So I like to think I'm pretty decent with figuring out equity in interesting spots, but multiway pots always confuse me a bit. Hopefully someone can shed some light on possible FE and actual equity in this spot.


Villain (UTG+1) $260: Late 30's-early 40's. Pretty tight/passive. Watched him get raised off a few hands post flop where it looked like he was ahead.

Other villains (CO $220, & BTN $140) are typical loose/passive fish. Bet when they have it, check when they don't.

Me (MP) $cover all: Playing pretty TAG. Only been involved in 3 or 4 hands in almost 2 hours. All of them were pretty big too, and I won all (only 1 didn't get to showdown).

My hand: 42

UTG+1 raises to $10, I 3bet to $30, CO calls, BTN calls, UTG+1 calls

Pot = $116
Flop: Q63
UTG+1 checks, ????

Do I have enough FE here to bet? Or do I check and hope to pick up more equity OTT? What kind of ranges can I assume they all have? First instinct was to assign them all something like AQ+, 88-QQ. Too narrow/wide? Any input is appreciated.

Fold pre. You really don't want to be 3betting an early position raise from a tight-passive player with 4 high.

As played, I'd check behind. Betting here against 3 players is spew. If it was heads up, you could make an argument for betting flop and barreling a lot of turns.

I agree that folding is standard like 95%, but given my image I decided to balance my range a bit (yeah I know, lolrangebalancingat1/2). It's an easy fold to a 4bet and I believe I could get this guy to fold a ton of hands post flop. I just wasn't expecting 2 cold calls.

Let's pretend you are heads up against UTG+1.

You have four outs, or about 8% chance of winning per draw.

If you shove, and he folds you win $116.

If he calls, you get the pot ~$600 * 16% = $96. Less your investment of $230, net is about -134, which is your expectation he calls.

If he folds x% of the time, you break even when 116x = -134(1-x). Eyeballing it, he needs to fold more than 50%, right?

There are a number of variables that make this calculation more complicated. Let's focus on just one: the likelihood that all 3 are going to fold.

Correct me if I'm wrong, but if each villain has a 60% likelihood of folding, the likelihood all three fold is .6*.6*.6 = .21. If we assume a more realistic FE of 30% per player, then there is a only a 3% chance your bet will take it down.

So this is why you don't 3bet 42 from MP with a table full of calling stations left to act. Even if its suited.

Sucks because if you bet you pretty much pot commit yourself. I think check and see what happens.

I think you're right about their range, it should be something like 88-QQ, AQ+, althought the fish could have it a little wider with some good suited broadways or some lower pairs.
In fact even UTG+1 range could have some lower pairs as well as he was last to act and had good odds for his call. But it's only a question of a few combos more or less and it doesn't change much.

3-betting light an UTG or UTG+1 is not always a bad idea providing you don't do it often and choose carefully your spots.
But here, facing a tight player UTG+1 raise, with low one gapers (one gappers have a lot less value than real SC), in a bad position, with several fish IP left to act makes it very EV- in all cases.

When everybody and his brother call your 3-bet, your plan should be to give up.

OTF, it's a 4 way pot, OOP, a FD is on the board, almost no equity in your hand if your called (the 5 spade is not even a clear out), not only one but 2 fish left to act that will certainly call you with any Q, any FD, perhaps even some pairs lower than the Q makes a c-bet very -EV.

When you bet you want to rep AA/KK/QQ/AQ, but fish know that people c-bet routinely and the problem is that they will call at least one bet if they have any sort of a hand, figuring that you could also bet AK/JJ and so they won't give up at the first bet.

I think it's just a check/give up unless you catch a 5 OTT.

So as expected, the consensus is fold pre (ldo) and check/fold flop. I agree with both (the majority of the time preflop anyway) but I was just curious if anyone was interested in figuring out the EV of betting. I would assume checking is way better, but how much better?

OK, I'll do it, I like funny things.

