Small Stakes No-Limit Hold'em

Post edited 11:26 pm – July 22, 2009 by JJS

WheresNemo said:

Well I could be completely off with my thinking with this bit of reasoning but here's my stab at it.

You were brave enough to attempt to answer the question, and because no good deed ever goes unpunished I will now use your post as an example.

What you have done is the sort of thing that most reasonably intelligent people will do to solve such problems when they don't know about random variables and their statistics.  They usually come up with some procedure, which is a bunch of “if..then..” rules.  “If you see this it means that, unless you see this in which case you have to look for that and then…” etc.

And no matter how complicated you make your procedure, no matter how much sense it seems to make to you, a set of random numbers will eventually come along that will blow your procedure out of the water.  It'll happen every time.  Nothing can bend your mind like randomness can.

What you have to do is something like I attempted in my post above (I say “attempted” because I did it very quickly and did not check it so there could easily be an error in it).

First you calculate the standard deviation and the win rate for the sample.  Then you assume a Gaussian probability distribution (and if you have read Taleb's book that I pointed out above, you are already starting to feel a queasy stomach at this point).  Then you use the known characteristics of the Gaussian distribution to see if they are a winner or loser (i.e. 68% of samples within 1 standard deviation of the mean, 95% within 1.96 x standard deviation, etc.)

I'm not going to post all the details here because I encourage people to work it out.

If you don't like math formulas, then I encourage you to work with an Excel spreadsheet.  If you think about it for a while then you can figure out how to create a column of numbers with a known mean and standard deviation using Excel's random number generator.   I did this, and I was surprised to see that you can have two identical poker professionals (with identical win rates and standard deviations) where one makes twice as much as the other even after two years. 

Even though I am somewhat familiar with random variables and their characteristics, it still took me by surprise.  If you met two poker players where one had twice the earnings of the other after two years, would you conclude that they might have identical skill?  I wouldn't have, before I worked it out.