Hi guys, thanks for the responses so far. I thought this was an interesting spot because several concepts come into play here and I think determining the best action might be complex and unintuitive.
First, always taking aggressive action "because we have top pair" or "because we have an overpair" is autopilot thinking and limits our skill growth. I'm encouraged that we have not yet had a response like that so far, kudos to the community for that.
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OP, have you ever been "sure" about an opponent's range and been wrong? if so then you can't act as if V2's range is precisely that.
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It's rare for a villain to be that well-defined. Of course, maybe this dude is really special and you have some super special knowledge.
This point is important generally and is clearly important in this specific case since almost any change to the assumed range for V2 is good for us -- even if he is even tighter and 3bets only QQ+, AK that is actually good for us here. I agree that it's always important for us to include some margin of error in our reads since it's a game of incomplete information.
In this case, I do happen to have thousands of hours of data on this particular opponent and I trust this particular read on his preflop range in this spot to be ironclad. I concede that ironclad reads are never truely 100% accurate but for the purposes of this OP, let's assume that it is.
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he's def ahead of you here (3+3+6)/(8+[12]) = 60% of the time.
It's nice to see that someone has already pointed out the combinatorics which shows that we are behind V2's range on this flop. Recognizing that we so heavily block AK at game speed can be tricky.
AK = 8 combos (we are ahead)
KK = 1 combo (we are very slightly ahead)
AA = 6 combos (we are way behind)
QQ = 3 combos (we are way behind)
JJ = 3 combos (we are way behind)
I'm not clear about whether any assumptions can be made regarding card removal due to what the other two players in the hand may or may not be holding -- they might hold an ace, blocking V2's AK . . . they might hold a queen, blocking V2's QQ, etc.
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Without adjusting his range, you are WA/WB vs V2.
A small point, but I'm not sure if this is quite accurate -- I guess it depends how you define WA/WB. As seen in my notes regarding the combinatorics above, I think a better description is that either we are ahead, or we are way behind. In other words, AK has 7 outs twice to beat us at showdown. However, when we are behind, we have much fewer chances to improve.
This can be seen by assuming that this is a heads up pot VS V2 and plugging hand vs range into equilab -- we do not have 40% equity vs V2 here . . . we actually have only 37.8% equity vs V2 on the flop, despite holding the Ks. If V3 and V1 had both folded preflop and I had only called, seeing the flop heads up vs V2 oop -- I think that the correct line in that situation is pretty clearly to check and call the flop with the intention of just calling down (including a pretty gross read based river decision). Given our equity and our showdown value, I think we can all recognize that checking and calling down would be correct here even though "we have an overpair".
However, this is not a heads up spot, it's a 4-way spot where we have decent equity, making a flop bet more of an option than it would be in the theoretical heads up spot above.
I think that another important concept in this spot is relative position. . .
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I'd probably just bet and hope V1 or V2 raises.
In my opinion, if we bet and V2 raises and that causes V3 and V1 to fold, that's a particularly bad outcome for us. There is an old school concept of implicit collusion which might claim that this is a good outcome because those opponents might fold out some equity and therefore our winning chances improve by getting heads up. However, I think that math usually shows that this is generally a benefit to V2 in cases like this (when his raising range has us crushed) and not to us. If somehow the relative positions were different and we were first to act and V2 was last to act, I think betting would have a lot more merit because then the other two players might be putting money into the pot very badly before V2 acts and so our bet generally gets better value. Also, due to relative positions . . .
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You could check and If V2 bets just call. If it gets checked to V3 and he bets you can CR. Given your description it sounds like there is a decent chance V3 has hit this board.
Now we are getting somewhere -- especially since there is some chance that this action might cause V2 to (incorrectly?) fold AK which would quite clearly improve our winning chances to take down this large pot against V3's weaker range.
Here are some responses so far which favored betting:
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Checking leaves too much to chance.
This is not a good enough justification for betting in my opinion.
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If V2 likes to slowplay his monsters then maybe bet flop and bet/fold turn is a better option assuming you trust your read.
If V2 isn't going to raise the flop with AK you can bet/call and fold turn UIP.
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so personally i think giving a free card to the 8 combos of AK here isn't great and the pot is also now big so i'm not a fan of checking even if we do get raised.
if we get raised otf, we know it's not AK and can play the turn accordingly continuing only if we pickup equity or feel we may be off slightly on our read and then just k/c down.
While I can somewhat understand the thinking behind these posts from an exploitative point of view, in my opinion in and of itself these are not good enough justifications for betting when behind. To me, this is sort of the equivalent to "betting to see where I'm at" which is not generally good overall poker strategy.
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It may be that betting is better than checking here. But I think it's complex and should not be automatic. I've had some offline discussions about this spot with a couple of very good players and the best action still seems unclear to me. One player had some very mathematical justifications for betting and I invite him to share those thoughts in this thread, but I'm not sure if that will happen.
Keep the responses coming!