This is more of a mental block thread than a strategy thread, and I may very well have answered my own question in it.

Relatively early in the session. So far it seems like a reasonable but not ideal table - the player to my left is almost as tight as I am, 4 or 5 people are seeing flops.

3 limps, I'm in the HJ with ATo and I raise. BTN coldcalls, BB calls, limpers call.

6 players, 12.5sb, flop comes KT3r.

Checks around to me.

In the actual game, I thought to myself "someone always has a king there in a 6-way pot" and just checked behind.

6 players, 6BB, The turn was a 9, one of the limpers bet and I folded (I was sure he had a king and didn't have the odds to chase a 5-out draw), and he ended up showing down 98o and winning the pot. By the way, the river was an ace.

It's easy to feel like a mistake was made when you fold the best hand, so I wanted to analyze my play.

To calculate the probability that nobody has a K, there are 10 cards in the other 5 players' hands. The probability that the first card is not a king is 46/50, then 45/49, 44/48 et al.

1 - 92% 46/50
2 - 84% 45/49
3 - 77% 44/48
4 - 71% 43/47
5 - 65% 42/46
6 - 60% 41/45
7 - 54% 40/44
8 - 49% 39/43
9 - 44% 38/42
10 - 40% 37/41

So there's actually only about a 60% chance that someone has a king. Of course, this assumes that the other 5 villains all have random hands. Even at *this* table, they're not - they'll play just about any hand that has a K, but they won't play, for example, just about any hand that has a 3 or just about any hand that has a 5. The probability is probably closer to 65%.

I will assume that if somebody does have a king they're going to check/call the flop, turn and river. I will further assume that nobody would raise a hand that can't beat ATo. What I *don't* know (which makes the analysis a little more complicated) is what worse hands will call 3 streets. A worse T might, and if a hand containing an 8 or a 9 picks up a pair they might. I also have to be worried about a hand with a Q or a J pairing up to pull ahead of me.

Having taken time to think about the hand away from the table, it seems like the general idea would be to bet the flop and turn for sure (especially if the turn is a card lower than a T), and then probably just check behind on the river unimproved (especially if the river is a Q or J).

Thoughts on this (over)analysis?

Bet the flop for sure, even if someone has a king, you have 20ish percent equity, the pot is big, and you want Qs and Js to fold their equity. You can always check later streets.

Don't tell Captain R that you did this calculation.

In order for you to definitively shift that percentage up, you're ALSO assuming that they will NEVER bet any kings, which is probably a false assumption. You're also assuming that they never raise preflop, and all sorts of other things. So it gets dicey if you want to start fudging that number around, and it becomes less helpful the more you tweak it. Treat this number as what it is, a blind starting point for a rough estimate, and don't try to fine tune it. (If you really want to know how things change under various assumptions, you'll need to do simulations.)

Here's the thing: Even *IF* someone has a king 60% of the time, that means that 40% of the time they DON'T have a king. If you bet and get two callers, you're still making money because you've put in 1 bet and the field has put in 2, and you're winning 40% of the time (which is more than 33%). So it still shouldn't bother you to bet here.

Once you factor in the fact that it was checked to you, you've actually eliminated a lot of the chances that there are kings out there, and you're probably doing better than the estimate above.

I always want to fold in the dark when i see this.
I have my mental block: i fold preflop. Just dont know how to realise my preflop equity. Ace comes - nobody pays (or plays perfectly). No ace - i'm in the dark.
ATs is ok.

Call pre flop. This hand isn’t strong enough to raise multiple limpers.

As played, the flop check is fine as long as you don’t fold later streets for one bet.

Turn fold doesn’t make sense. You’re narrowing your opponents range to only hands that beat you far too soon and without enough information. If this was NL, where it pays to be pessimistic, folding the turn would be fine maybe. In LHE, it pays to be optimistic.

Reasons to call the turn,

1. You may have the best hand (your opponent may be betting a worse hand for value or may be bluffing).

2. If you don’t have the best hand, you’re getting the right price to draw to a better hand.

3. Because you checked the flop, your actual hand is under represented. Your opponents don’t think you have a T and that makes it more likely your opponent may value bet worse hands or bluff to get you to fold Ahi.

i agree with both of these!

Another thing to consider: Even though its 4/8 and most people aren't paying attention, if you only ever bet top pair or better, the regular players will start noticing and will have an easier time playing against you.

