I am trying to figure out spots where opponent can bet any two. Section is "How profitable should our opponent's bluffs be in position on the flop?"
For a simple example, raising the button, bb calls, pot is $4.50. He checks, button bets $3. Button paid $2 to see the flop, and for his cbet to have an EV of at least $2 with his worst hands, he needs the big blind to fold 67% of the time.
However this doesn't seem right. The flop isn't always seen, sometimes he gets 3bet and loses right away. Say he's holding his worst hand, 20% he gets 3bet and folds, 30% of the time he steals the blinds, and 50% of the time, he sees a flop.
How much is he actually paying to get to the opportunity of cbetting?
20% of the time he folds to a 3bet, if I multiply the $2 he pays to see the flop by 120%, it goes to $2.40. However, he wins $1.50 30% of the time stealing blinds, so he wins back $0.45. Which isn't a big difference, it only adds up to him needing to win back $1.95 the 50% of the time he sees the flop. All assuming SB folds, BB checks 100% postflop, ranges of BB is bluffcatchers, button is polarized.
Something seems missing with this model.