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Poker math: Why is AKs more of an underdog vs 77 than it is versus 66?

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  • Poker math: Why is AKs more of an underdog vs 77 than it is versus 66?

    Hi guys,

    to cut to the chase:

    Pre-flop equity:
    AKs vs QQ: 46.049%
    AKs vs JJ: 45.961%
    AKs vs TT: 45.937%
    AKs vs 99: 47.422%
    AKs vs 88: 47.524%
    AKs vs 77: 47.690%
    AKs vs 66: 47.694%

    AKs vs 55: 48.034%
    AKs vs 44: 48.587%
    AKs vs 33: 49.206%
    AKs vs 22: 49.893%

    I think I understand all pocket pair equity drops as the table descends (it has to do with straights that outdraw the AKs draws, i. e., at least one straight for each 88+ makes an Ace high straight for AKs, and at least one straight for each 55- straight has an Ace in it); please correct me if I'm wrong, and please add to what I've missed.

    The problem for me to grasp the above presented table in its entirety lies in the 66 and 77 pocket pairs. Why is there an equity drop? I can't see any additional outs for AKs vs 66 compared to AKs vs 77.

    Please, help me out; I'm studying poker and strive to have as few loose ends as possible. (The game already has enough incomplete information!)

    Thank you!

    NB: All data comes from PokerStove's Enumerate All.

  • #2
    i dont know for sure, but i'd guess that it's on the tiny % of boards that run " 2 3 4 5 "

    66 will beat the ace high straight but 77+ will not




    edit: im actually not sure, because i've just realised that in your post the equity increases, while in my theory it should decrease. strange



    edit2: if 66 plays worse than 77 it'll likely be due to counterfeiting? 66 has 77xx counterfeit boards while 77 only has 88xx (where x is Ace to card+1)
    Last edited by ouchbadbeat; Mon Jan 27, 2014, 02:43 PM.

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    • #3
      i dont know what calculator u use, but the one i use is different, 77 have a slight edge on 66 (0.01%)

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      • #4
        Originally posted by 666bonez187 View Post
        i dont know what calculator u use, but the one i use is different, 77 have a slight edge on 66 (0.01%)
        If you check out my OP, it lists AKs's equity, i. e., the higher it is, the weaker the opponent's hole cards are; that means that 77 does indeed have a slight edge over 66; our calculators are in agreement here

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        • #5
          Wrong way!

          Originally posted by Cod On Tilt View Post

          I think I understand all pocket pair equity drops as the table descends (it has to do with straights that outdraw the AKs draws, i. e., at least one straight for each 88+ makes an Ace high straight for AKs, and at least one straight for each 55- straight has an Ace in it); please correct me if I'm wrong, and please add to what I've missed.
          Originally posted by ouchbadbeat View Post
          edit: im actually not sure, because i've just realised that in your post the equity increases, while in my theory it should decrease. strange
          OK.

          I have just realized that I realized what you had realized: I share your theory! I mean... If 88+ catches certain straights that attempt to outdraw a successful AKs's draw, they will have been drawing dead, for the straight will continue for AKs to an Ace high straight!!!

          And we all know what THAT means: QQ should be (in that situation) more of an underdog than, say, 66, since their outs of outdrawing a successful AKs draw are fewer!

          We must be simply making a fatal math mistake somewhere, and I have a grave feeling it lies in the recalculations of draws; we need to strip it all down to the real basics, discarding successful AKs draws, because they MUST be compensated for elsewhere.

          Originally posted by ouchbadbeat View Post
          edit2: if 66 plays worse than 77 it'll likely be due to counterfeiting? 66 has 77xx counterfeit boards while 77 only has 88xx (where x is Ace to card+1)
          Please expand this idea and elaborate on it with an example. Thanks!
          Last edited by Cod On Tilt; Mon Jan 27, 2014, 04:54 PM.

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          • #6
            It's got to do with counterfeiting like ouchbadbeat says.

            Lets look at an example of boards;

            Board 1: 885 5 3
            Board 2: TT6 6 3
            Board 3: JJ8 8 3

            Now if we have pocket 4s we effectively have 4 high on all 3 boards.

            However, if we have pocket 7s, our pair plays on boards #1 and #2.

            This is where the equity difference comes in.

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            • #7
              Okay.

              Could you please give me an example of where 77 does better vs AKs than 66 does?

              How does this apply to the counter-intuitive QQ having higher equity than 77 when QQ-related straights are dominated by AKs?

              Thanks!

