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Old 11-15-2009, 05:07 PM   #26
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Re: Statistical Analysis of Flops

I see what you're saying wrt the code and pattern matching. And I'm not sure what my goal is, really. This post has far exceeded my expectations.
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Old 11-15-2009, 05:09 PM   #27
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by statmanhal View Post
Maybe I misinterpreted what the data represent. I assumed it was the observed percentages over millions of hands. For the rainbow flop, for example, the results match to 7 decimals with the theoretical. But, on reflection, that is really, really unlikely, so I am beginning to think that some of the percentages may in fact be the theoretical.

Any comment?
Those are all calculated frequencies. The pot sizes are actual. I mentioned in another post that I'm withholding the actuals for now so as to not spoil the surprise of the other research I'm working on, which includes measuring the offsets. It will be very interesting to the rigtards.

Last edited by spadebidder; 11-15-2009 at 05:15 PM.
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Old 11-15-2009, 05:17 PM   #28
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by violi View Post
Your second run increased the difference from the Largest pot size to the Smallest:

Difference first run: 9.3
Second run: 10.3

For the second run:
Largest and Smallest: 31.5 and 21.2

Largest:
[ 3-Straight 2-suited] 1.95475% 3c-5d-4c 31.5

Smallest:
[ KA2 dbl-cnct rainbow] 0.10860% 2d-Kh-As 21.2
I think a 50% increase from smallest average pot to largest average pot, is pretty significant actually.
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Old 11-15-2009, 06:13 PM   #29
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Re: Statistical Analysis of Flops

spade, I hope this isn't too much to ask, but could you please do a statistic analysis for all (if not, some) of the micros?
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Old 11-15-2009, 06:27 PM   #30
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Re: Statistical Analysis of Flops

Yeah, agree.

When do you think your research will be published? Would you consider posting a pre-print at xxx.lanl.gov in the statistics sectioni?
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Old 11-15-2009, 06:28 PM   #31
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Re: Statistical Analysis of Flops

If you're doing requests I would love to see A 8 5 with the 8 and 5 suited.
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Old 11-15-2009, 07:05 PM   #32
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Re: Statistical Analysis of Flops

This is the same as the second set of results posted by Spadebidder I've just ordered by pot size from High to Low. I found it easier to read and compare.

[ Two-suited ] 55.05882% 2d-8s-4s 28.0
[ Monotone ] 5.17647% Kh-9h-6h 26.9
[ Rainbow ] 39.76471% Kc-8d-Qh 26.4
[---check suit types---] 100.00000%

[ Unpaired flop ] 82.82353% 2d-8s-4s 27.6
[ Triplet flop ] 0.23529% Kc-Kd-Ks 25.8
[ Paired flop ] 16.94118% 3h-3c-Kd 25.7
[---check suit types---] 100.00000%

[ 3-Straight ] 3.47511% 3c-5d-4c 30.7
[ Connector & 1gap ] 6.95023% Qd-Ts-Kh 29.6
[ Double gutshot ] 3.18552% 6s-8s-4c 28.6
[ Connector & 2+gap ] 26.93213% Kc-8d-Qh 27.6
[ Other 1gaps ] 21.42986% 2d-8s-4s 27.4
[ No cnct no 1gap no pr] 20.56109% Kh-9h-6h 26.7
[ Pair & connector ] 2.82353% 6s-6d-7c 26.5
[ Pair & 1gap ] 2.60633% 3s-Ad-3d 26.3
[ Triplets ] 0.23529% Kc-Kd-Ks 25.8
[ Pair & 2+gap ] 11.51131% 3h-3c-Kd 25.4
[ KA2 double connector ] 0.28959% Kh-2d-Ad 22.9
[---check suit types---] 100.00000%