No raise pre? With like a top 11% hand? What’s your raising range there?

99+, AQo+, A9s+, KQo, KJs+, QJs, JTs, T9s

I'm very surprised to hear people saying they would overlimp on the HJ with this hand. I know I said this was early in the session before I had a chance to devleop a lot of reads, but when 3 people have limped before action gets to me in the HJ you can be pretty sure you're up against 3 hand ranges that ATo crushes. So folding is out of the question.

Raising at least gives you a CHANCE to buy the button, which is always valuable and is EXTREMELY valuable when playing a mutliway pot with a hand that is terrible multiway.
Raising charges the villains double to limp all those ace-rag, king-rag, offsuit-1-gap, baby pocket pair et al hands.
Raising often gives you an opportunity to take a 4-card flop when it's appropriate.
The hands that dominate ATo (TT+, AJso+) only make up about 6% of all hands, so there's only about a 22% chance that one of the four players behind you has you crushed, and even when they do you still have position.

The hands I would overlimp with here are hands like 22-88, 45s-T9s, 97s-J9s, K5s-K9s, A2s-A8s. Pretty much everything else I either fold or raise.

I will admit that I would fold A9o here (though I would raise it on the button and it's the worst hand I would raise on the button) and I can't quantitatively justify why ATo is a slam dunk raise and suddenly one pip less is a slam dunk fold.

If my thoughts are way off base I welcome correction, but to me ATo is a no-brainer raise from the HJ at a prototypical SSHE table.

crushes? really?
maybe you have 4-5% advantage if none of them have a pair

Unless they limp JJ+, you're only a small underdog to a pair. A 4-5% advantage is pretty big 6 ways.

I'd snap raise against loose passives, who are going to play a lot of worse aces and a lot of worse tens. Against tight passives, it's much closer - because they may limp some better hands like AJ or AQ and will limp far fewer crappy aces and crappy tens.

I disagree with making this assumption. It may be true, but a lot of people also donk kings here (to see where they're at). Some percentage should also be going for a check raise with their kings.

Actually, I probably limp along with KQo.

I find this somewhat fascinating. I raise KQo with no hesitation.

To be completely honest, in practice, I probably raise it most of the time, but think I should limp along.

I think the one justification is that 4/8 players are so comically passive that they almost always have the goods when they bet.

But yes, even if that's true, pots too big to fold what is a decent hand on this board.

Preflop
Ed Miller recommends raising preflop with hands as weak as ATs and KJs. Your hand (ATo) is just below that threshold, so I’m inclined to just call with it pre. However, depending on the table dynamics and my table image, I might raise with it sometimes. So your play is fine.

Postflop
Here’s where things break down. Once you’ve raised preflop, you are in control of the hand. What line do you plan to take with some likely flops now that you're in control? This is something you should have thought about in advance.

Granted, you will sometimes flop a straight (or straight draw) or two pair or better, but more realistically, you’re hoping to flop one of the following:
1. An Ace-high flop
2. A Ten-high flop
3. A flop with a Ten and one face card

All three of these hands are vulnerable.
1. Suppose the flop comes A96. Now you're worried that someone has AK, AQ, AJ, A9, or A6. (Lots of passive players won't raise AK preflop, especially if they're in the blinds and someone with position on them has already raised.)
2. Suppose the flop comes T73. Now you’re less worried about someone having a Ten and a better kicker (not possible) or a sidecard that pairs the board, but you’re more worried about potential overcards and straight cards to come. Any King, Queen, Jack, 9, 8, 6, 5, or 4 could give someone a higher pair or a straight (or two pair, of course).
3. Suppose the flop comes KT3. Now you’re worried that someone has you beat with a King.

So what line should you take in these scenarios in which you've connected with the flop but are still vulnerable? Here’s what I do (in position): I bet the flop, I check the turn, and I either call a bet on the river or bet myself if the action checks to me for the third time in a row.

Bet flop. Check turn. Call (or bet) river.

By the way, this line also works well when you have an overpair (like AA) against a paired flop (like Q99). You don’t want to get check-raised on the turn, because you won’t know if your opponent has a 9, a Queen, or some semibluff like JT with a flush draw. So checking the turn removes the possibility of a check-raise and allows you to get to showdown more cheaply.

You could also, of course, choose the line you suggested: Bet flop, bet turn, check river.

