Statistical Variance of Poker (including rake).

[RiverMise]

This is a fundamental theory question that may have been previously discussed on these boards, but here it goes.

Lets say you want to move up in levels (on say, Party Poker). How many hands of poker do you think that you need to play at that level to determine what you expected win rate is? What type of swings can you expect if you are a 1.5BB/100 winner of the game (after rake is taken)? How soon should I get discouraged if I am not winning?

I am hoping to spark some smart theoretical discussion with these question. Thanks in advance.

[NYplayer]

please PM mikel for the answer to this question.

[MikeL]

I not really sure if I am the mikel that was recommended for this, but...

Surprisingly, there is very little by way of research or documentation
telling us how to determine if our sample size is sufficient for the type
of information we want it to tell us. As much as it pains an Iowa State
alumnus to say,
there is a good article by the University of Iowa Medical college that
really sums this up:

Some Practical Guidelines for Effective Sample-Size Determination (http://www.stat.uiowa.edu/techrep/tr303.pdf)

This link might help, also:

http://www.childinfo.org/mics/Manuals/English/chap04.pdf

Best of luck!
Mike L.

[Mason Malmuth]

Hi RiverMise:

In my book Poker Essays, Volume II there is an essay called "Moving Up" that addresses this subject and gives some pretty good guidelines. Of course I'm not going to post the essay here.

best wishes,
Mason

[kiddo]

After 100K hands u can be pretty sure u are within 1BB/100 from your true winrate.

If your true winrate is 1.5BB/100 you will have big swings. Its also dependent on your standard deviation. But if u play limit holdem more then 400BB is something that will happen sooner or later.

[MikeL]

While I agree 100K is probably (pun intended) a sufficient sample size for NL, this begs the question. The OP wanted to know how we can be sure our sample size is large enough.

Somewhere in the calculation, one must make an assumption. You either need to assume what you think the expected win rate will be in order to compute your sample size, or you need to assume what a sufficient sample size is. It's not a great choice, but it has to be made.

Regards,
Mike L.

[RiverMise]

If after a few thousands hands (~5K) I am down or even, should I be worried? I am making noriceably smarter (mathematically) decisions than most of my opponents. Thanks for all of your excellent responses.

-RiverMise

[MikeL]

Depends what your goal is. If you have moved up to a substantially different buy-in level, for example. You might expect to have a learning curve for the "new" game. As an example, the weak-tight strategy that works (+BB/100) at the small stakes table probably doesn't work at the medium stakes table. You would expect to have a =BB or -BB/100 for a time, until you've altered your game to match the new level of play.

I would not, however, expect a huge swing in your winrate. If you were winning +3BB/100, for example, at the small stakes and you are now -3BB/100 at the medium stakes, you've got a big hole in your game that needs to be plugged.

Do you have some poker analysis software (like poker tracker)? If so, this will help you find the hole.

Regards,
Mike L.