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Old 11-14-2009, 09:19 PM   #1
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Statistical Analysis of Flops

This question is with respect to NL Holdem.

What flops produce the biggest pots? What flops produce the smallest pots? I'm trying to find a rigorous analysis from the logs of online play. It's certainly not a trivial analysis to do - does anyone know a reference?

I'd also be interested in knowing what experienced players think. In Dan Harrington's NL Cash game book volume 2 he interviews Bobby Hoff who mentioned the wheel draw hands tended to produce the biggest pots (p. 364).

Thanks.
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Old 11-14-2009, 10:30 PM   #2
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Re: Statistical Analysis of Flops

It would depend on players and their positions, not just flops I would say.
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Old 11-14-2009, 10:42 PM   #3
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by violi View Post
This question is with respect to NL Holdem.

What flops produce the biggest pots? What flops produce the smallest pots? I'm trying to find a rigorous analysis from the logs of online play. It's certainly not a trivial analysis to do - does anyone know a reference?
I can do it for flops, I have a template set up that I can easily modify and I have about 500 million NLHE cash game flops to get the stats from. However, you seem to be asking a different question. It sounds like you are asking what combination of hole cards and flops produces the biggest pots (you mention wheel draws), which is pretty much unknowable since most hands have no showdown. No one could do that analysis except a poker site, since they have all hole cards. Or you could do it only for hands you yourself play, which isn't representative of anything but your own play.

If you just want the table of flop types vs. final pot sizes (in BB), I can do that easily. I have flops separated into 28 types in my template. I can also filter for stakes.

Last edited by spadebidder; 11-14-2009 at 10:58 PM.
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Old 11-15-2009, 12:56 AM   #4
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Re: Statistical Analysis of Flops

Hi spadebidder,
Thanks so much for the reply! (I didn't mean to give the impression of knowing the player's whole cards. As far as I'm concerned it's completely irrelevant.)

It would be great if you could use your data set for the analysis. I would love to know the results! And how did you get such a great data set? That's huge!

Also, can you share your 28 different types of flops? And did you you come up with the groupings your self or is this a poker standard I'm unaware of?
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Old 11-15-2009, 05:50 AM   #5
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by spadebidder View Post
I can do it for flops, I have a template set up that I can easily modify and I have about 500 million NLHE cash game flops to get the stats from. However, you seem to be asking a different question. It sounds like you are asking what combination of hole cards and flops produces the biggest pots (you mention wheel draws), which is pretty much unknowable since most hands have no showdown. No one could do that analysis except a poker site, since they have all hole cards. Or you could do it only for hands you yourself play, which isn't representative of anything but your own play.

If you just want the table of flop types vs. final pot sizes (in BB), I can do that easily. I have flops separated into 28 types in my template. I can also filter for stakes.
Is this all from HEM or something other program (possibly a small one you wrote?) Is there any cool/useful analysis you've been able to come up with, and if so, would you be willing to discuss on here or through PM?
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Old 11-15-2009, 09:24 AM   #6
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by violi View Post
It would be great if you could use your data set for the analysis. I would love to know the results! And how did you get such a great data set? That's huge!

Also, can you share your 28 different types of flops? And did you you come up with the groupings your self or is this a poker standard I'm unaware of?
Quote:
Originally Posted by asdfasdf32 View Post
Is this all from HEM or something other program (possibly a small one you wrote?) Is there any cool/useful analysis you've been able to come up with, and if so, would you be willing to discuss on here or through PM?
The hand data is from pokerftp.com. I have some interesting research that I'll be publishing soon about flops and all-ins and random distributions and so on.