[ Flop Combinations ]
[ 3-Straight 2-suited] 1.95475% 3c-5d-4c 31.5
[ Cnctr & 1gap 2-suited] 3.90950% 5d-3c-6c 30.2
[ 3-Straight-Flush ] 0.21719% 4s-6s-5s 29.3
[ Dbl gutshot 2-suited] 1.79186% 6s-8s-4c 29.2
[ Cnctr & 1gap rainbow] 2.60633% Qd-Ts-Kh 28.8
[ Cnctr & 1gap monotone] 0.43439% Tc-8c-Jc 28.6
[ Cnctr & 2+gp 2-suited] 15.14932% 6d-Jh-Td 28.2
[ Other 1-gaps 2-suited] 12.05430% 2d-8s-4s 28.1
[ Dbl gutshot monotone] 0.19910% 6d-2d-4d 27.9
[ Dbl gutshot rainbow] 1.19457% 3d-7c-5s 27.8
[ Pair & cnctr 2-suited] 1.41176% 4h-4c-3h 27.3
[ No cnt/gp/pr 2-suited] 11.56561% Jh-6h-As 27.3
[ Pair & 1gap 2-suited] 1.30317% 3s-Ad-3d 27.2
[ Cnctr & 2+gp monotone] 1.68326% Ac-Jc-2c 27.0
[ Cnctr & 2+gap rainbow] 10.09955% Kc-8d-Qh 26.8
[ Other 1-gaps monotone] 1.33937% Td-Qd-6d 26.5
[ Other 1-gaps rainbow] 8.03620% 5s-7h-Ad 26.5
[ Pair & 2+gap 2-suited] 5.75566% 7s-7d-4d 26.3
[ No cnt/gp/pr monotone] 1.28507% Kh-9h-6h 26.3
[ Triplets ] 0.23529% Kc-Kd-Ks 25.8
[ No cnt/gp/pr rainbow] 7.71041% 2d-Tc-6h 25.8
[ Pair & cnctr rainbow] 1.41176% 6s-6d-7c 25.6
[ Pair & 1gap rainbow] 1.30317% Qs-Ad-Ah 25.5
[ Pair & 2+gap rainbow] 5.75566% 3h-3c-Kd 24.5
[ KA2 dbl-cnct monotone] 0.01810% Ks-As-2s 24.0
[ KA2 dbl-cnct 2-suited] 0.16290% Kh-2d-Ad 23.9
[ KA2 dbl-cnct rainbow] 0.10860% 2d-Kh-As 21.2
[---check suit types---] 100.00000%

[More Interesting flops]
[ 3 to a Wheel no pr ] 2.89593% 3c-5d-4c 28.5
[ 2 to a Wheel no pr ] 23.16742% 2d-8s-4s 27.5
[ Double-BWay unpaired ] 23.16742% Kc-8d-Qh 25.2
[ Triple-BWay unpaired ] 2.89593% Jc-Tc-Qc 24.9
[ Any A or K or both ] 40.07240% Kc-8d-Qh 24.7
[ Double-BWay paired ] 4.34389% Qh-4c-Qc 24.1
[ Triple-BWay paired ] 2.26244% Kh-Ks-Td 22.5
[---check suit types---] 100.00000%
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Old 11-15-2009, 07:07 PM   #33
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Re: Statistical Analysis of Flops

Use the [code tag for preformatted text and end it with /code] both with brackets on both sides, to preserve the columns. You can still edit it.
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Old 11-15-2009, 09:28 PM   #34
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Re: Statistical Analysis of Flops

There's actually a way to do tables. Quote this post to see how:


column 1column 2column 3
1,11,21,3
2,12,22,3
3,13,23,3
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Old 11-15-2009, 11:28 PM   #35
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by violi View Post
And is it easy for you to do something as specific as Ax 8y 5y, for example? (Personally I've had some memorable big pots with a 6-7 offsuit especially when the turn card is 4z. But perhaps it's an illusion of a selective memory.)
Easy on the scale of maybe 15 minutes work to set up the filter for it and then run the scan. Is that something that would be useful information? Why?

Quote:
Originally Posted by jewbinson View Post
spade, I hope this isn't too much to ask, but could you please do a statistic analysis for all (if not, some) of the micros?
I don't have any NL hands with less than $0.25 big blind. About 3/4 of what I have is in the range of the stuff I posted, up to $4 BB, and the rest is higher stakes or other Holdem formats (and some Omaha). I'll be getting some more hands soon but probably not micros.