The exact EV is obviously very difficult to figure out because it depends on a whole lot of factors, mainly if your plan his to fire a second barrel, on most turns if called OTF, and whether or not they are believers and would fold AQ OTT often. Moreover, they all have different stack sizes and won't fold a the same frequency on a shove turn...

If we simplificate a lot we can still try to make gross approximation.
OTF, we assume:

- They all have the 88+/AQ+ range (55 combos)

- Both fish call with a pair of Q or better, or a FD w/AK and 30% of the time with TT-JJ (22 combos).

- the Tight-passive only call with at least a pair of Q and with AK spade (16 combos)

So, you make them all fold 25% of the time with a c-bet of say $70.
The immediate EV of the c-bet regardless of later streets (that is if we consider that you lose whenever you are called) is :

(25% * 116) - (75% * 70) = $-23.5

Now we will assume that 25% of the time you have more than one caller and in this case we consider that you don't 2nd barrel and the pot is lost. Likewise, if a flush card hit OTT (20% of the 50% remaining = 10%), you give up and it's lost.

In the 40% remaining, you always fire a 2nd barrel and gets a fold about 30% of the time with your average $100 bet (that is from JJ-TT, AK spade but never AQ).
Let's also say that overall, 4% you catch one of your outs and win a big pot.
The final calculation for a $70 c-bet and a shove about $100 OTT is:

EV = (25% * 116) - (25% * 70) - (10% * 70) - (23% * 170) + (13% * 186) + (4% * 300) = +$1.58

Of course, that's a very gross approximation and a slight change in their ranges could tilt the balance far in either direction.

Thanks. Goodnight.

Lol.... Excellent. Your approximations were very similar to mine. I did my own math based on EV for each player calling a cbet individually, and FE for all 3 folding (used 50% fold for my estimation though). In the end, I really think it's all dependent on rough estimations and it ends up very slightly + or - EV, which in the end causes me to err on the side of caution..... Check.

Thanks for the input by the way. I always enjoy seeing and hearing different points of view.

super marginal spot...dont like the multiway w/action behind us because i assume your planning to fold to 3 bet? :/

Close? Puh-leeeze!

If you're going to get it all in (!!!) you might as well jam the flop. Which maximizes hand equity (two shots at draw instead of one) and maximizes fold equity. I don't think the numbers are all that different if -- if! -- you assume each villain has a 60% fold rate.

You guys are smoking crack if you think they all fold 25% of the time to a cbet of any size. V1 maybe folds one time in 10? He is showing huge strength with a raise from that position.

But even if we give V1 a 30% fold rate, the other two fish have to fold at a 90% rate to reach your target.

This reaches the point of absurdity. A 90% fold rate would justify playing every single hand for a shove OTF against these guys. Which is precisely what you are proposing, isn't it. That you can play any two cards, from any position, and run all over the table. And you have the math to prove it.

You know, there are people on these forums who are trying to figure this stuff out. At some point, somebody has to say, "Kids, don't try this at home!"

So if we assign them a range of 88-QQ (KK+ is 4betting with this much action) AQ+, you're telling me of the 55 possible hands, villain 1 is calling more than 90% of the time? That means he's calling with AQ (12), QQ (3), JJ (6), TT (6), 99 (6), 88 (6), and AK ~69% (11). If you read my description of UTG+1, he's tight PASSIVE. The reason I took this line in the first place was 1) range balancing, and 2) I watched him fold in spots because he felt he might be behind and he didn't want to risk it, even though to me it was pretty obvious he was ahead. This guy is NEVER calling with AK to a cbet, and probably folds 88-JJ a decent amount also. So yes, the math Zarathoustra gave is pretty accurate. It baffles me how/why some people in LLSNL refuse to explore the mathematics of this game when away from the table. In the end it's only going to make you better.

Also, who said anything about getting all in OTF?? Last I checked this isn't a tournament.

Heads up, if you think you have 50% or more fold equity, knock yourself out.

But you're not heads up. You are trying to do the math for a multi street line against 3 other players. That's not math, it is speculation. You can prove anything you want by making whatever assumptions you want.

