Setting a Solid Player on Tilt

Here is the hand of the night (not the biggest pot, but the most interesting to analyze) from last Thursday night.

First, the set-up:

Villain is the same guy from this hand. Excellent player, sitting to my immediate left. He moved from another table when two short-handed tables consolidated. He’s clearly stuck, and he’s playing big pots with solid hands in an effort to double up.

On one prior hand, I has Ac-Kc in the SB. 6 limpers around to be. I think about raising, but just call. Villain then raises to $30. All but one other player folds. Villain has about $250 or so behind. I think about just pushing, because I think he’s on a steal. I should have pushed, but I just call. Flop is 8-4-2, and Villain pushes. Other player folds.. I think for a while then fold. I show him my AKs and say, “This could have been a fun hand.”

He looks surprised, and then shows me a deuce. I ask what he would have done if I had just pushed PF after his raise. He says, “Well, if I had pocket deuces I would have definitely called.”

I replied, “Yeah, like you didn’t.” He just smiles, confirming (I believe) that he hit a set of deuces on the flop. But that was an odd push rather then check if he hit his set, so maybe he really had junk, like the Hammer or something...

So, back to the hand in question.

I have about $1100 and have everyone covered. I am UTG with Kd-Qs, and I raise to $20. Four callers, including Villain. Pot is about $85.

Flop is Td-9d-3s. I bet out $40. Villain pushes. Everyone else folds. Pot is now $289, and its $129 more for me to call. I think for a long time, and here’s where I end up:

Villain has either has (1) a diamond flush draw, or (2) a decent but not great hand, like maybe a pair of tens, something like JT or AT. Since he’s stuck, I believe he would push a diamond flush draw. I don’t think he has a great land like a set or two pair because I’m fairly certain that he would have checked to induce a bet, and then pushed. I don’t think he has a big overpair, like AA through JJ -- I think he would have checked either of those hands, also, to induce a bet and then push.

So where does that leave me? I think that I have between 7 and 10 outs -- any J for the straight (maybe less the Jd), any K and any Q (maybe less then Qd). I run some calculations for all of these possibilities in my head and then say, “I’m getting over 2 to 1 on my money, so I think I have to call.”

He replies, “Ace king?”

I say, “No, not that good.” I show my K-Q and he reveals Q-T, no diamonds. Just about exactly one of the two hands that I put him on. So I actually have 7 outs, or runner-runner flush.

The final board is Td-9d-3s-Kc-8h, and I win with a pair of kings.

Villain starts berating me. “What a terrible call! Horrible!” He proceeds to stomp out of the poker room. Very uncharacteristic behavior -- he’s always been Mr. Cool. I guess he’s not used to losing. I wish he would have rebought, but it was late.

So I’ve been wondering ever since whether I calculated correctly and if the math backs up my decision. Was my call right? With calculator and pencil in hand, here’s what I come up with:

First his range of hands. Since I’m torn between flush draw and one pair, I’ll say 50% flush draw and 50% one pair. I think he would push with the nut flush draw or a lower flush draw. To run some calculations for the hands I’m guessing, lets say he has these combinations:

Ad-Xd -- 25% probability
6d-7d -- 25%
Q-T -- 50%

My equities for each hand:

Against Ad-Xd, he is a 75/25 favorite.
75% x -129 = -97
25% x +297 = 74
My total equity = -23

Against 6d-7d, he is a 55/45 favorite.
55% x -129 = -71
45% x +297 = 134
My total equity = 63

Against Q-T, he is a 69/31 favorite.
69% x -129 = -89
31% x +297 = 92
My total equity = 3

-23 x 25% = -6
63 x 25% = 16
3 x 50% = 1
My total equity for the hand is about +11. This is close to a coin flip, but this justifies a call.

If his hands was turned up and I could see his actual hand, its still a call, as my equity vs. Q-T alone is roughly a coin-flip but just positive.

So, I did calculate correctly in the heat of battle and made the right call. However, I don’t think I could ever convince him that I was right...