Strongest hand against pocket aces

    • danufford
      danufford
      Basic
      Joined: 26.12.2014 Posts: 3
      Hi,
      I am new here and I am not sure if I am posting at the right forum. I have a question regarding the poker math. Here it says 56-suited is the strongest hand against pocket aces in a heads-up match (ignoring the case when your opponent is also holding pocket aces) . Does anybody have any explanation for this?
      Thanks,
      Dan
  • 6 replies
    • grbell
      grbell
      Bronze
      Joined: 31.05.2014 Posts: 102
      Not too good at explaining this but I'll give it a try. Suited connectors would always have the best chance against pocket aces as you are more likely to hit a straight/flush/two pair than a pair would. Middle suited connectors are more likely to make a straight - high or low e.g. 34567 or 56789. 67s is better than 78s or 89s because it denies AAo from making the nut straight if you hit 2345x as 23456 beats A2345. Compare this with 9 10s where 910JQK is beaten by 10JQKA. I think though the differences in probabilities will be marginal for 67s, 78s, 89s and 10Js.
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,904
      Originally posted by grbell
      I think though the differences in probabilities will be marginal for 67s, 78s, 89s and 10Js.
      Hi, danufford

      Check out Equilab from the Poker Tools page.

      This is what it says for 56s vs AA:

             Equity     Win     Tie
      MP2    77.50%  77.29%   0.21% { AA }
      MP3    22.50%  22.29%   0.21% { 65s }


      78s vs AA

             Equity     Win     Tie
      MP2    77.54%  77.37%   0.17% { AA }
      MP3    22.46%  22.29%   0.17% { 87s }


      too close to say there is any real difference, so grbell's assessment is pretty much spot on.

      I'm not sure why Equilab and the website have very slightly different answers, but it may be due to rounding errors in the algorithms the different programs use.

      Or maybe it's luck :coolface:

      Best of luck,
      VS
    • danufford
      danufford
      Basic
      Joined: 26.12.2014 Posts: 3
      Thanks for your answers.
      I'm not sure why Equilab and the website have very slightly different answers, but it may be due to rounding errors in the algorithms the different programs use.
      I think it's because pokerpredictor.com apparently has calculated all the possibilities and therefore shows the "exact" probabilities while Equilab shows the "estimated" probabilities based on the simulation, right?. But as you said the differences are negligible.
      Grbell's answer makes totally sense to me. However I think 10Js should have lower chance of winning than 56s, 67s and 78s.
      Can we also explain intuitively why A9 is the weakest hand against AA?
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,904
      Originally posted by danufford
      Can we also explain intuitively why A9 is the weakest hand against AA?
      Hi, danufford...
      Equilab has 2 modes "Monte Carlo" -- where they run the hands several million times, and "Enumerate All" where they supposedly do just that. I used "Enumerate All"

      I think A9o vs AA because it pretty much can't make a straight that beats AA, unless the board has 4 of those cards. If the A9 hand has a suit that the AA doesn't have, then 4 flushes on the board also give it the win.
      The only possible other outs then, are the other 9s, and there needs to be two of 'em on the board for it to help.
      A6o - A8p are all very similar.
      ATo and A5o the equity suddenly skyrockets from 6% to 8% Woot!

      Cheers,
      VS
    • danufford
      danufford
      Basic
      Joined: 26.12.2014 Posts: 3
      Great answer, thank you!:f_drink:
    • StandardBacking
      StandardBacking
      Bronze
      Joined: 20.02.2015 Posts: 109
      T5o is the best you can make all the straights and flushes :f_drink: