Folding KK pre,cumulative equity calcs, math tutor needed

    • dallievas
      Joined: 30.11.2007 Posts: 822
      I had hard decision to fold KK preflop to big action 3way ,during hand didn't know my exact equity,only had a hunch that it can be low.
      Hand converted with online hand converter:

      Play hand

      $0.02/$0.04 No-Limit Hold'em (5 handed)

      Known players:
      SB (Hero):

      Preflop: Hero is SB with K, K.
      MP3 folds, CO raises to $0.16, BU raises to $0.56, Hero raises to $1.25, BB folds, CO raises to $3.62, BU raises to $7.48, Hero folds.

      Flop: ($12.39) 9, 7, 5 (2 players)

      Turn: ($12.39) 3 (2 players)

      River: ($12.39) T (2 players)

      Final Pot: $12.39.
      I didn't had enough sample size (only ~100 hands) on opponents:
      No1 raiser vpip 20/pfr 12/af 3,1/ 3bet 0/4bet range 4 (only 2)
      No2 3beter -32/12/1,5 3bet 3,2 (350 hands), 4bet range 4,2(8 hands);
      My image normal tag.
      For theory discussion sake let's assume that they have tightest ranges,at least one of them should have AA.I assumed 2 ranges :I - AA ( 6 combos+ KK 1 combo cos I have KK) and II- AA (1 combo if opp I have AA,+KK 1 combo+rest AK+QQ).
      equity win tie pots won pots tied
      Hand 0: 81.946% 81.71% 00.23% 50371344 142614.00 { AA }
      Hand 1: 18.054% 17.82% 00.23% 10986372 142614.00 { KK }

      equity win tie pots won pots tied
      Hand 0: 68.884% 68.46% 00.42% 9378330 57670.00 { KcKs }
      Hand 1: 31.116% 30.70% 00.42% 4204762 57670.00 { AdKd, AhKh, AcKd, AcKh, AdKh, AhKd, AsKd, AsKh }

      equity win tie pots won pots tied
      Hand 0: 50.000% 02.17% 47.83% 223260 4913652.00 { KK }
      Hand 1: 50.000% 02.17% 47.83% 223260 4913652.00 { KK }

      Main question how to calculate my cumulative equity against those 2 ranges?
      My try (I'm not math guy so ...... :D )
      vs Ist range (16%KK (cos 1 combo left of 6 possible)+ 84%AA)= 0.16x0.5+ 0.84x0.178=0.229=22.9%
      vs IInd range (16% KK+16% AA+68% AK+QQ)=0.16x0.5+0.16x0.178+0.68x 0.68=0.57=57%
      So 50% of the time we have 22.9% equity and other 50% we have 57%,
      so overall our equity should be 0.5x0.229+0.5x0.57=0.39=39%
      Pot odds to call is 2:1 (I need 33% to be break even)
      but pokerstove says :

      equity win tie pots won pots tied
      Hand 0: 15.611% 12.34% 03.27% 12515509 3319668.67 { KdKs }
      Hand 1: 71.280% 67.44% 03.84% 68410482 3892605.67 { AA, KcKh }
      Hand 2: 13.109% 12.28% 00.83% 12453447 844083.67 { AcAs, KcKh, QQ, AcKc, AhKh, AcKh, AdKc, AdKh, AhKc, AsKc, AsKh }

      Q:1)are my calcs right?
      2) what to do in situation like this?( when you strongly suspect that one of them have AA).
      3) how to calculate cumulative equity?
      4)any thoughts on other possible ranges
      Thanks for long reading and answers. :)
      very :f_confused:
  • 5 replies
    • Bliausmas
      Joined: 11.03.2010 Posts: 741
      Well it's pretty tough decision. Both opponents look fishy but not maniacs. It's very likely that both of them have no less than {QQ+;AK}. And against those ranges you're just a slight favorite:

      equity win tie pots won pots tied
      Hand 0: 36.266% 34.40% 01.87% 130146252 7058028.00 { KdKs }
      Hand 1: 31.867% 29.00% 02.87% 109697442 10864470.00 { QQ+, AKs, AKo }
      Hand 2: 31.867% 29.00% 02.87% 109697442 10864470.00 { QQ+, AKs, AKo }

      Being 100BB deep I'd say call, but now being 200BB deep maybe fold isn't a bad choice. Unless you could put them on wider range, like {JJ+;AQ+}.

