Where is the Top of a Polarized Range?

This hand from the 2+2 high-stakes multi-table tournament forum got me thinking about what it means to be “at the top” of a polarized range. Here’s a quick summary, for those who can’t/won’t follow the link:

It’s a tournament, and blinds are 100/200. Hero raises to 475 UTG with KK, and good loose aggressive regular calls out of the SB. The flop comes Qd 4s 9d. SB checks, Hero bets 625, Villain calls.

The turn is the 4d, pairing the board and putting three diamonds out.  Both players check. (I don’t think it matters much, because the turn decision isn’t the important thing here, but Hero has the Kd.)

The river is the 4h, giving Hero Kings full of Fours. Villain checks, Hero bets 1400 into a 2300 pot, and Villain shoves for 11080. Hero has him covered.

Most of the forum seemed to think this was a call, and in many cases not a particularly close one. To me, it’s a clear fold.

Not everyone articulated it this way, but the general sense seemed to be that a pair of K’s is at the top of Hero’s range, and that folding hands at the top of your range isn’t what you do against a LAG.

The problem here is that Hero actually has two very separate ranges: a bluff range and a value range. KK is actually only around the middle of Hero’s value range, which I would set at roughly TT+. Unless Villain is floating the flop from out of position, a possibility made even less likely since Hero can account for two of the K’s, meaning he won’t see stuff like AK/KJ/KT very often, Villain probably has showdown value. He called a bet on the flop, and the most obvious draw came in on the river.

This means that Villain will primarily combat Hero’s bluff range by calling rather than by check-raise bluffing. When Villain check-raises, it no longer matters much where KK fits in Hero’s full range, because Villain isn’t really playing against the bluff portion of that range any longer. Villain’s shove is rarely a bluff, so it matters only where KK fits relative to Hero’s value range, and more importantly relative to Villain’s value range.

If you’re thinking that this is just a very fancy way of saying that Hero has a bluff catcher in a spot where Villain is rarely bluffing, you’re correct. The thing is that many people tend to use this flawed “top of my range” or “hand under-represented” logic (which are really the same argument, in my opinion) to justify some calls that I would say are clearly bad. Yeah, your hand can be a bluff quite often, but Villain can usually combat that by calling. When he shoves, KK is in trouble.

5 thoughts on “Where is the Top of a Polarized Range?”

  1. Great post as always.

    Maybe I’m missing something, but what I can’t get past here is Hero’s check on the turn. After Villain’s c/c on the flop, Hero has to think he’s looking at a large range, with many of the holdings having him beat. On the other hand, Hero has the Kd and the board is paired, so he’s got 9 outs to beat a made flush (unless Villain has the Ad). Don’t you absolutely *have* to bet for info and possibly drive out the Ad draw?

    If I had to guess, I’d surmise that Hero was playing scared post-flop. He’s probably thinking something like this: “Grr, he called my flop bet. That’s probably two garbage diamonds, with this guy being a LAG-tard and all. [turn] Crap, the flush just hit. He’s going to crack my $(!#& kings with seven-three, I just know it. Maybe I should bet here and see if I’m beat. No, wait. If I do that, he’s just going to bluff-shove back at me even if I do have him beat. And I won’t know. So, umm, okay, I’ll check behind. [river] Oh, fabulous, crabulous day! Now I’ll punish him for playing those garbage diamonds….”

    It seems to me that the way out of *that* dilemma is to shove the turn, right? It’s either that or bet and fold.

    • With black Kings, I think betting the turn makes a lot of sense. In that case, there’s a lot to lose by letting a random diamond see the river for free. With the Kd, though, Hero is likely way ahead/way behind. Getting check-raised on the turn sucks because Hero may have 11 outs but he also may have only 2 outs. Combine that with the fact that Hero probably can’t get two streets of value out of his hand anyway, and I’d rather check the turn and bet the river than vice versa.

  2. You can’t be folding here except against ubernits. Villain will be bluffing here some of the time but mostly I’d expect villain to have Qx here. Yeah sometimes villain will have the last 4 here or even AA,QQ,99 but that’s poker. If you’re going to be folding KK in this spot against LAG you’ll get pounded on relentlessly.

    • I’m open to arguments to the contrary, but I think shoving a Q here is pretty bad on Villain’s part without a very specific dynamic that almost certainly does not exist in this hand. Hero can have better and is never calling with worse, so check-shoving a Q is just a reverse freeroll for Villain.

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