Re: River play? - relevant math inside.
you are correct pdx.
Based on the way villain played the had, he either has a flopped straight or set on the turn.
55,88,99 make up 9 combinations. There are also 9 remaining combos of 67. On the river, there are 7 set/quad combinations, and 9 combinations of straights. When villain caps the turn, he is betting the river.
If we check-call the river we get 1BB 56% of the time and lose 1 BB 44% of the time for a total of .13 BB EV profit
If we c/r the river, villain will 3-bet when he has the set, and call the c/r when he has the straight. (We assume that every once in a while villain 3-bets with a straight or worse, so we can call his river 3 bet).
We earn 2 BB 56% of the time and lose 3 BB 44% of the time for a total of -.17 BB EV loss
If we bet/call the river villain will raise with the straight less frequently than he raises with the boat. He will always raise with the boat, so we lose 2BB 44% of the time. In order for the EV of bet/call to be greater than check/call:
.56*(1*(1-x)+2*(x))-.44*2=.13
where x is the frequency with which he raises when he has a straight. Solving, we find he has to raise when bet into with the straight at least 80% of the time for bet/call to be more profitable than check/call. This kind of analysis is important, hope I did it right.
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