Quote:
Originally Posted by violi View Post
When do you think your research will be published? Would you consider posting a pre-print at xxx.lanl.gov in the statistics sectioni?
I don't get why they would be interested in it. Is that a serious question? I'm not going to be writing a formal paper suitable for any kind of academic journal, and I'm not a PhD anyway. I'm just going to publish my findings on a web site where people can discuss it. And I'm a curious guy. The flop distribution stuff is only one of the areas I'm working on. I'm also doing turns and rivers, all-ins preflop, correlating things to stack size, and so forth. Some of the ideas grew out of the rigtard debates, where before now no one had any real data. I do. Another purpose is to recognize and quantify unknown card removal effects.

Last edited by spadebidder; 11-15-2009 at 11:39 PM.
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Old 11-15-2009, 11:42 PM   #36
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Re: Statistical Analysis of Flops

Quote:
I don't have any hands with less than $0.25 big blind. About 3/4 of what I have is in the range of the stuff I posted, up to $4 BB, and the rest is higher stakes. I'll be getting some more hands soon but probably not micros.
Ok, but do you think av. pot size per board will be dramatically different at the micros. At first, I though it might be similar to the results you posted, because if someone is spewing their money @ the micros, it will be done on random boards. But then some boards occur more frequently than others e.g. more 2 3 4 than K K K board. So does this mean that at the micros, the frequency of the type of board is more relevant, because of the spew going on?
Note that lately at the micros, there is much less spewing- in the extreme sense of the word- than there used to be. You hardly see maniacs, but occasionally do, moreso than higher stakes (although in higher stakes you get a lot of LAGs). Ok, clearly I'm rabling. help
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Old 11-16-2009, 12:17 AM   #37
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Re: Statistical Analysis of Flops

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Originally Posted by jewbinson View Post
Ok, but do you think av. pot size per board will be dramatically different at the micros. At first, I though it might be similar to the results you posted, because if someone is spewing their money @ the micros, it will be done on random boards. But then some boards occur more frequently than others e.g. more 2 3 4 than K K K board. So does this mean that at the micros, the frequency of the type of board is more relevant, because of the spew going on?
Note that lately at the micros, there is much less spewing- in the extreme sense of the word- than there used to be. You hardly see maniacs, but occasionally do, moreso than higher stakes (although in higher stakes you get a lot of LAGs). Ok, clearly I'm rabling. help
I looked at the 0.25 BB hands I have (about 8 million NL) and everything is about the same. In fact, the average pot sizes were a little more tightly grouped than the higher stakes, but essentially the same, and the flop distribution was the same.

I would expect the .05 and lower stakes to have a character all their own, but I have no data.
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Old 11-16-2009, 01:16 AM   #38
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Re: Statistical Analysis of Flops

How do the results look if you filter for 6-max hi-stakes games, 10/20 NL and higher? I'm especially curious as to how QT7 and QT8 rank up relative to JT9 and 543, all with flush draws. Don't imagine 543 generating more actn than QT7, but happy to be proven wrong..
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Old 11-16-2009, 01:28 AM   #39
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Re: Statistical Analysis of Flops

such a great post
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Old 11-16-2009, 04:42 AM   #40
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Re: Statistical Analysis of Flops

Any reason this was done in for the micros? (existing db?) I would love to see if there was any difference in say nl 200-400 where the play is much better.
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Old 11-16-2009, 05:09 AM   #41
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by spadebidder View Post
There is no expectation or probability for pot size, it just is what it is.
What do you mean by this? The pot sizes for a given board texture form a distribution. You computed its mean (actually the sample mean). You can also compute the sample variance.
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Old 11-16-2009, 09:09 AM   #42
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Re: Statistical Analysis of Flops

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Originally Posted by zyx View Post
What do you mean by this? The pot sizes for a given board texture form a distribution. You computed its mean (actually the sample mean). You can also compute the sample variance.
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.

Last edited by spadebidder; 11-16-2009 at 09:24 AM.
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Old 11-16-2009, 10:08 AM   #43
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Re: Statistical Analysis of Flops

Sticky thread already plz
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Old 11-16-2009, 11:32 AM   #44
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by violi View Post
And is it easy for you to do something as specific as Ax 8y 5y, for example? (Personally I've had some memorable big pots with a 6-7 offsuit especially when the turn card is 4z. But perhaps it's an illusion of a selective memory.)
Quote:
Easy on the scale of maybe 15 minutes work to set up the filter for it and then run the scan. Is that something that would be useful information? Why?
Well yes, it's sort of a selfish request but my intuition/playing experience tells me that board makes big NL pots. Your analysis could help distinguish if that's just my selective memory at work or if there's maybe something to it.