Here's something I've seen happen when I've taken that line. An opponent with a King and a weak kicker (say, K9) calls my bet on the flop but folds his hand face-up when I bet the turn, saying, "This hand can't possibly be good." Remember, you don't always need the best hand to win. You need some combination of good cards, position, initiative, and the courage to keep betting when you're not sure whether you're ahead or not.

Now let’s talk about levels of thinking for a moment.
Level 1: What do I have?
Level 2: What do I think my opponent has?
Level 3: What does my opponent think I have?

The answer to question 2 has to be a range, and it has to be based on the actions your opponent has taken throughout the hand. On the flop, when no one has yet to show any strength by betting or raising, it’s way too early to assign any of your opponents to a King exactly. That’s MUBsy thinking, right (monsters under the bed)? One of your opponents might have a King; then again, they might not. It’s hard to make a pair in Hold’em.

If you bet the flop and get check-raised, you will gain information. Now it’s much more likely that one of your opponents has a King, and if you want to fold after a turn card that doesn't improve your hand, that seems more reasonable than folding to a single bet on the turn after checking back the flop. But when you check the flop, you miss out on this chance to gain information—and you give your opponents a false sense of your own hand strength.

This flop smashes your preflop raising range. What does a typical opponent think you have when you raise preflop at these stakes? The most likely answer is AK. Bet the flop and you will confirm that suspicion. Check the flop, and now your opponents think you have AQ or maybe an underpair like 66.

So when your opponent bets the turn, is it because he has a King or because he thinks this flop missed your hand entirely? You don’t really know, do you? Because you’ve underrepresented the strength of your own hand, you’re a bit lost—and you’ve given your opponent an opportunity to outplay you.

Don’t let your fear keep you from C-betting. Bet the damn flop. Check the turn if you’re still scared of a King, but do so with the intention of calling a bet on the river unless you find compelling reason not to.

Good luck.

what about raise or fold concept, Mr.Oldschool?

It goes out the window when someone limps.

thanks for the post agamblerthen

I was looking back at this, and I think I actually butchered the math in the OP.

Let's assume, for the moment, that all 5 villains have random hands. They don't, but to simply the math for now, let's assume they do.

I have ATo in my hand and there's a KT3 on the board. That leaves 47 cards, not 50! Also, only ***3*** of them can be kings, not 4!

So adjusting my errors:
44/47 * 43/46 = 87.5% chance 1 villain does not have a king
* 42/45 * 41/44 = 76.1% chance 2 villains both do not have a king
* 40/43 * 39/42 = 65.7% chance none of 3 villains have a king
* 38/41 * 37/40 = 56.3% chance none of 4 villains have a king
* 36/39 * 35/38 = 47.9% chance none of 5 villains have a king

I'm going to have to think about how to adjust these numbers to account for the fact that all 5 villains aren't playing 100% of their hands - that may be a very complex problem. Villains are probably going to play any hand that has a king and fold hands like J3o, 94o et al, so these numbers are probably a bit inflated.

I thought about posting this calculation in a separate thread, but I think it's relevant to this topic (since it's more about trying to break up a mental block than actually how the hand should have been played).

There's a prevailing mentality that if you build a big pot before the flop, you're predominately showdown-bound. I wanted to test that mentality mathematically.

Let's take the example in the OP where I built a 6.25BB pot before the flop. Suppose, to keep the math simple for now, that I get bet into on the flop, turn and river, 2 other villains will call the flop, one the turn and one the river. Suppose further, for now, that there are no raises at any point.

It's going to cost me 2.5BB more to show down my hand. The pot, not including what I contributed to it, is going to be 5.25BB+1.5BB + 2BB + 2BB = 10.25BB. So I only have to have or make the best hand 1 time in 5 to show a profit. Seems like I'm showing this down more often than not, certainly in the absence of overwhelming evidence that I'm beat.

Now let's look at the case where I'd built a big pot with a big pair (for this example, say QQ) instead of AT. My hand is stronger, but I have fewer outs to improve if I'm beat. If someone bets into 3 or 4 villains on that board you have to give them a higher (but not 100%) probability of having a king than my calculations indicate. Are we showdown bound with QQ barring an ace hitting the turn or river and/or crazy action telling us we're beat? This is a tougher spot IMHO.

EDIT: I'm pretty sure there's a section in the SSHE book that discusses a similar topic - I'll review that, but I'd love to hear other insights as well.