5/10 e~1k
UTG limps.
MP TAG reg to 50.
Hero is SB AAhd to 175.
UTG flats?
MP folds.
HU
410) flop 822ccs
Hero bets 135. V calls.
680) turn 4d
(Stack at this point is 725)
Hero bets 230?

So weird But I think it’s right idk what size do u like here?

I think an overbetsize makes sense here with these stacksizes, to put his smaller overpairs like 1010 or JJ in a tough spot with a polarizing turnshove.

We can pretty easily balance this shove line with club semibluff combos like KQc or AQc.

I’m really confused as to why we’re betting small on the flop. For UTG to cold call our 3bet after limping in, what weak hands could be in his range that we are trying to induce a bad play from? I’d rather just bet 275 instead and then the turn jam is easier for Villain to call.

Go 1/2 pot - 3/4 pot on flop ,I like $225-$265 , and bigger on turn,

Broadway/sc stuff in clubs, or JJ-? Though he shouldn't be calling that w MP still to act PF. Shrug.

822ccs shouldn't have helped us, we appropriately downbetted, cbetting small, so V'll float. EDIT: my guess is V folds a lot of their range to a 275 flop bet, which isn't great for us on this flop. /EDIT.

Which happened. V's put in 310 of 1,000. Any bet should be committing from here on out.

What size makes sense to induce a call from V's clubs range?

If you think V folds a lot of their range to a 275 flop bet, but floats a smaller one, how big is their range that it has enough stuff in it to care about that? You said yourself that V shouldn’t have a super wide range. So this seems like an ideal spot to target a strong range for value.

I was thinking I could just bet 3 streets geometrically and get all the money in...

It seems like people want me to play a 2 street game here tho.

Why do u think we’re incentivized to play a 2 street game rather than a 3 street game?

Because if Villain has a smaller overpair, we could lose value if an overcard to that pair (esp. an ace or king) comes (or perhaps a club), and if he somehow has a nut flush draw (which you don’t block) then you don’t get the last bet on the river if it misses.

Basically I want to give Villain fewer chances to get away, and if he does get away he’ll lose more money before he does.

My understanding is that geometrically putting your stack in across all the remaining streets actually gives villain fewer chances to get away.

My thinking is this:

Suppose v has 100 combos in his range (for simplicity)
Then OTF when we bet 135 into 410 v must defend w 75 combos to hit MDF.
Then OTT when we bet 230 into 680 he must again defend 75% of his range which is now 56 combos.
And OTR we jam 495 into 1140. And he must defend 70% of his range which is 39 combos.
So by geometrically betting across all 3 streets we get 135 from 19% of his range, 365 from 17% of his range, and the full stack (875) from 39% of his range.


Alternatively if we decide to bet across only 2 streets by betting 275 on the flop and 600 OTT
Then OTF we bet 275 into 410 and villain must defend 60 combos.
And OTT we bet 600 into 960 so v must defend 62% of those 60 combos or 37 combos.
So by geo betting across just 2 streets we force v to put in 275 with 23% of his range and the full stack (875) with 37% of his range.

Now assuming we always have the best hand....
case A yields,
(135)(.19) + (365)(.17) + (875)(.39) = 428.95
And case B yields,
(275)(.23)+ (875)(.37) = 387

Kinda like a turn check

Seems kinda DansGame no?

Thank you. This is an interesting way of approaching the problem of maximizing EV across V's range. Making an explicit mathematical model for guidance, instead of what I had been doing before: blindly using rules of thumb and poorly understood concepts to guide my actions in a hand like this.

It'll be fun to play around with some of the values and concepts in your post. Great post.

This is an interesting post. Thanks indeed. I think this model is entirely valid when we’re considering making a polarized value bet on turn and board is static/dry, like 2223. Your math says we would always prefer to go for 3 streets in this case.

However, I think the model might fail if the board is dynamic/wet. That’s because nuttish hands on turn might no longer be nuttish hands on the river. I.E., your assumption that we always have the best hand on river may fail.

For instance, I noticed this phenomenon when I doing solver analysis on your recent BB vs BTN 3bet pot hand. Flop was T63r. On a T turn, BB is supposed to use 30% on turn and river (geometric sizing) with almost any hand that wants to bet. However, on a J turn, BB is supposed to jam turn when he decides to bet.

For example,
Consider the case where we have red AA OOP and the board is T923sscc. Suppose we know the IP opponent has 87ss or 87cc. We don’t know which. Pot is 100. We have 80 left. Optimal sizing is jam. If we use non all-in turn sizing, we will be forced to check any spade, club, J, or 6 (well over half the deck). Plus opponent gets to bluff us off our hand some of the time. We also miss value on any other river card when draws brick.

Yes, geo sizing becomes more appropriate as our value range approaches 100% eq, and this forces v to defend widest.

