Flop texture vs. final pot sizes

Dec 15th, 2009 | Posted by spadebidder

This came up in a 2+2 post, where someone was interested in comparing final pot sizes to the flop type.  It turned out to be a little interesting but no big surprises.   The original thread with more discussion is here:  http://forumserver.twoplustwo.com/15/poker-theory/statistical-analysis-flops-633448/

Here’s the data for a 9-player run and a Heads-Up run, showing the calculated frequency of the flop types, and the actual pot size data.  The actual flop frequencies will be shown in the flop analysis articles on this site, where I analyze and explain the card removal effects that alter flop frequencies. I don’t want the focus to be on that in this post, so I’ve omitted them and only shown the calculated probabilities.

Note that these final pot sizes include the final bet whether it got called or not. These are also without regard to what other streets were seen, as long as there was a flop.

 

Site B, 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. And the smallest pots happen when 2 or 3 broadway cards flop (especially AKx), which isn’t surprising.

 

Here’s the Heads-Up run:

 

Site B, 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

 

And here’s one for BB of $20 to $400, 6-max and 9-player combined. Surprisingly, the average pot sizes go up nearly 50%. 

 

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

 

It would be interesting to show the actual pot won (before any uncalled final bet) and I may try that later when I get time.

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