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              • #8
                Originally posted by Cod On Tilt View Post
                Okay.

                Could you please give me an example of where 77 does better vs AKs than 66 does?

                How does this apply to the counter-intuitive QQ having higher equity than 77 when QQ-related straights are dominated by AKs?

                Thanks!
                dont quote me on this, im an armchair theoretical mathematician , this is just my brain ticking over:
                i think if you take all boards 66 can face and 77 can face, i think there will be more 2 pair boards that 66 loses than 77

                obv on a 77xx board 77 has quads but the same is true for 66 on 66xx

                again, im not sure at all. interesting thread


                id like to see that list of numbers as a graph because it's definitely non-linear

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                • #9
                  You quote

                  AKs vs 66: 47.694%

                  PSO Odds Calculator gives

                  AhKh v 6c6s 48.01%

                  and if the 66 has the same suit it drops

                  AhKh v 6c6h 47.11%

                  When I put in the 'range' of 66 (all combos) it gives 47.38%

                  So I am not sure the figure you have is right.

                  I don't do maths - but I don't think these differences are significant.

                  Its still a flip.

                  Ed
                  4 Time Bracelet Winner


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                  • #10
                    Originally posted by EdinFreeMan View Post
                    You quote

                    AKs vs 66: 47.694%

                    PSO Odds Calculator gives

                    AhKh v 6c6s 48.01%

                    and if the 66 has the same suit it drops

                    AhKh v 6c6h 47.11%

                    When I put in the 'range' of 66 (all combos) it gives 47.38%

                    So I am not sure the figure you have is right.

                    I don't do maths - but I don't think these differences are significant.

                    Its still a flip.

                    Ed
                    The figure I have should be right, PokerStove runs all the possible boards, juxtaposes them with the hole card holdings, and determines the hand winner/split pot.

                    Comment


                    • #11
                      Thread continues...

                      I only ever see quads.

                      77XXY; (7 < X < K)

                      Sure, 77 beats AKs (and 66 doesn't) on 77XXY; ((X > Q) ∧ (X ≠ Y)), but 66 beats AKs (and 77 doesn't) on 66XXY ((X > Q) ∧ (X ≠ Y)) on a 66XXY board, so in those cases 66 = 77.

                      Am I missing something?
                      Last edited by Cod On Tilt; Mon Jan 27, 2014, 08:43 PM.

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                      • #12
                        I'm not sure but I think you're asking why does one pocket pair have a better chance than another pocket pair? Since the AK has the same chance of hitting an A, K, straight or flush no matter what the pair is.

                        Well if that's the question I believe it is that the lower the pair the greater the chance of that pair being counterfeited by the board coming a higher two pair. This would equate to a very slight difference in equity for any overcard hands vs a smaller pair.

                        Tournament of Champions Winner 2013

                        Bracelet Winner

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                        • #13
                          Originally posted by Fadyen View Post
                          I'm not sure but I think you're asking why does one pocket pair have a better chance than another pocket pair? Since the AK has the same chance of hitting an A, K, straight or flush no matter what the pair is.

                          Well if that's the question I believe it is that the lower the pair the greater the chance of that pair being counterfeited by the board coming a higher two pair. This would equate to a very slight difference in equity for any overcard hands vs a smaller pair.
                          Yes, but what are the counterfeit cases when it comes to 66 vs 77?

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                          • #14
                            For example when a board comes 9977x where x is not an A or K, 77 would win where 66 would not.

                            You kind of got it in one of your earlier posts. Although when you say 66 wins on boards where 66 comes so it makes them the same value this is not true. If we take my example of 99x66, where x is not A or K, the 77 still beats the AK, so 77 have more value than 66 vs overcards.
                            Last edited by Fadyen; Mon Jan 27, 2014, 09:05 PM.

                            Tournament of Champions Winner 2013

                            Bracelet Winner

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                            • #15
                              77(pair of 8+ e.g 88 99 TT etc)x where x isn't A or K, 7s win, 6s don't due to counterfeit.
                              66(pair of 7+ e.g 77 88 99 TT etc)x where x isn't A or K, 6s win, 7s also win due to a higher 2 pair.

                              When there's 2 pair on board and 6s would make quads, provided AK doesn't pair up aswell 7s would've won anyway.

                              If 7s make quads and there's 2 pair on board, provided the second pair is higher, 66 would be counterfeited and can't beat AK on that board

                              I think I'm late xD sorry
                              Last edited by Quaquaversal; Mon Jan 27, 2014, 09:20 PM.

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