Would generally just flat vs a normal sized raise, but $15 is so tiny I think it's best that we 3bet for value.

After extra info. I think if we 3bet 55-60 there is a chance we end up multiway which I think we should avoid. Which leaves larger three bets which will most likely take down the 35 in the middle or set mining. I think taking it down is the way to go. Bet 70-75.

I actually don't think it's close and think 3-betting is quite bad.

Haven't heard one reason to do anything but flat.

If you 3-bet here, it's more of a semi-bluff than for value.

Which hands "give us value?" Barely any, really. V is very likely to fold most lower pocket pairs (hands against which we are 4:1 favorites). V will stick around with 99+, AK. From the other broadways, we sometimes get calls from hands like KQs, AJs, AQ, etc.

So a 3-bet generally builds a pot against a range that a) is 50/50 vs. TT and b) is such that we need to slow down/lose on any non-T flop with a card > T.

There's very little "value" in 3-betting.

3-betting is mostly a semi-bluff because V might (or might not) fold QJ, KJo, AJo, etc. In that case, our 3-bet uses fold equity to get V to fold out ~50% equity. That's actually a fine outcome - but it's not sufficient for 3-betting given all the other variables.

If we 3-bet, we are of course 3-bet/folding, but there's nowhere near enough value (if any) in a 3-bet to justify a 3-bet knowing we'd have to fold to further action.

Do we get 4-bet a lot? Probably not. But we're not even doing so well against V's likely calling range pre-flop, so there's no reason to open yourself up for a 4-bet.

Another thing to consider:

We are basically readless. That's another reason to flat. 3-betting would really only make sense if we think V will open/call a lot more hands than your average V.

Another reason to flat. V3 may play the hand no matter what we do. Raising to say $60 and getting a call from V3, which could trigger more calls from an earlier Vs, would be a mess. We'd go to the flop without the best position with TT multi-way and a $120-$180 pot and $400 behind, allowing for no maneuverability and giving up on a lot of flops.

Also, V3 reaching for chips could suggest he's raising. That would be even worse.

Garick, I know you want to look at "math," but that's really difficult. It's like looking at chess game and asking for an evaluation of your position. A computer program could calculate a piece-adjusted score, but it will change so much with subsequent moves.

We could however look at V's range further. It's insufficient because there are other active villains (other possible moves from them), other villains left to act, and future streets to consider with too many permutations to justify calculating, but it's a start:

Against that total range, TT has 58% equity.

Let's assume V calls a 3-bet with 88-JJ,AQ-AJ,KQs?

Against that range, we have 57% equity.

Let's assume V 4-bets with QQ+,AK.

Against that range, we have 0% equity because we fold and lose our 3-bet chips. (We actually have 36% equity against this range, but realize 0% when we fold).

Let's then look at the range V might fold to a 3-bet - 22-88,JTs,QTs,QJs,KJs,KTs,AT.

Against that range we have 75% equity.

I'm not too excited about discussing exact ranges and flatting and 4-betting ranges - I'm sure there are good arguments to make tweaks to all of the above. I also did it quickly, and I missed things. The point, which I think is intuitive and less beneficial and more time consuming to calculate, however, will stand here with any reasonable V range:

3-betting TT in this spot gets V to fold with a range of hands we crush, call with a range of hands against which we are ~flipping, and 4-bet with a range of hands against which we actually have some decent equity but against which we still need to 4-bet fold.

A lot of hands don't play well multi-way - that doesn't justify a 3-bet.

Being ahead of an opening range doesn't justify a 3-bet. What matters is what V does with his range and what gives us value/continues.

Having initiative and c-betting doesn't justify a 3-bet. May as well play ATC.

Again, his opening raise is less important than his continuing range. And the range that Garick gave us is a ~standard opening range, anyway. If V was opening much wider such that there are many more combos that could give us value, maybe then we could consider 3-betting for value.

I don't see any reason to 3-bet here.

I think that's some good analysis, Willyoman, but it leaves out V2. I think it's a clear flat if we were still HU, even with V3's likely call. With V2 in there, I think the equity fold outs and size of the pot make the semi-bluff much more valuable, esp as V1 and V2 are both pretty fit-or-fold and easy to read post flop, so if called I should be able to semi-bluff a lot of flops too, and take down an even bigger pot, etc.

How do we know V is likely to fold lower pocket pairs? If he is the type to open all PP's in EP but set-mine/fold after being 3!, than shouldn't we be 3! him if he is likely to be fit/fold post flop?

