Also mostly just going by OP's judgment

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seems like an easy jam

Actually after looking at it more closely, I think there's still a mistake :

You take blockers into consideration but villain doesn't know we have 88. For all he knows, we could have QhJh or 99.

88 is a part of the 46 combos villain needs to call to remain unexploitable.

His calling range includes 20 combos of str8 (67,32s) 15 combos of sets (AA,KK,88,55,44) and 11 combos of 2 pairs (AK,A8s). Now that's when you take blockers into consideration : villain wants to call with his 46 combos but we block 4 of them (88, and 1 combo of A8s).

So villain will effectively call with 42 combos and we beat only 16 of them. 16/42 = 38% equity.

That is a good point. He would have to factor out some hands from his range for constructing his value betting range on the river, but 88 certainly isn't it.

Also thank you for the correction.

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jam. think villain should vb wider than AQ otr aswell...

Why are we including KK when we are removing the other pocket pairs 99 through QQ as non-triple barrell hands. Turn had Ace, so that should have slowed him down KK right?

Considering his min-raise before the flop, hands like A2,A3,A6,A7 also have a good chance of being in villian's range. Flopping a gutshot+ overcard and then hitting top pair ott are good reasons to triple barrel too?

Just to clarify, we are assuming villian is not bluffing because he is reg or because we don't have stats on him? I am trying to understand why we are only looking at value range.

Just curious, why is 67 non-suited but only 23 is suited. If we assume villian opens wide I don't see why we need to included suitedness in 23 but not in 67. It changes the number of hands quite a bit. Suited is 4, but non-suited is 16 and this affects the results.

I have another question. Why is it relevant what range villian came to river with if our decision is to analyze only a jam or call decision we need to only look at hands in his value range that would call a jam right (2 pairs and str8 and sets + AQ)?

^Villain shouldn't open 32o on the button and maybe not 32s
Why?
Depends on our preflop calling range and wether or not we have a flop/turn raising range. If we don't have a raising range before river, vbetting AQ would be a big mistake imo.

Remember villain needs more than 50% equity to vbet river since he'll sometimes face a raise and be forced to fold the winning hand.

KK is a set on the river, QQ isn't. I do think villain is checking back KK some % on the turn. The range is merely an estimation. If you want a more realistic range, you also have to remove some A5, A4 combos.

We are assuming villain is bluffing at an optimal frequency, or 31%.

We are assuming he's bluffing and that he's bluffing optimally. If you reread our posts we say villain is value betting the range we provided plus 40 bluff combinations. We just didn't care what those combinations were.

Edit: Looks like ForeverLearning covered this sorry.

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Wouldn't raise turn. Just ship the river.

Anything wrong with raising the flop in this hand?

I am super confused why anybody would think anybody at 100nl is bluffing an optimal range.

Oh and raise flop, or raise turn, or raise.....

by far the best part in this thread is giving villain 32s and 76o otr yet failing to 3 bet preflop

this tiger and lulz guys are spot on

I guess for me it was just the process of deriving the answer that was more important and just using a range and some estimates to fulfill that need.

Obviously once we have the process down you can adjust your range and estimates to get a more practical answer.

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Great thread.

So math and combinatorics proves that raising sets vs complete unknowns when there's exactly one straight (unlikely and no I'm not adding 32 in here) and no flush possibilities is bad?...mmm, ok
It's not like there's a myriad of other variables to consider

I guess I should quit poker as I have no ability to do the math in my head in real time.

It's interesting that your math can make shoving seem bad and it makes for a good thread but in reality it's pretty silly.

It was just the best way to at least get an idea of what villain's bluffing range should be without getting bogged down by logistics of what combinations villain can actually bluff here.

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^^We're assuming villain is a reg. And yes, shoving 88 on the river vs an optimal opponent is a clear losing play, even if he isn't opening 32s.

What could make shoving ok in practice is that people are defending too frequently vs river check/jams.

Shove

You don't do the math at the table in real time. No one does. You do the work away from the table during hand review to better enhance your learning from spots you were unsure about.

For everyone that is all upset about the conclusion we reached I'll re do the work here using a more appropriate range:

Villain's value betting range on the river with only board cards removed. Also lowered KK combos to account for turn check back and removed some A two pair combos due to preflop dynamics and protection for villain's checking range on the river:

67s (4) 4
AA (3) 7
KK (1) 8
88 (3) 11
55 (3) 14
44 (3) 17
AK (9) 26

Bluffing combos assuming balanced range:
x/(x+26) = .31
.69x = 8.06
x = 11.68 ~12 bluffing combos

Villain bets 38 combos total and has to defend 36 % of the time so .36*38 = 13.68 or about 14 combos meaning villain is defending down to 55. Once we take into account our actual hand villain has 8/11 hands that beat us and 3/11 hands he optimally defends that beat us making the shove -EV. In all reality villain is probably over defending down to 44 for 6/14 combos we beat which still isn't enough.

If we want a profitable raise:

Let x be the additional number of calling hands we beat in villain's bet/call range then:

(6+x)/(14+x) >= .5
6+x >= 7+.5x
.5x >= 1
x >= 2

So if villain calls with 2/9 = ~22% of his AK hands then the shove is break even. Since humans are imperfect beings I would argue that if villain defends any AK he will over defend and the shove will be profitable.

How wide will villain have to bet in order to correctly defend AK vs our shove?

Well villain would be defending 26 combos and that would have to be 36% of his range. So let x be added combos to the value range above then:

26/(x+26) = .36
.36x = 26 - 9.36
x = 46.2222 ~46 combos

So villain would have to be betting worse for value + bluffing 46 more combos or about 72 combos total to defend down to AK and make a shove profitable for you.

Given the range estimates in our earlier posts it's reasonable to assume villain can easily have that many combos in his river betting range making the shove a clear good theoretical call.





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88$

level him into thinking you're repping 88

it's probably the best size given our hand yes

Ever wonder why most other people don't post the math on 2+2 too? hint; it's not because they can't do it.