What’s Your Play? Medium Pair in a 3-Bet Pot Results

Thanks for all the great comments on this week’s What’s Your Play? As I’d hoped, your suggestions have helped me to think more about both the river decision and my play on earlier streets.

One point I want to emphasize up front about playing against tough/tricky opponents is that I’m going to try to avoid making exploitiable assumptions about how Villain will play. When you’re squaring off with really good players, I think it’s better not to assume they will “always” or “never” do something when there’s no structural reason for it. By “structural”, I mean something dealing with the fundamental mathematics of the game. So I can assume that Villain won’t call my 3-bet with 82o, because that’s both opening and calling would be fundamental errors, but I can’t assume that he won’t flat with AA because there’s no reason he shouldn’t some of the time.

As I talk about each street, I’m going to try my best to use game theory and other mathematical concepts rather than assumptions about how Villain is likely to play in order to get a sense of his range.

Pre-Flop

I hate calling raises out of position against good players, especially when those good players have really wide ranges. Even though I have an advantage in terms of card strength, I’m at both a positional and an informational disadvantage, and without raising I don’t push my card strength advantage. So even though 88 can be tricky to play in a 3-bet pot, it’s way ahead of Villain’s button opening range and I want to make him fold or pay with hands like Q9 and A6.

A raise also keeps the BB from coming in very cheaply, which I was more concerned about than a squeeze. Pre-ante, I’m a lot more likely to flat this, but when the pot is already kind of large, I’m going to put a premium on winning immediately when possible, especially with a vulnerable-but-probably-best hand. Although there will be plenty of tricky spots, I expect to have good equity and decent playability against his calling range.

My 3-bet risks 3000 to win 2300, so ignoring any equity in the pot, it has to get folds about 56% of the time to show an immediate profit. This means Villain should be raising or calling roughly half of his opening range. If he opens 50% of hands on the button, that would mean 25% of the deck. Of course we don’t know his exact opening frequency nor which hands exactly he’d choose to defend, but just to get a rough idea of how wide that is, this seems like a reasonable 25% of hands defend: {22+,A2s+,KTs+,QTs+,J9s+,T7s+,96s+,86s+,76s,65s,A9o+,KTo+,QTo+,JTo,T9o}

Nate and Leo Wolpert both raise good questions about the size of the 3-bet. Nate points out that a smaller 3-bet could still fold a lot of that air without bloating the pot as much. It would also make a 5-bet shove more profitable if that’s something I’m committed to doing.

On the other end of the spectrum, Leo points out that if I’m mostly concerned with pre-flop fold equity, then a larger size might be better: “Maybe it’s results-orientation, but the small preflop 3b seems like the kind of small mistake on an early street that not only prevented your opponent from making a big mistake, but opened the door for you to make larger mistakes (or at least have to face extremely tough/marginal decisions) on later streets.”

I think these are good suggestions, though I still don’t hate my size. I’m not wild about using different 3bet sizes depending on my hand, and for my 3bet range in general I kind of like a size that gets a fair number of folds but also encourages calls over 4bets. All in all I’d like to 3bet a depolarized range and that means I’d rather get called than 4bet.

Flop

Several of you correctly point out that this is a good spot for Villain to flat with some big pairs, and I agree, but I still think he’s going to raise them more often than not. Here’s a very rough range that has Villain opening 50% of the deck on the button, then 4-betting a 5% mix of monsters and bluffs and calling 20% (that ratio may be a little off but remember the size of my raise was engineered to induce calls over 4bets): {AA,99-22,ATs+,A5s-A2s,KTs+,Q9s+,J8s+,T7s+,96s+,86s+,76s,AJo-ATo,KTo+,QTo+,JTo,T9o}. Note this range contains a fair number of slowplayed big pairs and big suited Aces and is maybe even a little generous in that regard. Again, this isn’t meant to be a representation of his actual range, just a sense of how wide his range could be. I encourage you to put it into PokerStove so that you can visualize it better.

