Operation Lamprey

well, here goes my jumping on the "operation" bandwagon. thanks to mike and lhoney for getting me off of my unfocused ass!

i've been trying to figure out what a solid, sustainable winning rate is for no limit holdem. tyson doesn't use poker tracker, so he's no good informationally, and this is actually a bit of a heated topic on 2+2.

the consensus seems to be that 10BB(big bets)/100 hands is very solid. the touchy part is that poker tracker's "big bets" for no limit are 2xbig blind, so there's always some question in how people report their results --->in BB(big blind) versus BB(big bet).

so, i was thinking about a quest to try to determine a solid winning rate for no limit, especially with multi-tabling. since 10/7/04, i've been two tabling the party $25 NL game, and the poker stars .10/.25 game (not together - one site or the other).

i will be taking my stats from poker tracker and reporting in BB (big bets = 2 x big blind)/100 hands.

questions to be answered:

- what constitutes a good enough sample (# of hands) - i can hit up a statistician friend for some help with this
- what is a sustainable BB/100 earning rate?
- what kind of standard deviation can be expected ?

and Operation Lamprey was born...

"The sea lamprey is an aggressive parasite... ...An anticoagulant in the lamprey's saliva keeps the wound open for hours or weeks, until the lamprey is satiated or the host fish dies. "

Whats your goal?

-'rilla

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Originally Posted by a500lbgorilla

Whats your goal?

-'rilla

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to determine a sustainable earn rate (in big bets/100 hands) playing lower stakes no limit holdem.

where i'm fuzzy - what is an adequate sample size of hands?

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Originally Posted by fishstick

where i'm fuzzy - what is an adequate sample size of hands?

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It really depends on your variance. You are trying to determine a distribution of your win rate rather than a fixed number (which is why you report both numbers). There is no single number that tells the whole story.

Because of this, you need the sample variance to converge. The sample variance for a large number of samples from a normal distribution is close to 2*SD^4/N where SD is the true standard deviation and N is the number of samples, i.e., 100 hand chunks you have played. For your sample SD of 35, it suggests that you need to play 10,000,000 or so hands to get decent convergence on the sample variance. I suspect your sample variance will come down a bit as you play more hands. If your true variance is closer to 20, for example, then you'd be relatively certain of it's value after only 1,000,000 hands. At a SD of 10, you'd only need maybe a couple of hundred thousand hands.

In a statistical sense, the long run is truly long.

After you take a couple really nasty swings you should be able to figure out where you stand.

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Originally Posted by koolmoe

It really depends on your variance. You are trying to determine a distribution of your win rate rather than a fixed number (which is why you report both numbers). There is no single number that tells the whole story.

Because of this, you need the sample variance to converge. The sample variance for a large number of samples from a normal distribution is close to 2*SD^4/N where SD is the true standard deviation and N is the number of samples, i.e., 100 hand chunks you have played. For your sample SD of 35, it suggests that you need to play 10,000,000 or so hands to get decent convergence on the sample variance. I suspect your sample variance will come down a bit as you play more hands. If your true variance is closer to 20, for example, then you'd be relatively certain of it's value after only 1,000,000 hands. At a SD of 10, you'd only need maybe a couple of hundred thousand hands.

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umm, that's a lot of hands! :?

first off, i will say that i am not a stat/math guy. i have a biostatistician friend looking at this and he's talking markov models to help determine sample size. markov models make my brain hurt. i'll be curious to see what he comes up with.

regarding standard deviation - my non-statistical mind says that the SD will NOT converge due to the nature of no limit holdem, and that we should be looking for a stabilization of the SD, while still continuing to show a profit.

am i way off base here?

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Originally Posted by fishstick

first off, i will say that i am not a stat/math guy. i have a biostatistician friend looking at this and he's talking markov models to help determine sample size. markov models make my brain hurt. i'll be curious to see what he comes up with.

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A Markov chain is a good way to model your bankroll, but it doesn't really address the issue at hand.

You still have to model the win rate as a random variable with a given mean and variance. Markov doesn't get around the fact that your mean win rate will be a small number compared to the variance of your win rate. Model a random walk with your mean and SD and see how easy it is to eyeball the slope of the line to see what I mean.

If you go with standard sample size calculations, where you replace the population standard deviation with the sample standard deviation, the results will be much smaller than I quoted earlier, but still quite large. For example, assume you wanted to be 95% sure that your win rate was within 1 BB of the sample mean given a standard deviation of 35. Then you would need (1.96*35/1)^2 = 4706 samples = 470,600 hands. If you wanted to be within 2BB, it would be about 1/4 of that, or 118,000 hands.

At 10,000 hands, if your mean and SD are still the same, you can be 95% sure that your win rate is greater than 1.

Quote:

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Originally Posted by fishstick

regarding standard deviation - my non-statistical mind says that the SD will NOT converge due to the nature of no limit holdem, and that we should be looking for a stabilization of the SD, while still continuing to show a profit.

am i way off base here?

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If you mean that your SD may not decrease, I agree with that, but it should converge to a relatively small range (perhaps around 35, perhaps higher, perhaps lower).

koolmoe,

i tell you markov models/chains make my brain hurt, and what do you do. YOU TALK ABOUT MARKOV STUFF! :lol:

thanks for the insights, i appreciate it.

i'm thinking a simple confidence interval/SD approach (as you discussed) with a large sample size of 10000 or more may be the best way to look at winning rate when talking about no limit holdem.

soooooo many variables...

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Originally Posted by fishstick

i tell you markov models/chains make my brain hurt, and what do you do. YOU TALK ABOUT MARKOV STUFF! :lol:

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No pain, no gain. :D

Any news on this, or still collecting data?

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Originally Posted by TylerK

Any news on this, or still collecting data?

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I think fishstick has been on holibobs for the last couple of weeks, but he's back now and ready to burn some cards!

{Sticky removed per new sticky policy}

it's been a combination of holibob's and getting killed on the NL tables. i can't seem to sustain winning on party's tables.

to give a little update, at party i'm at -.82 BB/100 hands :( and at +7.59 BB/100 hands at pokerstars.

i don't know what the problem is at party, although, part of it (at party) is not being able to take down many pots on the flop (when i've missed) when i've raise preflop, as opposed to this working ~75% of the time at pokerstars.

i will soon resume Operation Lamprey on pokerstars and absolute.

in the mean time, i've switched back to sng's (at party, stars, absolute) and am doing well.

unstickied is fine - although keep on eye on johnny... first it's unsticky the operations, then next thing you know, he'll want to be president of the board! :lol:

temporarily on hold to pursue Operation "build my sad bankroll through SNG's" :lol:

Current stats:

Operation Lamprey
Game: Party $25 No Limit - Poker Stars .10/.25 No Limit (PP killing me - only playing Stars)
Hands: 2617
Earning Rate: 5.28 BB (big bets = 2 x big blind)/100 hands
Standard Deviation: 33.19 BB/100 hands