We aren't getting any more value out of him if he misses the flop. So why not give him the option of making a costly mistake by calling a 3! without the proper odds to do so?

I guess the counterpoint is we don't *NEED* TT here to 3! if V is likely to play fit/fold in a 3! pot than we can simply 3! ATC and call with our value range. Is that the way to think about this?

But V2 is loose/passive and limp/calls a lot.

That might not correspond to calling 3-bets... but it will be correlated.

And V3 is on the BTN, and our tell (good work there) says he wants to play.

I think you're probably overestimating the "value" of TT in this pre-flop spot. You're also probably overestimating your ability to play it profitably if/when other villains stick around, creating a multi-way low SPR situation.

If and when would it be spew to put more chips in the pot with overcards on the flop? You can end up with like > 40% of your chips in the middle with a hand that has ~no value. I think you end up having to check a lot of flops, allowing V's to realize more of their hot/cold equity. And c-betting a lot of flops multi-way here isn't that much different than playing with ATC.

TT is valuable, but 3-betting in this situation makes it far less valuable.

I think people are seeing pre-flop in a vacuum in a lot of posts ITT. For example, if you post this exact hand but show that you 3-bet to $60 and got called by V3 and V2, go to the flop with $180 in the pot, and the flop is broadway-x-x, and you ask for advice, you will get flamed for 3-betting.

Also, we're discussing TT, but let's also ask what's our complete 3-betting range?

Specifically, do you 3-bet 99? 88?

Why or why not? I think the answers have nothing to do with:

a) The size of V's open raise.
b) Whether the hand "plays well multi-way."
c) The ability to have i. initiative and ii. c-bet flops.

It probably has everything to do with

a) The ability to capture pre-flop value.
b) The ability to capture post-flop value.

Isn't this what gimmick accounts are for?

/derail.

I like the analysis Willyoman.

Hard to do the math without some assumptions. Let's start off with flatting, because that will be easier

With a flat, we're treating TT like a small pair. To simplify it, we'll assume that if we don't hit the set, we'll c/f. I realize that if we have an OP and every whiffs, we can take down the pot. Against 3 villains, I assume that someone will have something that I can't bluff against. Therefore, 88% of the time we'll lose $15. With 3 players in the hand, only 28% of the time nobody will have anything, so all we'll get is the existing pot ($45). 72% of the time we are going to collect at least 2 bets. We'll collect $200-$400.

So the math is:

EV = 0.12*0.28*45 + 0.12*0.72*(200 to 400) - 0.88*15

5.6 to 22.9 = 1.5 + (17.3 to 34.6) -13.2

People can substitute whatever factor they want for the stack off probability.

For the 3 bet, the first step is size. I think using the 3+1 method is good. We want everyone to fold. Therefore, I'd go to 75. Based the range you gave us and the fact that the other villain just called, I'd assume we'd get folds 2/3 of the time. It means we'll collect $30. So it adds to our EV $21.6.

The problem is that we'll have to fold to a 4 bet. That's going to happen about 10% of the time based on his range(AA and KK) and we'll lose $75*0.1 or -$7.5. If we can break even with the rest, the result is a +EV of about $14.1.

So it is going to come down to how often with the players stack off with TP. At 2/5 with a bunch of regulars, my sense is that they won't often enough. I'd go with the 3bet.

Postscript. After reading Willy's analysis, I think the issue is that Garick's EP raising 3BB range is too wide. Tightening his raising range pushs the analysis towards calling. I discount the equity analysis because if we are raising, we aren't looking for the hand to go to show down. If we 3bet and get to showdown without a set, we've lost the hand.

You're telling me we should 3-bet 73o because the pre-flop EV is +14.1.

That's way better than folding, which has a pre-flop EV of 0.

Your math isn't terrible or anything, but realize that you can easily replace TT with ATC in your analysis and show that a 3-bet is +14.1 profitable

We know that's not really the case. How can we reconcile that?

If Garick posted his hand was 73o, would you advocate a 3-bet?

Actually, in your analysis, 3-betting 73o is better than 3-betting TT, because 73o has no value otherwise, and turning 0 value hands into +14.1 value hands is big win for us.

That's a valid point, though I'd at least want a blocker for a pure squeeze play, and would be happier about it if V3 hadn't already shown interest. Nonetheless, I feel like playing TT primarily for its FE is a waste of TT.

Still, this is the kind of road I'd like to go down to figure out which of these plays is better. IMO, I think we prefer one caller to all folds here if we 3-bet. That one caller will usually miss the flop, giving us another profitable semi-bluff spot.