      However I'd probably call, since I don't like to give fishes too much credit :)
    • dallievas
      Joined: 30.11.2007 Posts: 822
      Hi Bliausmas, why u still not in bed :) :D
      Overall I agree with you almost 100% and I'm usually not folding KK pre,but I wanted to know how I'm doing if one opp has a lot AA combos in his range? And wanted to know how to calculate my equity vs 2 by hand.
      Thanks for reply.
    • Bliausmas
      Joined: 11.03.2010 Posts: 741
      I never sleep :D
      What exactly do you mean about equity vs 2 opponents? You calculated it right before, also you can just use the "Preflop" tab for simplicity when entering opponents' ranges.
    • pzhon
      Joined: 17.06.2010 Posts: 1,151
      A big complication is that there is a side pot. One of your opponents started with only 90.5 BB, while the effective stack depth is 187 BB. In the 272.5 BB main pot, you have two opponents. In the 194 BB side pot, you only have one opponent. So, there isn't just one equity you need to have in the main pot, there is a tradeoff between equities you can have in the main pot and side pot to justify a call.

      For simplicity, suppose each opponent has a range of QQ+ AK. In the main pot, your equity is 36.266%, as Bliausmas reported, so you get 36.266% of 272.5 BB, or 98.82 BB.

      From the side pot, you might want to pit KK against the range of QQ+ AK; KK would have 57.191% equity. Unfortunately, that's not right because of the card removal effect, which takes some work. PokerStove lets you pick specific dead cards, but not dead cards taken from a range of hands. I don't know of a simpler way to get the exact answer using PokerStove than removing each hand individually, and taking a weighted average. To see that this might have a significant effect, imagine your opponents either have KK or AK while you have KK. If you know that both opponents have KK or AK, then they must both have AK, since if the first has KK it is impossible for the second to have a king.

      I don't advocate doing the following, but for completeness I'll show it.

      When you have K:spade: K:club: , there are 21 possible combinations of QQ+ AK, and 276 ways both of your opponents could have hands in QQ+ AK.

      A:spade: A:club: 12 combinations, equity 73.792%
      4x A:spade: A:heart: 12 combinations, equity 74.429%
      A:heart: A:diamond: 12 combinations, equity 75.066%
      K:heart: K:diamond: 12 combinations, equity 40.418% (50% chance to start ahead but you can't hit a set if you are behind)
      Q:spade: Q:club: 16 combinations, equity 50.171%
      4x Q:spade: Q:heart: 16 combinations, equity 50.530%
      Q:heart: Q:diamond: 16 combinations, equity 50.889%
      2x A:heart: K:heart: 12 combinations, equity 61.054%
      2x A:heart: K:diamond: 12 combinations, equity 61.552%
      4x A:spade: K:heart: 12 combinations, equity 61.012%

      So, to find your equity in the side pot, you can take a weighted average of these possibilities, weighted by the number of combinations, counted with multiplicity. The result is that your equity in the side pot is 60.021%, significantly higher than if you ignore the card removal effects. You would get 60.021% of 194 BB, or 116.44 BB.

      The total amount you get back for your 155.75 BB call would be 98.82 + 116.44 = 215.26 BB, for a net profit of 59.51 BB by calling.

      Of course, if you feel that your opponents' ranges are more weighted toward AA than QQ, then you get different values, and these can make folding correct.
    • dallievas
      Joined: 30.11.2007 Posts: 822
      Thanks a lot ,very deep explanation,have to study it a bit.