Quote:
I don't get why they would be interested in it. Is that a serious question? I'm not going to be writing a formal paper suitable for any kind of academic journal, and I'm not a PhD anyway.
Yeah, I'm very serious. Your doing original work and contributing to the poker literature. Having a "credential" isn't always relevant. It's impressive work - big data sets are hard to deal with and hard to come by.
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Old 11-16-2009, 01:03 PM   #45
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Re: Statistical Analysis of Flops

Someone asked about higher stakes so I did a run counting only BB of $20 and up, which is mostly under $100 and a few higher. I only have about 3 million hands at these stakes. But the interesting thing was that average pot sizes are a lot higher. For hands with flops seen, final pots range from ~30 to about ~41 BB with about the same flop type distribution as the other stakes.

I'll have time after while to post that chart.
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Old 11-16-2009, 03:25 PM   #46
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Re: Statistical Analysis of Flops

Here's the higher stakes games. Same flops correlations, but bigger average pots (in BB).


Code:
Site #0, 6 to 9 players, NL Hold'em,  BB $20.00 to $400.00
Number of hands analysed:  3,278,928
              Flops seen:  1,067,927 (32.6%)


FLOP TYPES FREQUENCY

-----------------------------------------------------------
                         Calculated              Avg. Final
[ Flop Type ]             Frequency    Example   Pot in BBs


[ Rainbow              ]  39.76471%   Tc-5s-3h   36.9
[ Monotone             ]   5.17647%   2d-Td-6d   36.8
[ Two-suited           ]  55.05882%   Ah-Qc-3c   39.8
[---check suit types---] 100.00000%  

[ Paired flop          ]  16.94118%   Ac-Ks-Kh   36.1
[ Triplet flop         ]   0.23529%   Ad-As-Ac   33.7
[ Unpaired flop        ]  82.82353%   Tc-5s-3h   39.0
[--check match types---] 100.00000% 

[ Pair & connector     ]   2.82353%   Ac-Ks-Kh   37.1
[ Pair & 1gap          ]   2.60633%   6d-8h-6c   36.5
[ Pair & 2+gap         ]  11.51131%   4h-Kh-4c   35.7
[ Triplets             ]   0.23529%   Ad-As-Ac   33.7
[ 3-Straight           ]   3.47511%   8s-6d-7h   39.8
[ Connector & 1gap     ]   6.95023%   7h-4s-5s   39.7
[ Connector & 2+gap    ]  26.93213%   7s-Td-Jc   39.0
[ KA2 double connector ]   0.28959%   Kh-As-2s   31.7
[ Double gutshot       ]   3.18552%   Ah-Qc-3c   39.7
[ Other 1gaps          ]  21.42986%   Tc-5s-3h   39.0
[ No cnct no 1gap no pr]  20.56109%   9d-2d-Ks   38.5
[-check connect types--] 100.00000%   

                         Calculated              Avg. Final
[ Flop Combinations ]     Frequency    Example   Pot in BBs