Right.

AK is a great semi-bluff/value 3-bet/squeeze here because

a) It blocks AA,KK.
b) It makes nut post-flop hands (nut no pair, pair, two pair, straight, flush, etc).
c) It gets V to fold many hands with good equity vs. AK (e.g. pocket pairs).
d) V's pre-flop calling range contains some dominated hands (AQ, KQs).

TT has none of these benefits.

Willyoman, Venice implied that the 7/30 times villain calls our 3-bet that TT will break even. So your 73 offsuit argument needs to hold with that logic as well

Also, just for arguments sake

TT can make a nut post flop straight
TT gets V to fold many hands with good equity (QJ,KQ,AJ,KJ)

This is not true based on what it does to your entire 3 betting range when you widen it out to include 73o

No. You missed the caveat that we would break even when we are called. It is possible in my opinion with TT. It is not possible with 73o. If we start losing when called, the EV goes down considerably.

To summarize, against a villain that is going to open wide in EP with a raise at a table that is not going to stack off with TP, the math shows that there is a slight advantage to 3betting with TT. I'm not stating that people should always 3 bet TT in late position. Give the villain a more typical LLSNL open raising range of TT+, AQ+, this becomes a call.

Edit: Ah, my numbers don't add up to 100%.

It's still doesn't make a ton of sense, Venice.

Take your analysis and say we have 73o and lose a whopping (and unrealistic) 90% of the time V calls.

2/3*30 = +21.6
1/10*-75 = -7.5
~.23*0.9*-75 + ~.23*0.1*75 = -15.7 + 1.7 = -14.0.

= 0.1. That's a break-even 3-bet. Intuitively we know it's worse than that.

I think your pre-flop math doesn't consider many other factors (the possibility of a cold 4-bet from villains left to act; everyone's ability to realize their hot/cold equity; our potential position in the hand if V3 sticks around; stack depth and pot size; multi-way dynamics; our ability to extract additional value with the best hand post-flop; our ability to get away from better hands; etc).

I'll summarize your findings in plain English:

a) When we 3-bet and everyone folds, we win quite a few chips.
b) When we 3-bet and someone 4-bets, we lose some chips.
c) When we 3-bet and someone calls, we're ~50/50.

That's super simplistic. And we can run numbers that show almost any outcome; but intuitively, looking at the above, this just doesn't feel like a good 3-bet. Parts a) and b) are true for ATC. And in part c), just having 50% equity vs. villain's calling range isn't particularly profitable.

Also, is 99 that different than TT in your analysis? If we're break-even vs. continuing ranges with TT, then where are we with 99? Pretty damn close to the same %. 88? The math just isn't going to support the analysis. Again, even if we're losing like 90% of the time that V calls, it shows it's a (barely) profitable 3-bet with ATC. We know that's not the case.

It's definitely not a semi-bluff because we crush all of the player's ranges here.

To be honest, based on player descriptions I wouldn't be surprised if we got calls from virtually the entire range of any or all of the 3 villains mentioned in this OP. We just don't want to size our 3bet too big.

This hand range seems way too tight. $15 is a miniscule raise. Does he always size his raises like this? Could he ever be getting tricky with his raise sizing? If the answer to either of these questions is no (which they would be for the vast majority of players in this game) then villain virtually never has JJ+ in his range here or AK. A $15 raise is more indicative of a hand like A9/AT, small/middle pocket pairs, QJ than any hand of real value.

Continuing ranges?

OK. So you do mean continuing ranges.

So you want to 3-bet small - say, to $50 - and you want to get 3 calls?

Flop pot is $200, we are oop to BTN and have 425 left in effective stacks.

What's your plan for post-flop?

1. Do you plan to stack off every time you have an overpair?
2. What are you doing on any flop with a broadway card?
3. What else are you considering post-flop?

I'd guess the odds of flopping at least one card > T are > 70%.

Actually, I think we often get calls if we make it $65 for the simple fact that $65 is such a small relative amount (most 3bets will be much larger due to larger openings). I'm fine getting 1 to 3 calls. I prefer being in position but if we aren't it's not the end of the world.

Play poker. No point in discussing without knowing action or callers.

Lot of questions about postflop that doesn't exist but I can certainly answer #1 which is of course I'm not stacking off just because I have an overpair. Why would i do that?

Everybody has made their points. And they are good ones. Let's hear what you did & the flop

Agree -- good points. I'm actually fine with flatting or 3betting to $60 - $75.