My flop types and their calculated frequencies are these:

Code:
FLOP TYPES FREQUENCY

---------------------------------------------------------------------
[ Flop Type ]            Calculated     Example
[ Rainbow              ]  39.76471%     Kc-8d-Qh
[ Monotone             ]   5.17647%     Kh-9h-6h
[ Two-suited           ]  55.05882%     2d-8s-4s
[---check suit types---] 100.00000% 

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

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

[ 28 Flop Combinations ]  Calculated     Example

[ Pair & cnctr  rainbow]   1.41176%     6s-6d-7c
[ Pair & cnctr 2-suited]   1.41176%     4h-4c-3h
[ Pair & 1gap   rainbow]   1.30317%     Qs-Ad-Ah
[ Pair & 1gap  2-suited]   1.30317%     3s-Ad-3d
[ Pair & 2+gap  rainbow]   5.75566%     3h-3c-9d
[ Pair & 2+gap 2-suited]   5.75566%     7s-7d-4d
[ Triplets             ]   0.23529%     Kc-Kd-Ks
[ 3-Straight    rainbow]   1.30317%     2s-3d-Ac
[ 3-Straight   2-suited]   1.95475%     3c-5d-4c
[ 3-Straight-Flush     ]   0.21719%     4s-6s-5s
[ Cnctr & 1gap  rainbow]   2.60633%     Qd-Ts-Kh
[ Cnctr & 1gap monotone]   0.43439%     Tc-8c-Jc
[ Cnctr & 1gap 2-suited]   3.90950%     5d-3c-6c
[ Cnctr & 2+gap rainbow]  10.09955%     Kc-8d-Qh
[ Cnctr & 2+gp monotone]   1.68326%     Ac-Jc-2c
[ Cnctr & 2+gp 2-suited]  15.14932%     6d-Jh-Td
[ KA2 dbl-cnct  rainbow]   0.10860%     2d-Kh-As
[ KA2 dbl-cnct monotone]   0.01810%     Ks-As-2s
[ KA2 dbl-cnct 2-suited]   0.16290%     Kh-2d-Ad
[ Dbl gutshot   rainbow]   1.19457%     3d-7c-5s
[ Dbl gutshot  monotone]   0.19910%     6d-2d-4d
[ Dbl gutshot  2-suited]   1.79186%     6s-8s-4c
[ Other 1-gaps  rainbow]   8.03620%     5s-7h-Ad
[ Other 1-gaps monotone]   1.33937%     Td-Qd-6d
[ Other 1-gaps 2-suited]  12.05430%     2d-8s-4s
[ No cnt/gp/pr  rainbow]   7.71041%     2d-Tc-6h
[ No cnt/gp/pr monotone]   1.28507%     Kh-9h-6h
[ No cnt/gp/pr 2-suited]  11.56561%     Jh-6h-As
[--check combinations--] 100.00000%

I'm probably going to add another type to differentiate exactly 2 gaps from over 2 gaps (3gap+) since that grouping is pretty large relative to the others, and since 2 gaps are pertinent to poker hands. That will add 3 more combinations for a total of 31.

Are these groupings helpful for your purpose? If so, I can run some stats on final pot sizes pretty easily. If it comes out interesting I may include it in my stuff as well.

Last edited by spadebidder; 11-15-2009 at 09:35 AM.
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Old 11-15-2009, 12:51 PM   #7
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Re: Statistical Analysis of Flops

I've almost finished it, but I'm adding a few more rank-specific flop types like double and triple broadway flops, and 3 wheel cards on flop. Post in a couple hours.

Last edited by spadebidder; 11-15-2009 at 12:56 PM.
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Old 11-15-2009, 01:02 PM   #8
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Re: Statistical Analysis of Flops

Very cool. Published where, btw? I'm not sure (judging from the examples on your site) how useful most of the information will be, but that doesn't really matter, because it's very interesting regardless of its actual viability as a study tool.

Keep us updated.
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Old 11-15-2009, 01:17 PM   #9
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Re: Statistical Analysis of Flops

spadebidder, this thread contains potentially the most useful information about NLHE I will ever need.
Thanks a million
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Old 11-15-2009, 01:25 PM   #10
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Re: Statistical Analysis of Flops

Spade – you probably did some checking yourself but I did a quickie on the suit cases. The observed probabilities match the theoretical to 7 decimal places.

So, the "On-line Poker is Rigged" proponents will likely ask – Ok, what about the eighth place?

Thanks for sharing the data.

Hal
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Old 11-15-2009, 01:31 PM   #11
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Re: Statistical Analysis of Flops

Spadebidder, This is very exciting - I've never seen anything like that breakdown before. I agree with adding more categories. It seems like adding in even more could be justified, too, depending on what analysis you're doing. For example you could take almost all of your current categories and break them into less than 6 high flops. (Ex: flop is less than 6 high and is Pair & Connector, etc...)

