Luck Metric

[garion888]

This is the first time I have posted in this forum so what's up everyone /images/graemlins/smile.gif

I have been trying to come up with a luck factor to determine how bad one might run with respect to raw receipt of hands.

The question comes up when you have a small sample size of whether you are getting cold decked or if you are just playing badly. I want to determine a way of understanding the amount of cold decking going on to determine what might be the cause of a bad or breakeven run. This could also be used to understand if you are running exceptionally well during a short stretch of hands.

For my test case I have been using a 4958 hand stretch of my PT database in which I held 288 pocket pairs. I wanted to determine the luck factor associated with flopping sets. During this stretch of hands I flopped 28 sets. I should have flopped 35-36 sets during this sample(someone correct me if i'm wrong).

So I took the sum of the binomial distribution between n=0 and n=28 for N=288,p=1/8. I took the same sum between n=0 and n=36. The former result was .087 and the latter result was .54. Dividing the former by the latter and you get the luck factor L = .16.

If the luck factor is less than 1 you have been running bad in terms of raw receipt of said hand(a set on the flop in this case). If its greater than 1 then you are running well.

I think I need a little help in understanding the metric a little more. How unlucky is a .16 vs a .17. And is the metric linear. Is the difference in luck between a .16 and a .17 the same between a .56 and a .57?

Thanks
-j

[LetYouDown]

Any reason you're not just using standard deviation?

[AaronBrown]

I'm not sure I fully understand. Are you trying to adjust the results of your play? For example, if you lost money over the 4,958 hands, but discovered that your luck had been extremely bad you wouldn't worry as much as if your luck had been good over the interval. Is this the kind of thing you want to do?

In that case it makes some sense to me, although obviously you'd need to choose more metrics than just pairs flopping sets. Your basic calculation is reasonable, although you could get there more simply using a Normal approxmation.

When you have a pair, you should flop a set or better 144 times out of 1,225 (a bit less than 1 in 8). Out of 288 pairs, you should have 33.85 sets. The standard deviation of that is 5.47, so your 28 was 1.07 standard deviations below the mean. The probability of this is 0.16 (not the 0.087 you computed using 1/8). There's no reason to divide by 0.54, you can just regard the probability as a number between 0 and 1 with 0.5 meaning average luck.

The measure is definitely not linear. 0.07 difference between 0.54 and 0.47 costs you one set, from 34 to 33. The same 0.07 gets you from 20 sets to 0, which would cost you a lot more money.