Statistical Analysis of Flops - Poker Theory

violi · 11-14-2009, 08:19 PM

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.

Donkson · 11-14-2009, 09:30 PM

It would depend on players and their positions, not just flops I would say.

spadebidder · 11-14-2009, 09:42 PM

Quote:

Originally Posted by violi

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.

violi · 11-14-2009, 11:56 PM

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?

asdfasdf32 · 11-15-2009, 04:50 AM

Quote:

Originally Posted by spadebidder

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?

spadebidder · 11-15-2009, 08:24 AM

Quote:

Originally Posted by violi

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

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.

spadebidder · 11-15-2009, 11:51 AM

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.

asdfasdf32 · 11-15-2009, 12:02 PM

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.

jewbinson · 11-15-2009, 12:17 PM

spadebidder, this thread contains potentially the most useful information about NLHE I will ever need.
Thanks a million

statmanhal · 11-15-2009, 12:25 PM

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

violi · 11-15-2009, 12:31 PM

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.

violi · 11-15-2009, 12:43 PM

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?

violi · 11-15-2009, 12:48 PM

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...

spadebidder · 11-15-2009, 01:29 PM

Quote:

Originally Posted by asdfasdf32

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

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.

spadebidder · 11-15-2009, 02:00 PM

Quote:

Originally Posted by violi

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.