blinds.

[rufus]

Just to put this into perspective:
Any particular pocket pair occurs about once every 220 hands. So, if you've played 15,000 hands, you're only expected to see about 75 AA and KK's, and it wouldn't be all that unreasonable to see 50 AA and 100 KK. That means that if you're measuring total profit rather than profit per hand, the KK could be less profitable than the AA, but have produced more profit. (Typically AKo is less profitable per hand, but produces more net profit than AA,KK or AKs because it's two or three times as common as those hands are individually.)

Now, 75 is already very small for statistical sampling, but position is also a factor in profitability, so we could reasonably divide by another 10 to get 7.5 which pretty obviously too small.

Now, there's certainly room for a sophisticated attack, but the sample sizes here are relatively small since the expected frequency of any particular holding is only 50,75,or 150 for suited, paired, and unsuited unpaired respectively. You should, at minimum, look at the frequencies of AA and KK.

[tikipirate]

Wow, these were all excellent answers, thank you all who posted. You totally explained what I wanted to know and gave me some new things to think about. Thanks guys!

[sapol]

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Wow, these were all excellent answers, thank you all who posted. You totally explained what I wanted to know and gave me some new things to think about. Thanks guys!

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yw, any time