The rest of us are scratching our heads trying to figure out whether your assumptions are valid and useful, or whether this entire thread is just a lost transmission from the Planet of Irrelevant Impulses.

I am merely arguing the latter.

I am answering just for myself, for clarifying my point, you don't have to answer.

Why being so hysteric? And why involving Roger Rabbit in this story, he didn't do anything.
We're trying to get an gross approximation of the EV of a bluff, and I don't think we're very far.

Huh?! Yes, but we neither maximize risk/reward (risking 230 to take only 116, with 3 people left to act) nor information exploitation.
If we make a normal bet on the flop we can still give up in case of multiple callers/raisers or bad turn, and we win more when we bluff OTT.

An UTG raiser always shows strenght, but that doesn't mean he's sitting every single time on AK/QQ+, and if it was AA/KK, he certainly would have 4-bet pre with 2 fish calling our 3-bet. Even UTG raisers have an average range of about 6-7%.
We on the other hand are showing tremendous strenght by 3-betting an UTG raiser!
Given the odds he's been offered for over-calling pre, I think we are not very far from the truth when we give him a range of 88-QQ, AQ+ and saying that he won't call without a pair of queen or a FD is not a crazy assumption (that make him fold 70% of the time.)

By 3-beting an UTG/c-betting a 4-way pot we rep QQ+, any player with a brain will fold 99 here. Saying that V1 is folding only 10% is at the very least a blatant exageration (in fact it's totally delirious)

That is exactly what absurdity is. If you cut off the folding rate of V1 by more than half, how can you excpect that we reach the same figures?? It's your reasoning that is totally absurd!

That's indeed clever!
Yes, exactly, we are not HU, in HU people have completely different ranges preflop, and completely different calling ranges OTF.
Here we play Full ring, in a 3-bet 4-way pot, how can you compare the FE of the two?? It's like comparing oranges and apples.

And I'm scratching mine trying to figure out where is the single usefull or backed up argument in your post...

So by your logic, assigning ranges is pretty much irrelevant since it's "not math, it's speculation". Interesting. But there's one major problem with that logic. You'll never win at poker without speculating what your opponent may have. The entire game is based on analyzing incomplete information. The more you do it, on or off the table, the better you get. Analyzing and posting on hands titled "AA on a AAJ72 board. Villain has 5bb's left. How do I get max value?" will never make you better. If you choose to be a nut peddler then by all means, play your game the way you want and only 3bet the top 3-4% of hands. But don't get upset when you get stacked for 200bb's when a guy calls you with 34s because your hand was pretty much face up from PF to river.

The two spots at the table that you typically don't want to 3 bet light are UTG and UTG + 1...why? Those spots almost never open light in the first place. If you do 3 bet light an EP raise, you want to do so from LP yourself and with a merged range rather than a polarized range.

Also, cbetting air in a multi way pot when you're OOP is almost never a good idea.

You're intentions were good in this hand and your play demonstrates you have the potential to crush, but you need to learn to make these plays in position. It may be tempting to do this OOP, but it's not profitable.

So check/fold flop and jot down a -$30 mistake for the day for 3 betting light OOP against an EP raiser. If you lead flop, write that down as a mistake for the day too.

+1

Although I haven't mentioned it in this thread, I did think to myself afterward that this play has much more value from the BTN or CO. It's a very unusual play for me, but for some reason I felt this guy wasn't extremely strong, so I decided to go with it, knowing it was a snap fold to any type of aggression. Luckily for me both fish checked behind OTF and the poker gods blessed me with the 5d OTT. I didn't make much more though, as UTG+1 bet $30, I raised and they all folded.

I'm not sure you need to worry about equity calculations. You should be more worried about why you are spazz 3betting a tight players UTG open with 42. You got called in 3 spots. You are OOP and I'll remind you, you have 4 high. Continuing here is ultimate spazzy spew, unless you have have some sick read like every single V has cards in the ready to muck position.