My 88 has only about 55% equity against that range on this flop. A bet certainly won’t cause better hands to fold, but it will be called by worse, and I’m quite vulnerable to overcards, so I’m happy enough just to get a fold from QTs as well. A half-pot bet with air would need to get a fold 33% of the time to break-even, so Villain should be calling or raising roughly two-thirds of the hands that see the flop. This is a range that has him continuing with any pair, any two overcards, and many of his gutshots (which also have at least one overcard to my pair: {AA,99-22,ATs+,A3s,KJs+,QTs+,J8s+,T7s+,97s+,87s,76s,AJo,KJo+,QJo,JTo}. I’m actually a slight dog to that range, though there’s additional value in making him fold hands like T9o and ATo that have good equity.

Turn

I couldn’t say exactly how often he’d call vs raise the turn with hands better than mine, but I don’t think it’s a great spot to slowplay somewhat vulnerable hands because the pot is quite large compared to his stack. In fact there’s some reason to think his value-raising and floating (as opposed to bluff-raising) frequencies are inversely proportionate, because both floating and value-raising are better if he doesn’t expect me to bluff the turn often.

What I’m getting at is that I feel pretty good about my hand on the turn, though I don’t see a case for betting. He’ll fold most if not at all worse made hands, and it won’t induce bluffs. There’s an important lesson here: even once you’ve decided you’re committed to the pot, it matters quite a bit how the money goes in. Here I’m much better off giving him a chance to stab it than just shoveling the rest of the money in myself.

Still, I’m happy to see him check. It further reduces the number of value hands in his range, because some percentage of his flop slowplays should be betting now.

Many commenters assume that Villain won’t check floats on the turn, but I think this is one of those exploitiable assumptions we should avoid making about a good player. He’s got enough weak hands in his flop calling range that he’d be really bluff-heavy if he bet them all on the turn, plus balance dictates that he preserve some weak hands for bluffing or getting there on the river. Think of it this way: if he bets all of his air on the turn, then he’ll either have no bluffs on the river or have to turn hands with appreciable showdown value into bluffs.

There’s some good discussion about this between eldodo42 and TaddisVonBaddis:

eldod42:

“His check-behind on the turn give us a treasure trove of information. He’ll fire the turn with most of his traps and most of his floats, so we can severely discount traps and floats, to the point where they don’t matter much anymore for our decision making (all IMHO, of course). Thus, after the turn action the majority of his range is middle-value hands. It is instructive to consider just middle-value hands when planning our river line.”

TaddisVonBaddis:

“I am torn here between eldodo’s conclusion of just middle hand strength from our villain or whether his range still includes some floats. If villain determines we aren’t folding here, why wouldn’t he jam any Jx hand or TT for value? At the same time if he feels we aren’t folding why wouldnt he peel a free river with those few floating hands? I’m not saying its a huge part of his range but I don’t think its to be eliminated completely if villain really is very good.”

River

Leo, posting as EMO MELTDOWN!!!, shares some interesting math in the comments. I haven’t reviewed his assumptions closely, but his conclusion is that shoving the river is profitable even if Villain never calls with worse simply because he so rarely has better. This makes me dislike any line that ends with me folding. It also points out the futility of bluffing, since any hand stronger than 88 will clearly be towards the very top of Villan’s range.

The main question to ask, then, is whether he’s more likely to call a bet with worse or to bet worse if checked to. Piefarmer is correct that the “Brokos Hand Reading Method” suggests Villain mostly has hands he wants to showdown cheaply, which should incline us towards betting.

Tricky players do things to subvert these simplistic hand reading techniques, though. I’ve already demonstrated why he ought to have more air than that method would suggest on a blank river. Tricky players are also capable of things like turning hands with showdown value into bluffs, something Villian should be especially inclined to do if he’s betting most of his air on the turn because otherwise he’ll have no bluffs on the river.

Finally, it’s worth nothing that I definitely want to value bet stronger hands than 88 that I might have in my range in case Villain checks back his 88 – TT. That means my checking range is often going to be folding or losing at showdown, and I’d like to get some more hands good enough to check-call in there to beef it up a bit.

Results

I checked intending to call any bet. Villain thought for a bit, checked behind, and berated himself when I showed my 88, saying that he should have shoved. This makes me think he did have something like 76 or 55 that he considered turning into a bluff. I didn’t tell him he saved himself money.