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Old 11-18-2009, 12:32 AM   #51
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Re: Statistical Analysis of Flops

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I'm no rigtard but if you have evidence I would sure as hell like to see it.

Good job spadebidder on the stuff you posted, I love this kind of stuff.

edit: ETA on when your site goes public?
I never said if I had evidence of riggedness. Or of randomness. But I have the data that answers some of those questions.

Maybe a week or two I'll open it up.

Last edited by spadebidder; 11-18-2009 at 12:48 AM.
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Old 11-19-2009, 07:54 AM   #52
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Re: Statistical Analysis of Flops

I think showing the median pot size would be interesting to supplement the mean data you show.
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Old 11-19-2009, 09:34 AM   #53
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Re: Statistical Analysis of Flops

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I think showing the median pot size would be interesting to supplement the mean data you show.
I think it would too, but in a very large set the processing power and time to do it might be impractical. You have to create an array of all the values (all pots in that category), then sort the array, then find the value corresponding to the halfway point in the list. I don't know what java's limits are on sorting arrays. I'll try using java's arrays.sort() and see if it can handle it.

Last edited by spadebidder; 11-19-2009 at 09:47 AM.
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Old 11-19-2009, 10:02 AM   #54
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Re: Statistical Analysis of Flops

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I think it would too, but in a very large set the processing power and time to do it might be impractical. You have to create an array of all the values (all pots in that category), then sort the array, then find the value corresponding to the halfway point in the list.
http://www.google.com/search?q=median+algorithm
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Old 11-19-2009, 10:06 AM   #55
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Re: Statistical Analysis of Flops

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Yes it can be done, I said I didn't think it would be useful. I'd have to code it as it takes two passes through the data to do this, one to get the mean and another to get every individual offset from the mean, so you can square and sum them. I would guess the pot sizes for a particular flop texture look a lot like a normal distribution with truncated tails.
It doesn't take two passes. E[(X - E[X])^2] = E[X^2] - E[X]^2.

There is also no reason to think the pot sizes would be normally distributed, and even if they were, you'd still like to know the variance.
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Old 11-19-2009, 10:19 AM   #56
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Re: Statistical Analysis of Flops

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It doesn't take two passes. E[(X - E[X])^2] = E[X^2] - E[X]^2.

There is also no reason to think the pot sizes would be normally distributed, and even if they were, you'd still like to know the variance.
This is an interesting algorithm and I had to look it up, and I'm not sure I understand it. Isn't this for the variance of a population with a normal distribution? I have a sample with an unknown distribution. Please explain.

On the median question, I know how to do it, I'm just not sure how intense the processing is going to be on a very large set, or the memory requirement. I have 4GB RAM, and the sets will be arrays of millions of integers, which have to be sorted. I'll give it a try.

Last edited by spadebidder; 11-19-2009 at 10:24 AM.
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Old 11-19-2009, 12:18 PM   #57
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Re: Statistical Analysis of Flops

I found an example that explains it.

Suppose x takes on the values 1, 2, 3 with probability 0.2, 0.3, and 0.5 (respectively).

E [ x ] = 1*0.2 + 2*0.3+ 3*0.5 = 2.3
E [ x2 ] = 12*0.2 + 22*0.3+ 32*0.5 = 5.9
Var (x) = E [ x2 ] - ( E [ x ] )2 = 5.9 - 2.32 = 0.61

Hmmm... I still don't see how to do this when the probability of particular pot sizes isn't known.
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Old 11-19-2009, 12:51 PM   #58
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Re: Statistical Analysis of Flops

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Hmmm... I still don't see how to do this when the probability of particular pot sizes isn't known.
You're right; you can't. This is why you won't actually be computing E[X] or E[X^2], but just estimates of them.

Assume they all have probability 1/N, where N is the number of samples you have. This gives the sample mean / variance.

Last edited by zyx; 11-19-2009 at 01:03 PM. Reason: population -> sample
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Old 11-19-2009, 01:00 PM   #59
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Re: Statistical Analysis of Flops

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You're right; you can't. This is why you won't actually be computing E[X] or E[X^2], but just estimates of them.

Assume they all have probability 1/N, where N is the number of samples you have. This gives the population mean / variance.
Then it seems like the way to do it is get the true mean on one pass, then do a second pass to get the true variance. It isn't that cumbersome.
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Old 11-19-2009, 01:06 PM   #60
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Re: Statistical Analysis of Flops

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Then it seems like the way to do it is get the true mean on one pass, then do a second pass to get the true variance. It isn't that cumbersome.
You'll get the same answer with one pass or two. This won't be the variance of pot sizes for all poker games that have ever been played and will ever be played, but only for the sample that you have. You can feel free to ignore this distinction.
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Old 11-20-2009, 06:09 PM   #61
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Re: Statistical Analysis of Flops

Very nice thread. Props to violi for the flop breakdown!
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Old 08-15-2012, 08:23 AM   #62
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Re: Statistical Analysis of Flops

this is awesome, any other flop combinatorics stuff out there?
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Old 08-15-2012, 09:46 AM   #63
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Re: Statistical Analysis of Flops

sick bump
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Old 08-15-2012, 11:09 PM   #64
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Re: Statistical Analysis of Flops

Exactly of what value is this info? How can it make me a better player? Also as of late I am mostly sng so is it void for sng?
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