[ Pair & cnctr  rainbow]   1.41176%   Ac-Ks-Kh   35.7
[ Pair & cnctr 2-suited]   1.41176%   2d-2c-Ad   38.5
[ Pair & 1gap   rainbow]   1.30317%   6d-8h-6c   35.2
[ Pair & 1gap  2-suited]   1.30317%   8h-8c-Tc   37.9
[ Pair & 2+gap  rainbow]   5.75566%   Ts-2d-2c   34.1
[ Pair & 2+gap 2-suited]   5.75566%   4h-Kh-4c   37.3
[ Triplets             ]   0.23529%   Ad-As-Ac   33.7
[ 3-Straight    rainbow]   1.30317%   8s-6d-7h   38.6
[ 3-Straight   2-suited]   1.95475%   Ac-Qc-Ks   40.8
[ 3-Straight-Flush     ]   0.21719%   4d-2d-3d   37.9
[ Cnctr & 1gap  rainbow]   2.60633%   7s-6c-4h   37.7
[ Cnctr & 1gap monotone]   0.43439%   Ks-Qs-Ts   38.8
[ Cnctr & 1gap 2-suited]   3.90950%   7h-4s-5s   41.2
[ Cnctr & 2+gap rainbow]  10.09955%   7s-Td-Jc   37.7
[ Cnctr & 2+gp monotone]   1.68326%   Kc-6c-Qc   36.4
[ Cnctr & 2+gp 2-suited]  15.14932%   Js-3h-2s   40.2
[ KA2 dbl-cnct  rainbow]   0.10860%   2d-Ah-Kc   30.0
[ KA2 dbl-cnct monotone]   0.01810%   Ks-2s-As   31.5
[ KA2 dbl-cnct 2-suited]   0.16290%   Kh-As-2s   32.9
[ Dbl gutshot   rainbow]   1.19457%   Qc-Th-Ad   38.1
[ Dbl gutshot  monotone]   0.19910%   Tc-Qc-Ac   37.1
[ Dbl gutshot  2-suited]   1.79186%   Ah-Qc-3c   41.1
[ Other 1-gaps  rainbow]   8.03620%   Tc-5s-3h   37.5
[ Other 1-gaps monotone]   1.33937%   3c-Jc-5c   36.7
[ Other 1-gaps 2-suited]  12.05430%   3c-Jc-As   40.2
[ No cnt/gp/pr  rainbow]   7.71041%   3h-Qd-9s   37.1
[ No cnt/gp/pr monotone]   1.28507%   2d-Td-6d   36.8
[ No cnt/gp/pr 2-suited]  11.56561%   9d-2d-Ks   39.6
[--check combinations--] 100.00000%   

                         Calculated              Avg. Final
[More Interesting flops]  Frequency    Example   Pot in BBs

[ Any A or K or both   ]  40.07240%   Ah-Qc-3c   35.1
[ Triple-BWay unpaired ]   2.89593%   Th-Qh-Jh   33.7
[ Triple-BWay paired   ]   2.26244%   Ac-Ks-Kh   31.3
[ Double-BWay unpaired ]  23.16742%   Ah-Qc-3c   36.4
[ Double-BWay paired   ]   4.34389%   Kh-8c-Kc   34.6
[ 3 to a Wheel no pr   ]   2.89593%   3s-2d-Ad   39.0
[ 2 to a Wheel no pr   ]  23.16742%   Tc-5s-3h   38.8

.
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Old 11-16-2009, 08:08 PM   #47
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Re: Statistical Analysis of Flops

Any difference [Cnctr & 1gap 2-suited, 2 thru 7] v. [Cnctr & 1gap 2-suited, 8 thru Q] for BB = $20-400?
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Old 11-16-2009, 10:16 PM   #48
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by Paraffinic Naphtha View Post
Any difference [Cnctr & 1gap 2-suited, 2 thru 7] v. [Cnctr & 1gap 2-suited, 8 thru Q] for BB = $20-400?
I thought the question was interesting so I ran this one. Note that your first case will occur 50% more than your second case, as the ranks can form the pattern 6 ways, but only 4 ways in the second one since your range was 1 less card.

With the lower cards, and the pattern and blinds stated, the average final pot size was 44.2 BB. For the higher cards, it was 41.6 BB. So we can assume from the overall average of 41.2 that when A or K is out the pot size tends to be even less. That's true in other patterns as well.
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Old 11-17-2009, 08:01 AM   #49
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Re: Statistical Analysis of Flops

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Originally Posted by spadebidder View Post
I thought the question was interesting so I ran this one. Note that your first case will occur 50% more than your second case, as the ranks can form the pattern 6 ways, but only 4 ways in the second one since your range was 1 less card.

With the lower cards, and the pattern and blinds stated, the average final pot size was 44.2 BB. For the higher cards, it was 41.6 BB. So we can assume from the overall average of 41.2 that when A or K is out the pot size tends to be even less. That's true in other patterns as well.
Many thx spadebidder. All of this is very interesting and greatly appreciated!
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Old 11-17-2009, 11:32 PM   #50
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Re: Statistical Analysis of Flops

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Originally Posted by spadebidder View Post
Those are all calculated frequencies. The pot sizes are actual. I mentioned in another post that I'm withholding the actuals for now so as to not spoil the surprise of the other research I'm working on, which includes measuring the offsets. It will be very interesting to the rigtards.
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?
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