Are my odds better than they seem?

[R_Ellender]

Here's a hand I played in a tournament recently, I'd like to hear your comments on my analysis.

The blinds are 25 and 50(pot=75). With two loose limpers ahead of me, I decide to limp from a middle position with A [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/spade.gif[/img](pot=225). There's a limp behind me followed by a +250 raise on the button from a tight, somewhat predictable player(pot=575). Both loose limpers fold, and the action is on me. Judging by a tell I have on the player, combined with his tendency to only raise his big pairs with so many people limping into the pot, I put him on KK or QQ. It costs me 250, so the pot is laying me about 2.33:1 odds, and my hand will beat KK or QQ about 33% of the time(2:1), so I call(pot=825), but not for the reasons most people would.

Yes, the pot is laying me 2.33:1 on a 2:1 shot, but my odds are 2:1 assuming that I only win as often as my cards allow me to. When I made the call, I took into account the odds that I could bluff my opponent, so I figured my +EV was higher than it should be.

Here's how it worked out... The limper behind me folds, and out comes the flop.

FLOP: Q [img]/images/graemlins/heart.gif[/img]T [img]/images/graemlins/club.gif[/img]6 [img]/images/graemlins/heart.gif[/img]

I'm either way behind(against a set) or drawing to five outs. Either way, I didn't come out in the lead on the flop. I check to the raiser, and he bets 400, laying me about 3:1. Based on my read of his betting patterns(he would have checked his set), I decide he has KK, so I have five outs... or do I have more?

My full outs were:

3 aces + 2 tens = 5

But then I considered my bluffing outs... three queens and nine hearts. If a queen comes, I can represent trips, and if a heart comes, I can represent the flush. So far, I've been checking to the raiser when I felt I was behind or when I was on a draw, so I was confident I could represent either hand with a check-call on the flop. I think any one of these cards can win for me about 75% of the time(since bluffing can't be 100%), so I count them as 9 outs.

3 queens + 9 hearts = 12 * 0.75 = 9

In my mind, I have 14 outs to win this pot. With 14 outs, my odds of improving on the turn are 2.2:1, and the pot is laying me 3:1, so I call(pot=1625).

TURN: 8 [img]/images/graemlins/heart.gif[/img]

I like this card alot, I just need to decide how to play it. I decide that a bet smaller than half the pot would be a good choice because this player has already seen me make small value bets on the turn and river on previous hands(where I knew I had my opponent beat, but my opponent couldn't lay down because of the small bets). I bet 600, representing the flush, and I can tell by his visible disappointment that he hates the bet. Meanwhile, I'm considering the odds in my head... I believe there's around a 75% chance he will fold here(because he knows I will bet the river), but if not, I still have a few outs.

I still have the aces and tens, but the A [img]/images/graemlins/heart.gif[/img] and T [img]/images/graemlins/heart.gif[/img] may be no good(if my opponent holds the K [img]/images/graemlins/heart.gif[/img]), so I count them as 1 out. Add the other 2 aces and the other ten, and I have 4 outs, giving me about a 9% chance of improving(10.5:1 or so). It's not looking good, but since I assess my chances of winning the pot right there at 75%, I'm not so worried.

He calls. (pot=2825)

RIVER: 2 [img]/images/graemlins/spade.gif[/img]

BOARD: Q [img]/images/graemlins/heart.gif[/img]T [img]/images/graemlins/club.gif[/img]6 [img]/images/graemlins/heart.gif[/img]8 [img]/images/graemlins/heart.gif[/img]2 [img]/images/graemlins/spade.gif[/img]

Well now my only chances of winning are representing the flush. With a pot of 2825, and my opponent having about 1600 remaining in his stack, I decide to bet 1200. He's really not happy here, but unfortunately for me, he was on some kind of "my kings just got cracked" semi-tilt. He tells me, "If you have the hearts, you win." and he shoves the rest of his stack in. Needless to say, the table was shocked when I said I had nothing and mucked my hand, but that's not the point.

The way the hand was played, he could have only beaten a bluff, because I wouldn't have played top pair or a pair of tens or sixes like that. I would have been long gone with a pair of tens, and I would've continued to play passively on the turn with top pair(when the [img]/images/graemlins/heart.gif[/img] fell), because I didn't represent a hand like AQ with a raise preflop(and my opponent represented a big hand). Also, I'm not going to be in there with a pocket pair unless I trip up on the flop(since he thought I had a boat), so he can't put me on a hand like JJ or 77. I'm not going to check-call the flop with those hands, much less bet out the turn and river with them. In other words, with creative postflop play, I increased my odds of winning against the big pair significantly, though the results weren't there on this particular occasion.

So are my odds better than they seem throughout this hand? Or should I eliminate counting my bluff outs, or stop considering my chances of bluffing at some point while calculating preflop odds? I believe thinking along the lines of maximizing my chance to win each and every pot that I get involved in, even without the cards, is a +EV play in the long run. That's not to say I'm playing to win pots, because Sklansky wouldn't agree with that philosophy. But I'm coming to find out that in poker, no-limit especially, each pot has alot more dead money in it than people are aware of.