musings on the theory of KK vs. K2

    • belayd
      belayd
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      Joined: 17.03.2011 Posts: 1,021
      One of the most extreme examples of dominance in holdem is KK vs. K2, where KK is a 19:1 favorite. But let's look at what happens when a good player and a poor player are HU with these two hands. Both the good and bad player will play the KK pretty much the same way, so neither has an edge. But while the good player will fold K2, let's say 93% of the time (except in big blind and when blind stealing), let's also say the bad player plays his K2 some 40% of the time (because, after all, a single King is a pretty high card). If the good player plays his K2 7% of the time and wins against KK on a 1:19 ratio, his win rate is 7% of 1/19 or 0.38% of the time. But if the bad player plays his K2 against KK 40% of the time and has the same win ratio, he wins 2.1% of the time. The bad player therefore has an edge over the good player to an ugly amount of 5.5:1 simply because of his bad play. So it looks like the nature of poker itself rewards bad play.

      I keep trying to find something wrong with my reasoning and not succeeding. Anyone want to comment?
  • 10 replies
    • EmanuelC16
      EmanuelC16
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      Joined: 02.01.2010 Posts: 13,897
      You've only considered AI pre for a percentage, so without any postflop actions and not considering ranges, just these hands, you are correct, the bad player will win a higher percentage of the time because he plays it everytime. Now do the math on the chips won or lost. ;)
    • Elroch
      Elroch
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      Joined: 08.02.2011 Posts: 150
      If poker was a game where you got 1 point for every pot that you won, the logic in the initial post would be correct. In that case, correct strategy would be to play every hand 100% of the time in every position. Perhaps the more usual game is a bit more interesting. :f_biggrin:
    • belayd
      belayd
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      Joined: 17.03.2011 Posts: 1,021
      Originally posted by EmanuelC16
      Now do the math on the chips won or lost. ;)
      Could you help me with that?
    • StoneJ
      StoneJ
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      Joined: 03.08.2010 Posts: 153
      This makes no sense.
    • SickAtHome
      SickAtHome
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      maybe its just me, but let's assume:
      each person has the same stack (therefore an AI would determine winner)

      However, if the good player doesn't play the hand, he 93% of the time has a good chance of winning the HU + 0.38% chance of winning.
      The bad player however, only has 60% chance of an average chance of winning the HU + 2.1%.

      What you forgot is that if you don't win the hand... you don't lose it either.
    • EmanuelC16
      EmanuelC16
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      Joined: 02.01.2010 Posts: 13,897
      Originally posted by belayd
      Originally posted by EmanuelC16
      Now do the math on the chips won or lost. ;)
      Could you help me with that?
      I'll try! So lets consider $100 stacks to make it a bit more simple to calculate. Folding has 0EV in both players case. Therefore, if we are dealt KK vs K2 100 times and get it AI 40% of the time, this means 40*$200=$8k to be split. KK has 93% equity = $7440 out of $8k, right? Since he invested $4k to win $7440 this gives him $3440 EV, yes? K2 has 7% equity = $560 and invests $4k => EV = -$3440 (obviously, since they are 1v1, what the other won, the other lost).

      Now, if the "good" player folds K2 usually and plays it 7% of the time.

      K2 vs KK 100 times, 7% => 7*200 = $1.4k. 7% equity => $98 for Hero with $700 invested which means a loss of $602, while in the other case Villain would lose $3.4k, therefore we would make a profit of ~$2.8k.

      Not sure all the math is OK since it's 3:30 AM here but wanted to get it done! :D I hope you understand what I mean... basically, if you get into +EV situations more than -EV it will end up +EV in the long run, even though you can't play perfect and always be +EV every hand in every situation because you cannot know exactly what your opponent has AND how he reacts to your actions.

      Like someone before said: it's not about winnings every hand, it's about winning the most chips/money.
    • belayd
      belayd
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      Joined: 17.03.2011 Posts: 1,021
      Thank you, emmanuel. :) But you gotta stop staying up so late on a weekday. ;)

      I also just thought of something. If hero plays 7% of his dominated hands and wins 0.38%, he loses only about 6.4% overall. But if villain plays 40% of them and wins 2.1%, he loses a horrifying 37.9% overall. Yes, he makes more profit on the K2 vs. KK HUs than hero does, but in terms of the bigger picture he's bleeding losses like a stuck pig while hero's losses are manageable. Which I guess is why the better players win in the long run.

      EDIT: I think that my observation sheds light on why donkouts are so noticeable to good players--they benefit from far fewer of them and lose to far more of them. But that doesn't mean bad play is profitable or recommended.
    • tokyoaces
      tokyoaces
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      Joined: 01.04.2009 Posts: 1,883
      I just want to add that this is concept, that winning players win more money as opposed to more pots, is one of the first things covered in The Poker Mindset.

      Everyone should read it!
    • Saruniks
      Saruniks
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      Joined: 30.08.2010 Posts: 1,213
      [ ] makes sense
      [x] proof that poker is rigged
    • Saruniks
      Saruniks
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      Joined: 30.08.2010 Posts: 1,213