Greater EV with passive play and flopped set?

[GoodOL]

BB: 40/10/.8 - 85 hands

3/6 Hold'em (6 handed)

Preflop: Hero is BTN with 4 [img]/images/graemlins/spade.gif[/img] 4 [img]/images/graemlins/heart.gif[/img].
3 folds, <font color="red">Hero raises</font>, SB folds, BB calls.

Flop: K [img]/images/graemlins/club.gif[/img]9 [img]/images/graemlins/diamond.gif[/img]4 [img]/images/graemlins/club.gif[/img]
<font color="red">BB bets</font>, Hero calls

Turn: 3 [img]/images/graemlins/club.gif[/img]
<font color="red">BB bets</font>, Hero calls

River: 2 [img]/images/graemlins/diamond.gif[/img]
<font color="red">BB bets</font>, Hero calls

I think the standard line here is to either raise the flop (or perhaps wait for the turn). However, might just calling both streets be better?

First, this only applies to specific opponents. I’ve made the following assumptions:
1.) He is relatively passive (i.e. won’t spew with top pair, draw, etc.). He will slow down to a flop raise and fold river with busted flush draw
2.) He has some kind of hand
3.) He will bet turn if flop is not raised (because of 2)
4.) He will bluff river with a busted flush draw if turn is not raised (only shot at winning pot)
These might seem like too precise assumptions, but I think there are enough players out there that play this way to make this analysis valid.

OK, back to the hand. With his flop bet, I put opponent on any two suited cards (his actual hand leads me to this conclusion), top pair, middle pair, bottom pair, or 99…a total of 262 hands. Of these hands, 21% are flush draws, 46% are top pair, 21% are mid pair, 5.5% are bottom pair, 5.5% are two pair, and 1% is a set (I’ve excluded TT+ assuming he would have three bet these preflop.

If he has a flush draw, there are 7 scenarios for the remainder of the hand.
1.) Turn blank, river non club
2.) Turn pair, river non club
3.) Turn club, river non pair
4.) Turn blank, river club/non pair
5.) Turn blank, river club/pair
6.) Turn club, river pair
7.) Turn pair, river club

Let’s look at two lines:
1.) Raise flop, bet turn, call/raise river
2.) Call flop, call turn, call/raise river
I calculate about 0.5 BBs more for line 2 (I used his actual hand, 9c2c, for this analysis; results will be slightly different for other flush draws; also, math/hands are not exact). Now, this only applies to the 21% of the time he has a flush draw, which we cannot know. The rest of the time, we still probably gain by waiting to the river to raise. I didn't do the math...but a flop raise and two bets is 3BBs....flop and turn call, river raise is 3.5BBs. This 0.5 BB will be gained about 70% of the time; 30% of time we would lose 0.5 BB, when we fail to raise when flush comes, but he has a hand like top pair. Also, if he has a weak hand, he might check and call river, but fold to a flop raise/turn bet (2.5 BB vs 1 BB).

An added benefit to playing some hands this way, is that observant players will give your flop calls more respect…perhaps allowing you to get free cards, get to showdowns cheaper, steal turns, etc…with just a flop call.