3 streets seems fine here, don’t think 2 streets is significantly worse though (v may overfold on high card turn/rivers and may call lighter vs 2 bc bigger size seems more bluffy so you are perceived to have more AK). Basically whatever you think gets the most out of TT.

What if our value range isn’t approaching 100%?

How does getting the money in across 2 rather than 3 streets help us?

So, this calculation is internally consistent in a self-contained way, but it's relying on assumptions that I don't agree with.

First, we're assuming that we'll always have the best hand. I think Villain can have some flush draws, especially since we don't block the Ac, and of course we'll still lose to a turned or rivered set some of the time too, but overall I mostly agree. The second assumption, though, is that Villain calls with MDF frequencies.

I think if you run this calculation again but assume Villain calls the flop significantly above MDF, now you're looking at a situation where you'll want to bet bigger. This is especially true if there are certain runouts that will cause Villain to over-fold later in the hand.

Underlying all of this, and what I haven't seen from anyone, is: what is Villain's range that he is limping UTG and then cold calling our 3bet with? I think Villain has to have a narrow, strong range to do this. And so on this flop, I expect Villain to play as if he still has the best hand, if he has something like TT+. I would expect that Villain's calling frequency on the flop is much higher than MDF, since I don't expect him to have too much in his range that he'll feel good about folding on this flop. (He would have folded it preflop!)

So I think betting bigger on the flop is better here. We shouldn't just go on auto-pilot and assume Villain's range is wide enough that we need to induce calls with marginal hands. Villain shouldn't have too many of those!

As our equity moves away from 100% we will gain more from equity denial by getting the money in across 2 streets vs 3

The UTG flat is very strange. I tend to agree he’s very heavy toward medium to large pocket pairs (88-JJ) — he might even have QQ-KK that was going for the l/rr. He can maybe have some very strong suited broadways and perhaps some suited connectors, but it’s a small part of his range. Guess that means that for the GTO analysis we should be using geometric sizing. But I dunno if we should really be applying GTO in this spot. Exploitatively, I think our line looks more value heavy when we take a 3-street line, and so, I think I’d rather go for 2 streets here, sizing up on flop and jamming turn would be my preference.

if we are bluffing it will work more. Like if villian has 9s. He is already scared after we bet 80 percent pot on flop.

If we actually have it are size matters less. I think you do get more calls with a smaller size but they also have a chance catch up.

I like the idea of blasting flop in turn mainly because I like the idea of bluffing when I don’t have it.

I agree with the approach but disagree about equity denial having much to do with it. It is nice in some spots for sure tho.

I think it comes down to how wide v will call large bets. If the board is super dry he is going to be able to talk himself into folding a ton of the hands we're targeting because we have exactly what it looks like we have. On wet boards he can "put us on" a bunch of draws and will call with those middling over pairs and, if he's sticky, any random piece of sdv he has

In general I like to try to play very close to theoretically sound but this is against a guy who limp called a 3bet. We should be playing more exploitative imo

As for the hand I think I like slightly bigger on flop (like 145 or 150) and/or slightly bigger on the turn (40% instead of third) If we can get an extra 50 bucks into the pot it makes folding river that much tougher for villian without changing his flop and turn calling range

My answer was just wrt the theoretical benefits of 2 streets vs 3 as our value equity moves away from 100%. Using all 3 streets allows villains calling range to fully realize it’s equity; when we have 100% we don’t care but as our eq goes down we start to prefer 2 streets for equity denial. This happens to map onto what you are saying bc dry boards are static and our nut hands will have very high equity (and benefit less from equity denial), so they often prefer geo sizing across all remaining streets, while on wetter boards our nut hands have less equity and benefit more from denying equity by using larger sizing across 2 streets. I agree that equity denial is not especially important in this spot though. And yes I’m not arguing we need to be playing gto here.

Chaos: Did you put this hand through a solver?

I'm really persuaded by your, Petrucci and jvds' argument. I don't see how we can have/protect any bluffs across three streets here. Also, our river bet would target a very narrow range anyway and some of that range would call our turn jam too getting ~2-1.

You started the hand with 100 BB's. Figure out your sizings to GII OTT.

Preflop bigger. Flop bigger. Turn bigger.

EZ game.

I will try to run it later today giving opponent 88-QQ (and I’ll run a second sim where I give the opponent a few combos of suited Broadway hands so that equities aren’t perfectly realized on turn). Geometric 3 street sizing for 2SPR would be (1+2b)^3 = 5 —> b = 35% per street. Geometric 2 street sizing for 2SPR would be (1+2b)^2 = 5 —> b = 60% per street. So I can just set solver bet sizing equal to 35% or 60% on every street. I’ll try to find a standardish 3bet range for SB. I guess that SB will have some flush draws in their range as well. Will tinker with ranges and see what solver says and report back.