Blocker effect

    • dydukas
      dydukas
      Platinum
      Joined: 01.05.2009 Posts: 1,271
      Hi fellow sngers,

      I was wondering if it is generally more profitable to shove suited connectors or small aces. For example:

      Calling range 10% (66+, A8s+, ATo+) and you wanna push Tc9c (35.8% equity) or Ac3c (31.9%). Now of course Tc9c has more equity but Ac3c blocks 21/126 (16.7%) of calling combos so 1/6th of the time you won't get called at all.

      How do I implement that 16.7% in equity calculations?

      Say I go AI for villains 500 chips (he's BB, no SB) then on average I gain:

      With Tc9c: 0.1*358 [when called by 10% range] + 0.9*1000 [when folded] = 935.8

      With Ac3c: 0.1*(1-1/6)*319 [when called by "blocked" 10% range] + (1-0.1*(1-1/6)*)*1000 [else folded] = 26.6 + 916.7 = 943.25

      Firstly, do those calculations make sense? I'm kinda sleepy. :) And then my initial idea was even if Tc9c has more equity but due to blocker effect Ac3c is more profitable?
  • 3 replies
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      One approach is to look at the expected cost of getting called relative to stealing the blinds. The expected cost of getting called depends on both your equity when called and the probability that you get called. My program ICM Explorer can do a lot of the calculations.

      Suppose the blinds are 120/240 with 4 equal stacks of 3375 on the bubble. Stealing is worth 26.12%. Getting called with T9s and 35.8% equity is worth 13.72%, lower by 12.4%, and this occurs 115 times out of 1225, 9.39% of the time. So, the total cost of getting called is 12.4% * 9.39% ~ 1.164% of the prize pool. Pushing gains 0.54%.

      Getting called with A3s and 31.9% equity (actually, there are 4.42% ties, which should make the effective equity 32.6%, but let's ignore that) is worth about 12.23%, lower than stealing by 13.89%. You get called 105/1225 ~ 8.57% of the time. The total cost of getting called is 13.89% * 8.57% ~ 1.191% of the prize pool, very close to the value for T9s. Pushing gains 0.51%. That means the blocking effect roughly cancels the lower equity when called. If you account for ties, then I think A3s turns out to be a stronger pushing hand.
    • dydukas
      dydukas
      Platinum
      Joined: 01.05.2009 Posts: 1,271
      Thanks for the calculations! A lot players say that small aces are considerably worse but I had a feeling that due to blockers it should be about even if they're suited. And I definitely need to play around more with your program.

      And about ties. I've been running a lot into ties, again with small ace vs another small ace, even had a few times where we had the same pocket pairs. Anyway does HEM count the $EV outcome for the red line correctly for those hands? I know that Sng Wiz has problems with ties.

      On the whole this month I've been getting a lot in 3way AI pots, loosing 40/60s, sucking out on 20/80s, getting a lot of ties, getting a lot in folding wars, running into aces with Ax, etc. Do you think this could result in such a graph?

      My June:



      Prior to June (the same games and I don't think my game has changed a lot):



      Those games are Ongame's turbos. But they are faster compared to other sites' turbos. Maybe just too less of a sample or I'm just BE player getting lucky? That red line puzzles me.

      Thanks again for the replies, really helpful.
    • pzhon
      pzhon
      Bronze
      Joined: 17.06.2010 Posts: 1,151
      I don't think ties have a large effect. I'm not sure if HEM analyzes ties correctly, but they are uncommon anyway. You can look up the luck adjustment made when you tied, if you can find such a hand. Multiway all-in pots are also not necessarily analyzed correctly.

      It could be that your play has not changed, but your opponents' play has changed. You should review your games to see if you can find leaks or missed opportunities. It is more of a concern if your red line is flat when your green line is positive than if your red line is flat when your green line is negative, since the red line may be biased in the direction of the green line.