Issue with Platinum article on Nash Equilibrium and Bluffing/Calling Frequencies

    • livelydolphin
      Joined: 12.04.2010 Posts: 30
      For example, let's imagine a board of JsTs4 2, that you are obviously on a draw (straight or flush), and that player 2 has a made hand. If the river is a 6s, completing possible flush draws, and you hold KQ, then, to determine how often to bluff, you should consider how often you would have a flush.

      (As9s-As5s, As3s, As2s, 9s7s, 8s7s, 8s6s, 7s6s, 7s5s, 6s5s, 5s3s) is an example for a realistic range, amounting to 14 different hands. You will hold a busted straight draw just as often (7 combinations each of KQ and 98, assuming that you would have played OESD+FD differently earlier on).

      I thought there'll be 15 combinations each of KQ and 98?
      e.g K :spade: Q :club: , K :spade: Q :heart: , K :spade: Q :diamond:
      K :club: Q :club: , K :club: Q :heart: , K :club: Q :diamond: , K :club: Q :spade:
      K :heart: Q :club: , K :heart: Q :heart: , K :heart: Q :diamond: , K :heart: Q :spade:
      K :diamond: Q :club: , K :diamond: Q :heart: , K :diamond: Q :diamond: , K :diamond: Q :spade:

      If my combinations are indeed correct, does that mean that in this case, my probability of having a busted straight draw = 30/44 = 0.681?
      Hence a flush board is actually not as scary as a straight board? (Assuming the hand range for a straight draw is only connectors, KQ/ 89)
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