So yes, it's a very helpful breakdown. Thanks.
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Old 11-15-2009, 01:43 PM   #12
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Re: Statistical Analysis of Flops

Spadebidder, When you add in the pot size for these categories of flops are you planning on doing the post size before the turn card or the final pot size? In the original post I had in mind the final post size but you could do both.

And this brings up the same questions for the turn and river. So, there's certainly a more general question to work on.

(btw I do statistical computing on large data sets as my day job for a proprietary trading company in Chicago so if you want me to pitch in just make the data set available. I'm happy to help and I use R for most analysis. What are you using?
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Old 11-15-2009, 01:48 PM   #13
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Re: Statistical Analysis of Flops

I'm sorry - I missed this part:
"The hand data is from pokerftp.com. I have some interesting research that I'll be publishing soon about flops and all-ins and random distributions and so on."

I'll take a look...
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Old 11-15-2009, 02:29 PM   #14
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by asdfasdf32 View Post
Very cool. Published where, btw? I'm not sure (judging from the examples on your site) how useful most of the information will be,
To be clear pokerftp.com is not my site. Pokerftp.com is the source of my billion hand histories. I have another web site that I haven't made public yet, with lots of stuff you've never seen.


Quote:
Originally Posted by statmanhal View Post
Spade – you probably did some checking yourself but I did a quickie on the suit cases. The observed probabilities match the theoretical to 7 decimal places.

So, the "On-line Poker is Rigged" proponents will likely ask – Ok, what about the eighth place?

Thanks for sharing the data.

Hal
Not sure what data you are referring to as your quickie, are you also using the hand database from pokerftp.com? I've done observed vs. actual for all the flop types I listed, for various types of games and various stakes. It will all be published soon. There are some flop biases but they are due to player behavior.

The pot size stuff is about done, post soon.
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Old 11-15-2009, 03:00 PM   #15
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by violi View Post
Spadebidder, When you add in the pot size for these categories of flops are you planning on doing the post size before the turn card or the final pot size? In the original post I had in mind the final post size but you could do both.

And this brings up the same questions for the turn and river. So, there's certainly a more general question to work on.
The one I have running right now is going to show average final pot size regardless of how far the hand progressed beyond the flop. I could easily do it for the flop pot size too, but since we're correlating with the flop pattern anyway, I don't think it will make much difference. The differences on later streets are going to be due to differences in turn and river cards.

As for turn and river patterns, I'm still working on my categories and pattern matching to count them. So I'm not prepared to do a breakdown on those.
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Old 11-15-2009, 03:22 PM   #16
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Re: Statistical Analysis of Flops

Ok, sounds good thanks. That pokerftp.com site is great. I really appreciate the reference.
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Old 11-15-2009, 03:24 PM   #17
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Re: Statistical Analysis of Flops

Ok, here's a run for full ring 9-player, minimum 7 dealt in, with a filter for BB of $0.25 to $4.00. I went ahead and stopped at 51 million flops as the stats aren't going to change. The average final pot size is shown in BBs. This counts the final pot size after the last bet went in, even if the last bet was not called (which is a lot of the time).

Note that I'm only showing the calculated frequency of each flop type here, not the actual frequency. I don't want to spoil the surprise when I publish a full analysis of the actuals soon on my web site. But this answers the question you posed. Notice at the bottom I added the wheel card flops you asked for, and a few others.


