Math - AK or AKs vs AA or QQ

    • Hackett77
      Hackett77
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      Why is there such an equity difference between AK and AKs vs AA compared to AK and AKs vs QQ?

      eg.

      Vs AA

      AKs 12%
      AKo 7%

      Vs QQ (no shared suits)

      AKs 46%
      AKo 42%

      Ok not a massive difference but why does AKs have 1% more equity vs AA than it does vs QQ?
  • 14 replies
    • Tomaloc
      Tomaloc
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      i think it's something along the way of that one of the only ways for AK to beat AA is by spiking a flush.
      vs QQ you'll just always have more outs in general...
    • metza
      metza
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      Joined: 28.01.2012 Posts: 2,220
      Originally posted by Hackett77
      Why is there such an equity difference between AK and AKs vs AA compared to AK and AKs vs QQ?

      eg.

      Vs AA

      AKs 12%
      AKo 7%

      Vs QQ (no shared suits)

      AKs 46%
      AKo 42%

      Ok not a massive difference but why does AKs have 1% more equity vs AA than it does vs QQ?
      I would assume the 1% equity against AA is because the queens are blockers to the broadway straight, whereas the aces are not.
    • VorpalF2F
      VorpalF2F
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      to win vs AA w/ AKo, you need a straight, two more kings (at least) or 4 cards of the same suit as whichever of your cards is of a different suit than the aces.

      With AKs, you have all of the above possibilities, but you only need 3 more cards of the same suit.

      No A will help you w/ AKo -- unless it is part of the 4-flush that matches your king.

      vs QQ, any K or any A helps too.
    • Hackett77
      Hackett77
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      Thanks metza, that makes sense.


      VorpalF2F and Tomaloc, its the opposite, The equity difference is 1% better vs AA than QQ.
    • Tomaloc
      Tomaloc
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      that doesn't go against what we are saying :f_biggrin:

      in relative terms having suited cards makes much more of a difference against AA than against QQ. this is the point that we're making
    • Hackett77
      Hackett77
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      Originally posted by Tomaloc
      that doesn't go against what we are saying :f_biggrin:

      in relative terms having suited cards makes much more of a difference against AA than against QQ. this is the point that we're making
      Yes I know that Suited cards do better than the non suited equivalent of the same hand vs XX but thats irrelevant to this question.
    • ihufa
      ihufa
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      The only way AK wins vs AA is with a flush, so being suited matters more than AK vs QQ, how are u not getting this
    • Hackett77
      Hackett77
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      Originally posted by ihufa
      The only way AK wins vs AA is with a flush, so being suited matters more than AK vs QQ, how are u not getting this
      who isnt getting what?

      maybe im wrong but last time I checked 3 or 4 kings plus 9TJQ also beats AA?
    • Jan217
      Jan217
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      The reason AKs makes less of a difference when up against QQ is that some of the time you make a flush with AKs you would have won by making a pair anyway, so those boards dont contribute any extra equity compared with AKo. Vs AA its much less likely when you make a flush you would have won anyway, so the suitedness of AK adds more equity.

      We can show this with a simple calculation

      the chance of hitting a flush is ~5% higher with suited cards which means suited AKs adds roughly 5% equity vs AA. Against QQ we need to take away all the times we hit a flush but also hit an A or K with the other two cards. Given a board that is :heart: :heart: :heart: xx there is 1-(41/47)*(40/46) ~ 25% chance that at least one of the two other cards is an A or K. So the equity added vs QQ is roughly 0.75*5% ~ 4%.

      To do it properly we need a much bigger calculation since we need to take straights and stuff into account, but thats what the equilator is for ^^
    • NightFrostaSS
      NightFrostaSS
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      It's actually because when you hold AKs, AA will never have any of your flush outs taken out while QQ will.
    • Jan217
      Jan217
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      Originally posted by NightFrostaSS
      It's actually because when you hold AKs, AA will never have any of your flush outs taken out while QQ will.
      True but AhKh has only 0.3% more equity vs QsQc than QhQc, so its not a huge effect.
    • antonnotna1984
      antonnotna1984
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      How about winning vs AA on straight or set of Kings?
    • NightFrostaSS
      NightFrostaSS
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      Originally posted by Jan217
      Originally posted by NightFrostaSS
      It's actually because when you hold AKs, AA will never have any of your flush outs taken out while QQ will.
      True but AhKh has only 0.3% more equity vs QsQc than QhQc, so its not a huge effect.
      The other part then must come from AKo being able to make two 1 card flushes vs QQ that are almost always good while AA can be blocking one of them by making a higher flush.

      I'm rly too lazy to look it up on stove, but it's pretty obv it's all about the flushes.
    • ihufa
      ihufa
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      Joined: 18.03.2008 Posts: 3,323
      Originally posted by Hackett77
      Originally posted by ihufa
      The only way AK wins vs AA is with a flush, so being suited matters more than AK vs QQ, how are u not getting this
      who isnt getting what?

      maybe im wrong but last time I checked 3 or 4 kings plus 9TJQ also beats AA?
      hmm