Equilibrium Play is non exploitable? Here in this example is that really the case??

    • iSoOwnYou
      iSoOwnYou
      Bronze
      Joined: 27.11.2014 Posts: 637
      Hey tournament experts. I am working hard on my game right now. Currently I'm reviewing equilibrium calling ranges.

      According to Kill Everyone, "If you play the equilibrium strategy your opponents best response is to also play the equilibrium strategy".

      Now lets say we play a million games where our opponent is on the button , and we are in the SB.
      Our opponent folds every single hand apart from AA , and when he has AA he shoves it no matter what.

      We play the equilibrium strategy and we ALWAYS call with the equilibrium calling range.
      So when we have a CSI (M) of 6 we always call with: 22+ , A5o, A2s+, KTo, K9s+, QTs+, (22% of our hands).

      Does this mean we break even against this player in the long run? I can't see how!!!! ? Am i misunderstanding something?

      or should this read 'if you play the equilibrium shoving strategy, your opponents best response is to play the equilibrium calling strategy' ?

      Thanks
  • 4 replies
    • Beatlemanic
      Beatlemanic
      Gold
      Joined: 14.10.2010 Posts: 2,991
      If you play the equilibrium strategy your opponents best response is to also play the equilibrium strategy".

      yep. Thats the definition of equilibrium.

      We play the equilibrium strategy and we ALWAYS call with the equilibrium calling range.
      So when we have a CSI (M) of 6 we always call with: 22+ , A5o, A2s+, KTo, K9s+, QTs+, (22% of our hands).
      Does this mean we break even against this player in the long run? I can't see how!!!! ? Am i misunderstanding something?
      You are not BE against him, you are actually printing tons of money - everytime he folds, your equity increase, coz your SB was not stealed. If hes folding eg. KK, he is ofc doing huge mistake here.
      Btw, if hes shoving only AA ----> hes not playing equilibrium strategy -----> your equilibrium strategy is not neccesary best response against his non-equilibrium strategy (in this particular case, you should be calling only AA vs. him). Check some game theory material, eg. this.
    • iSoOwnYou
      iSoOwnYou
      Bronze
      Joined: 27.11.2014 Posts: 637
      Hi yes I get shoving AA is not equlibrium it was hypothetical example.

      Equity increase with SB not being stolen this is interesting. I find it amazing to think there is a strategy that is just totally unbeatable. It's pretty amazing. Thanks for the advice and steeer Beatlemanic i may check out that game lecture at some time.

      So it appears I understood this correctly, what I found hard to believe is actually true? If we always call vs a Button shove with the equilibrium strategy - it doesn't matter what our opponent has open shoved it's impossible for him to beat us in the long run?!!!! Wow.

      I get that it's also not most ev, but still amazing i think.

      Thanks! :f_drink:
    • Gavron23
      Gavron23
      Bronze
      Joined: 26.05.2010 Posts: 2,863
      Well him shoving only AA kind of erases all talk of equilibrium play :)
    • yanchevadan
      yanchevadan
      Bronze
      Joined: 28.09.2012 Posts: 342
      A simple answer to your question. If you always play NASH, he can't find a RANGE to shove profitable vs you. That's all about the equilibrium. In the real game you want to win, not to be break even. So you should always know actual players ranges and take advantage of it. In your example, yes you will not lose if you stick to equilibrium, but you will not win either. You are not taking advantage of the huge leak of your opponent. So NASH is just a guideline and you should never stick to it. The only exception is when you are 100% sure that your opponent is playing it. So you can't find a better range to shove or call.