Code:
Site #0, 9-player NLHE, min 7 dealt in, BB $ 0.25 to $ 4.00
Number of hands analysed:  90,000,000
              Flops seen:  51,073,435 (56.7%)


FLOP TYPES FREQUENCY

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

[ Rainbow              ]  39.76471%   9s-3h-5c   24.3
[ Monotone             ]   5.17647%   7c-2c-6c   25.5
[ Two-suited           ]  55.05882%   3s-Qs-2c   25.9
[---check suit types---] 100.00000%    

[ Paired flop          ]  16.94118%   6h-Ts-6s   23.8
[ Triplet flop         ]   0.23529%   5c-5s-5h   25.4
[ Unpaired flop        ]  82.82353%   9s-3h-5c   25.5
[--check match types---] 100.00000% 

[ Pair & connector     ]   2.82353%   8d-9d-9h   24.4
[ Pair & 1gap          ]   2.60633%   Jh-9h-Jd   24.3
[ Pair & 2+gap         ]  11.51131%   6h-Ts-6s   23.5
[ Triplets             ]   0.23529%   5c-5s-5h   25.4
[ 3-Straight           ]   3.47511%   2c-3c-4s   29.1
[ Connector & 1gap     ]   6.95023%   9c-Jh-8s   27.6
[ Connector & 2+gap    ]  26.93213%   3s-Qs-2c   25.5
[ KA2 double connector ]   0.28959%   2d-Kh-Ad   21.3
[ Double gutshot       ]   3.18552%   Ah-3h-Qd   26.5
[ Other 1gaps          ]  21.42986%   9s-3h-5c   25.1
[ No cnct no 1gap no pr]  20.56109%   Jd-4s-As   24.5
[-check connect types--] 100.00000% 
                          
                         Calculated              Avg. Final
[ Flop Combinations ]     Frequency    Example   Pot in BBs

[ Pair & cnctr  rainbow]   1.41176%   4h-5c-4d   23.7
[ Pair & cnctr 2-suited]   1.41176%   8d-9d-9h   25.2
[ Pair & 1gap   rainbow]   1.30317%   Qd-Qs-Ac   23.6
[ Pair & 1gap  2-suited]   1.30317%   Jh-9h-Jd   25.1
[ Pair & 2+gap  rainbow]   5.75566%   Jh-Jd-4s   22.8
[ Pair & 2+gap 2-suited]   5.75566%   6h-Ts-6s   24.3
[ Triplets             ]   0.23529%   5c-5s-5h   25.4
[ 3-Straight    rainbow]   1.30317%   2d-As-3c   28.2
[ 3-Straight   2-suited]   1.95475%   2c-3c-4s   29.7
[ 3-Straight-Flush     ]   0.21719%   9d-8d-Td   28.3
[ Cnctr & 1gap  rainbow]   2.60633%   9c-Jh-8s   26.8
[ Cnctr & 1gap monotone]   0.43439%   6h-3h-4h   27.2
[ Cnctr & 1gap 2-suited]   3.90950%   Th-Jh-8c   28.2
[ Cnctr & 2+gap rainbow]  10.09955%   Kd-Qc-4h   24.7
[ Cnctr & 2+gp monotone]   1.68326%   7c-2c-6c   25.5
[ Cnctr & 2+gp 2-suited]  15.14932%   3s-Qs-2c   26.1
[ KA2 dbl-cnct  rainbow]   0.10860%   2h-Ad-Kc   20.4
[ KA2 dbl-cnct monotone]   0.01810%   2d-Kd-Ad   22.7
[ KA2 dbl-cnct 2-suited]   0.16290%   2d-Kh-Ad   21.8
[ Dbl gutshot   rainbow]   1.19457%   6c-4s-8h   25.7
[ Dbl gutshot  monotone]   0.19910%   Js-9s-7s   26.3
[ Dbl gutshot  2-suited]   1.79186%   Ah-3h-Qd   27.1
[ Other 1-gaps  rainbow]   8.03620%   9s-3h-5c   24.2
[ Other 1-gaps monotone]   1.33937%   6h-2h-8h   25.1
[ Other 1-gaps 2-suited]  12.05430%   8c-3h-5c   25.7
[ No cnt/gp/pr  rainbow]   7.71041%   Jc-8h-5d   23.6
[ No cnt/gp/pr monotone]   1.28507%   4h-9h-Qh   24.9
[ No cnt/gp/pr 2-suited]  11.56561%   Jd-4s-As   25.1
[--check combinations--] 100.00000% 

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

[ Any A or K or both   ]  40.07240%   5s-Ac-Qd   23.0
[ Triple-BWay unpaired ]   2.89593%   Qd-Ad-Kd   24.9
[ Triple-BWay paired   ]   2.26244%   Ac-Jc-Ah   21.6
[ Double-BWay unpaired ]  23.16742%   5s-Ac-Qd   24.2
[ Double-BWay paired   ]   4.34389%   Qc-Qs-6c   22.3
[ 3 to a Wheel no pr   ]   2.89593%   2c-3c-4s   26.5

.
So the biggest pots result from 3-straight flops, and next biggest are when there are lots of straight possibilities like connector+1gap and double-gut flops. Hoff's theory about wheel draw flops making the biggest pots, is wrong for low stakes anyway. It's smack in the middle. And the smallest pots happen when 2 or 3 broadway cards flop, which isn't surprising.

I'll do one for heads-up next, and maybe for 6-max.

EDIT - maybe you wanted "2 to a Wheel" and not 3? That may be more interesting.

Last edited by spadebidder; 11-15-2009 at 03:49 PM.
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Old 11-15-2009, 04:03 PM   #18
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Re: Statistical Analysis of Flops

Wow, this is so cool!

I think I'd want 2 to a wheel with an Ace. 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.)

Thanks again. I really look forward to seeing your research.
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Old 11-15-2009, 04:10 PM   #19
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Re: Statistical Analysis of Flops

Would it be possible for you to report the standard deviation with these means, too? I find the lack of variance sort of surprising.

The high and low (29.7 and 20.4)
High is:
[ 3-Straight 2-suited] 1.95475% 2c-3c-4s 29.7

And low is:
[ KA2 dbl-cnct rainbow] 0.10860% 2h-Ad-Kc 20.4

Interesting.
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Old 11-15-2009, 04:15 PM   #20
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Re: Statistical Analysis of Flops

Quote:
Originally Posted by violi View Post
Would it be possible for you to report the standard deviation with these means, too? I find the lack of variance sort of surprising.
There is no expectation or probability for pot size, it just is what it is. Sure we could do a standard deviation on it, but it wouldn't tell you any more than that average. I would expect that within types we will see everything from 2BB up to 2x the max buyin. I don't find these results surprising, but I've looked at this stuff a lot. Variation is going to be based more on how the hole cards hit the flop, not on the flop itself. There is some correlation between flop types and the likelihood they help typical hole cards that will see a flop, which is why we see any range at all.

I'm doing a heads-up run to see if it is more interesting, and I added a 2 wheel card type.
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Old 11-15-2009, 04:42 PM   #21
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Re: Statistical Analysis of Flops

Here's the one for Heads-Up. It isn't much different.

Code:
Site #0, Heads-up NLHE, BB $ 0.25 to $ 4.00
Number of hands analysed:  37,371,313
              Flops seen:  13,917,202 (37.2%)


FLOP TYPES FREQUENCY

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

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

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

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

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

[ Pair & cnctr  rainbow]   1.41176%   6s-6d-7c   25.6
[ Pair & cnctr 2-suited]   1.41176%   4h-4c-3h   27.3
[ Pair & 1gap   rainbow]   1.30317%   Qs-Ad-Ah   25.5
[ Pair & 1gap  2-suited]   1.30317%   3s-Ad-3d   27.2
[ Pair & 2+gap  rainbow]   5.75566%   3h-3c-Kd   24.5
[ Pair & 2+gap 2-suited]   5.75566%   7s-7d-4d   26.3
[ Triplets             ]   0.23529%   Kc-Kd-Ks   25.8
[ 3-Straight    rainbow]   1.30317%   2s-3d-Ac   29.9
[ 3-Straight   2-suited]   1.95475%   3c-5d-4c   31.5
[ 3-Straight-Flush     ]   0.21719%   4s-6s-5s   29.3
[ Cnctr & 1gap  rainbow]   2.60633%   Qd-Ts-Kh   28.8
[ Cnctr & 1gap monotone]   0.43439%   Tc-8c-Jc   28.6
[ Cnctr & 1gap 2-suited]   3.90950%   5d-3c-6c   30.2
[ Cnctr & 2+gap rainbow]  10.09955%   Kc-8d-Qh   26.8
[ Cnctr & 2+gp monotone]   1.68326%   Ac-Jc-2c   27.0
[ Cnctr & 2+gp 2-suited]  15.14932%   6d-Jh-Td   28.2
[ KA2 dbl-cnct  rainbow]   0.10860%   2d-Kh-As   21.2
[ KA2 dbl-cnct monotone]   0.01810%   Ks-As-2s   24.0
[ KA2 dbl-cnct 2-suited]   0.16290%   Kh-2d-Ad   23.9
[ Dbl gutshot   rainbow]   1.19457%   3d-7c-5s   27.8
[ Dbl gutshot  monotone]   0.19910%   6d-2d-4d   27.9
[ Dbl gutshot  2-suited]   1.79186%   6s-8s-4c   29.2
[ Other 1-gaps  rainbow]   8.03620%   5s-7h-Ad   26.5
[ Other 1-gaps monotone]   1.33937%   Td-Qd-6d   26.5
[ Other 1-gaps 2-suited]  12.05430%   2d-8s-4s   28.1
[ No cnt/gp/pr  rainbow]   7.71041%   2d-Tc-6h   25.8
[ No cnt/gp/pr monotone]   1.28507%   Kh-9h-6h   26.3
[ No cnt/gp/pr 2-suited]  11.56561%   Jh-6h-As   27.3
[--check combinations--] 100.00000% 

