Razz ($2/$4), Ante $0.25, Bring-In $1 (converter)

3rd Street - (1.00 SB)

Seat 1: xx xx J___folds
Seat 2: xx xx Q___folds
Seat 3: xx xx 4___folds
Seat 4: xx xx 7___calls
Hero: A 6 K___brings-in___calls
Seat 6: xx xx 7___raises
Seat 7: xx xx A___folds
Seat 8: xx xx 8___folds

4th Street - (4.00 SB)

Seat 4: xx xx 7 3___bets
Hero: A 6 K 2___calls
Seat 6: xx xx 7 Q___folds

5th Street - (3.00 BB)

Seat 4: xx xx 7 3 Q___bets
Hero: A 6 K 2 T___calls

6th Street - (5.00 BB)

Seat 4: xx xx 7 3 Q J___bets___calls
Hero: A 6 K 2 T 6___raises

River - (9.00 BB)

Seat 4: xx xx 7 3 Q J xx___checks
Hero: A 6 K 2 T 6 9___checks

Total pot: (9.00 BB)

The chances of me improving to a T low are: 3 3s, 3 4s, 4 5s, 2 7s, 2 8s, and 4 9s. There are 33 cards left in the deck, and 18 of them help me. I am 54% to improve to a ten-low.

The chances of him improving to a 9 low are: 3 2s, 3 4s, 4 5s, 2 6s, and 4 9s: 16/33, or 48%.

The chances of us both not improving are ~24% (.52x.46).
The chances of me improving and him not improving are ~28%.
The chances of us both improving are ~26%.
The chances of him improving and me bricking are ~22%.

So, by just calling, I'm calling 1BB at a 6BB pot, getting 1:6 on my money with 27% equity in the pot, which is def. +EV. However, by raising, I believe he'll fold to a bet the 24% of times we both don't improve.

Temporarily ignoring any money that goes in on 7th.

Calling 6th gives me 28% equity in a 7BB pot, or 1.96BB at the cost of 1BB. Calling 6th has an expectation of +0.96BB (ignoring 7th, which is bad, but I'm going to do it anyways because I'm lazy).

Raising 6th gives me 52% equity in a 9BB pot, or 4.68BB at the cost of 2BB. Raising 6th has an expectation of +2.68BB. This assumes he always folds unimproved, which is not an unreasonable assumption. I think my raise also gets me a free showdown in the case that we both improve.

So my line looks like this: Raise 6th. If improved, check behind. If unimproved, bet. I think this is an unusual enough spot that I don't have to worry about balancing my range in this spot. After the raise on 6th, I win a 9BB pot when he does not improve (52%). I lose an 11BB pot when he does improve (48%).

So: 48%: -2BB
52%: +7BB

= 3.64 - 0.96 = 2.68BB

If I call 6th, I believe he leads 7th 100% of the time. I will only call when I improve. So, 28% of the time I win a 9BB pot and 26% of the time I lose a 9BB pot. The other 46% of the time I fold.

So: 28%: +7BB
26%: -2BB
46%: -1BB

= .28x7-.26*2-.46*1 = 1.96 - 0.5 - 0.46 = 1BB

Thus, the difference between the two lines is ~1.68BB.

Can I get some feedback on this analysis? This actually seems to say that raising 6th is the best play by a wide, wide margin. It also seems that both lines lose money in the long run, but nowhere near as much as simply folding, as I have way too much equity in the pot for a fold here, and that raising 6th is the best way to maximize my equity at this point in the hand.

Fold Third and you don't have to do any math.

I'm aware. :P Not wondering about early hand, just the line once I've hit 6th.

Fold sixth as well. Also fourth and fifth.

You fold sixth here with >30% equity?

He'd fold with 49.5% equity. Why chase?

As cracked out as this hands is how do you not fire the river after RAISING ?? 6th?

I mean, if you're gonna go crazy - go crazy.

I agree with this 100%, but I see it happen all of the time. You chase and make a hand on the river and then check.

When he checks he is more or less telling you, I can't beat a T.

Alternatively, he's telling you "Well, you raised 6th, so now that I've made my 8 low, I'm going to check/raise you."

I thought about betting the river for a while, but finally decided to check because I don't see the value in the bet. Anything that beats me looks me up, and some portions of that range check/raise me, and I don't think he calls enough with an unimproved J to make this a worthwhile bet.

I think you rarely get c/r here. Sometimes, but not very often. He probably calls with a J more often than he c/r.