Hand Analysis plus Thinking about Bluffing

Hand Analysis
Played a hand yesterday, and the river decision interested me. Here's the hand history, first:

http://www.holdemmanager.net
NL Holdem $0.25(BB) Replayer Game#67215616617

Hero ($27.40)
pacs9 ($24.75)
Zhelya ($9.65)
carpfish ($8.16)
Swings_LOL ($63.21)
Helgutsa ($19.84)
FlowerQ ($11.86)
WuFm ($14.50)
B1GF1SH_1 ($15.26)

Hero posts (SB) $0.10
pacs9 posts (BB) $0.25

Dealt to Hero Js Qc
fold, fold, fold, fold,
FlowerQ calls $0.25
WuFm calls $0.25
fold,
Hero raises to $1.25
pacs9 calls $1
FlowerQ calls $1
WuFm calls $1
FLOP ($5) Ac Jc 8c
Hero bets $3
pacs9 raises to $6
FlowerQ folds
WuFm folds
Hero calls $3

I decided to call this small raise with second pair plus second nut draw. With all of the broad way flush cards I can see, made opponent flush hands are rare so I thought I had enough equity to make the call.

TURN ($17) Ac Jc 8c Jh
Hero checks
pacs9 checks
RIVER ($17) Ac Jc 8c Jh 4s
Hero bets $9.50
pacs9 raises to $17.50 (AI)

Basically on the river I bet believing that he would have hands weaker than trips that would call a river bet. His style is pretty loose passive so I can discount many bluffs. Let's create a range of hands that he might play this way. I've gone for {JJ, 88, AJ, A8s, AdKc, AhKc, AsKc, KcJd, KcJh, KcJs, KcTc, Kc9c, Tc9c}. The outcome of this analysis is so critical on that range given, and I'm pretty sure that it's reasonable. Without more reads on the opponent (I only had a few dozen hands on him) this seems fair. I'll assume he shoves on the river with flushes or better in this spot, and calls with all of the one pair and trips hands.

If he shoves over my bet and I feel pot stuck and decide to call the approx EV for betting is ~ -$0.70. So bet/calling is bad, but not a huge spew. If I can find a fold on the river despite getting 5-1 my EV improves to ~ $3.9. I think this is reasonable because I wouldn't expect any passive player at these stakes to ever bluff on that river.

If I decide to check instead and fold to a large bet (again assuming he'll check back his whole range except flushes or better) my EV is ~ $6.4. So in this instance it looks like I was better off check folding on this river (because he'll check back hands weaker than mine and allow me to win at showdown some of the time). This is known as checking equity.

In the actual hand I bet expecting to get called by worse but when villain shoved I felt completely pot committed and called to see Kc9c. Of the three options I could have chosen, my equity from checking was the best followed by bet/folding. I picked the worst choice and therefore I suck!

But this has taught me a valuable lesson on the merits of checking in this kind of situation.

To Float or To Bluff?

Just recently I've made one or two flop bluff raises in situations where I think my hand had enough equity to just call instead. The prime example I can think of is when an opponent c-bet into a three way pot on a 456r and I had Ac7c with backdoor flush draw. Any trey, eight, club or ace improves my hand which is 11 outs and 8 half outs. At the time I saw all of the excellent turn cards and decided to raise the c-bet. Perhaps, though, it is more technically correct to just call instead.

Then again, there are many advantages to raising on the flop. We have a good semi bluffing hand - and my previous work on bluffing with equity shows it doesn't have to work very often to be profitable. If an out does not come in, we're better off in this situation because of the extra fold equity.

But yet at higher stakes, continually raising in these situations is going to allow opponents to 3-bet a high % of flop raises where we're then pot committed to felting ace high.

It's a dilemma to be sure, and fortunately for me I doubt I'll ever have to truly find an answer as the mid stakes games are a million worlds away from my current ones. Raising is likely best at the micros, so I'll persevere with that approach.