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

[ Any A or K or both   ]  40.07240%   Kc-8d-Qh   24.7
[ Triple-BWay unpaired ]   2.89593%   Jc-Tc-Qc   24.9
[ Triple-BWay paired   ]   2.26244%   Kh-Ks-Td   22.5
[ Double-BWay unpaired ]  23.16742%   Kc-8d-Qh   25.2
[ Double-BWay paired   ]   4.34389%   Qh-4c-Qc   24.1
[ 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


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Old 11-15-2009, 04:55 PM   #22
violi
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Re: Statistical Analysis of Flops

I'm wondering if your flop categories are granular enough. If you did all possible flops: 52 choose 3 is 22,100 which means, given your data set, you would expect 2,311 observations of each unique flop. (And many of those are equivalent because of the suits so it's probably more like 52/4 choose 3 which is 286 giving you 178,578 observations of "unique" flops.)
If you ranked flops from big pot to small pot I'm wondering if you could naturally categorize flops. It's sort of a fuzzy thought but might be worth taking a closer look at.

This is just extremely interesting to me. Thanks again. Your data set is just outstanding.
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Old 11-15-2009, 05:02 PM   #23
spadebidder
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Re: Statistical Analysis of Flops

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Originally Posted by violi View Post
I'm wondering if your flop categories are granular enough. If you did all possible flops: 52 choose 3 is 22,100 which means, given your data set, you would expect 2,311 observations of each unique flop. (And many of those are equivalent because of the suits so it's probably more like 52/4 choose 3 which is 286 giving you 178,578 observations of "unique" flops.)
If you ranked flops from big pot to small pot I'm wondering if you could naturally categorize flops. It's sort of a fuzzy thought but might be worth taking a closer look at.

This is just extremely interesting to me. Thanks again. Your data set is just outstanding.
I don't know any shortcut to write the code for the pattern matching other than do them one at a time (other than just enumerate them blindly with no named or relevant patterns). So the 50 something lines I have in that chart took an individual block of code to recognize and count each one, and then a hand calculation to figure out the expected frequency for each one, and then an enumerated run of all flop permutations to check the calculation, and then another block of code to add each new type to the output.

I think this data shows us that there isn't going to be a huge variation in pot size based on the flop texture alone. If you could explain your goal then I may have another way to do it, or it may be something I'm already working on.
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Old 11-15-2009, 05:03 PM   #24
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Re: Statistical Analysis of Flops

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
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Old 11-15-2009, 05:06 PM   #25
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Re: Statistical Analysis of Flops

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Originally Posted by spadebidder View Post
[B]
Not sure what data you are referring to as your quickie, are you also using the hand database from pokerftp.com? I've done observed vs. actual for all the flop types I listed, for various types of games and various stakes. It will all be published soon. There are some flop biases but they are due to player behavior.

The pot size stuff is about done, post soon.
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?
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