I recently won a 500 big blind pot with an unimproved pair of Tens. Although I believed my play to be straight-forwardly correct, it created some surprise on Twitter. I began this article intending to demonstrate why my line of three-betting and then three-barreling for value was correct, but I ended up convincing myself that it was a lot closer than I originally believed, which is an interesting outcome in its own right.
It was a $5/$10 no-limit hold 'em game with $2,500 effective stacks. The button opened for $35, and I raised to $135 with TT in the small blind. I believe this to be a spot where, barring some extreme reads, three-betting is consistently better than calling. Against the range the Button ought to be opening, TT is a strong hand that benefits from fold equity but also will have good raw equity when called. Equity realization out of position with an unimproved pair can be tricky – this will be the focus of the rest of this article – but this is offset both by the sheer amount of equity the hand has as well as by the ability to realize well more than its equity when it flops a set.
The Button called, and we saw a 942r flop. I bet $175 into a pot of $280, and my opponent called.
The turn was an offsuit 6. I bet $425 into $630, and she called.
On a river 2, I moved all in for about $1,700, roughly a pot-sized bet. She eventually called, and my hand was good. She didn't show, but I imagine she had a smaller pocket pair.
When I reported this hand on Twitter, some people seemed to think that my opponent must have made a mistake, or that I must have had some sort of insanely aggressive image, for me to be ahead when called. I don't think either was the case here.
I'll admit, again, that moving all-in on the river is thin. There's a real chance that I'll get called by better. There's also a chance that, even though I'm often ahead, few worse hands will call me (though, as I'll argue, I think that would likely be a mistake on my opponent's part).
The thing to recognize is that, when you're out of position, you rarely have the opportunity to realize the full value of your marginal hands. When you bet, you risk folding out worse while getting called by better, but when you check, you allow worse to check behind and risk facing a large bet from a polarized range that essentially kills the value of your hand.
It's not enough to say, “Betting is risky and unideal, so I'll check.” Playing from out of position is often about choosing the less undesirable of two or more unideal options.
Before the River
I mostly want to discuss the river decision, but I'll quickly address the option of checking either the flop or the turn. TT is a hand that benefits a lot from betting on early streets. This is in part because it benefits from betting into unpaired Broadway cards, which give something up whether they call or fold, but mostly because lower pocket pairs and 9x are more likely to call early streets, when they are still ahead of the many unpaired Broadway cards with which I could be bluffing. An Ace on the river is bad for me not only because it may cost me the pot but because even when I am good, I am not likely to get in a value bet against a worst pair.
Many people have the mistaken idea that you can check for “pot control” when out of position. But the player in position is always in control. If she wants to put a bet into the pot, either with a better hand or with a bluff, she will have the option to do so even if I check. Worse, she will have the option to check and keep the pot small when she has worse pairs than mine that would have called a bet. So, I am convinced that betting the flop and turn is definitively better than checking either of those streets.
On the River
As for the river, I crunched some numbers and found the choice to be closer than I expected.
Assume that Villain reaches the river with 22-JJ, 65s, T9s, 98s, and 70% of her AK combinations (on the assumption that she sometimes four-bets these pre-flop). This is every hand that flops a pair or better, plus her best unpaired hands. It assumes that she never raises the flop and turn either for protection with smaller pairs or for value with bigger pairs and sets, and never folds a pair on the flop or turn. I think these are plausible, though certainly debatable, assumptions. The bigger assumption, to which we will return, is that she never just calls pre-flop with QQ, KK, or AA.
Against the above range, TT is good about 75% of the time when we see the river (which goes to show why betting on early streets is so valuable). That means that if I could wave a magic wand and see the showdown, I'd have an Expected Value of 75% of the pot or about $1,110.
The EV of shoving will depend on the Villain's calling range. In a worst case scenario where she calls always and only when she ties or beats TT, the expected value of an all-in bet is only $881. Needless to say, shoving will not be the best play if my opponent will play perfectly against it. But what is the cost to her of doing so?
If she calls only when she can beat TT, then she folds 73% of her range. Given that bluffing with a pot-sized bet needs to succeed only 50% of the time to show a profit, it would be very profitable against this strategy.
According to my CardRunnersEV analysis, my bluffs win anywhere from $300 to $555 when my opponent over-folds the river. Hands like JTs and AKo are squarely in my SB vs. BTN three-betting range, so the threat of bluffs from these hands is a very real one that my opponent ought to consider when constructing her calling strategy.
In order to make my river bluffs unprofitable, my opponent needs to call with roughly half of her hands that see the river. If I include 88, 99, and T9s in her calling range, then she makes me more or less indifferent to bluffing the river, though my very best bluffs (QJs and JTs, which block portions of her calling range) still show profits of $160 and $270, respectively.
Shoving into a calling range that includes 88, 99, and T9s, as well as better hands, has an EV of about $925. In other words, it enables me to realize about 83% of my equity.
If I check, I give my opponent the chance to do two undesirable things: she can check behind with weaker hands that would have called a shove, denying me a big value bet, and she can shove a combination of better hands and bluffs (which could be AKo, 33, or other hands with minimal showdown value) in order to make me roughly indifferent to calling with TT.
It turns out that although I functionally lose the pot if my opponent shoves a balanced, polarized range (I could call, but the EV is about the same as folding), I win so often against lesser hands that check behind that my EV is $934, about the same as if I'd shoved. And that presumes that my opponent actually takes advantage of the opportunity to shove a polarized range. If she checks back more than she should, or makes a smaller bet, as I believe many players would, then I do even better by winning the pot against some hands that could/should have bluffed me out.
Adjusting the range with which my opponent sees the river can have a dramatic effect on the EV of shoving or checking TT. If she sees the river with AQ, then she must add more bluff-catchers into her calling range or else get exploited when I shove bluffs. I found that adding 70% of AQ combos into her turn calling range required adding 98s and 65s to her river calling range in order to keep me indifferent to bluffing.
Against this expanded calling range, TT wins about $1,150, more than its equity share in the pot. Unless my opponents adopts an extremely exploitable betting strategy after I check, then shoving will be superior.
If Villain reaches the river with a tighter range of only pairs or better, then checking with the intention of folding to a bet becomes the most appealing strategy. This is because I will win the pot when she checks behind, and she will not be compelled to call the river with as many hands that I beat. Nor will I risk losing the pot when a weak hand shoves after I check, because she really has no weak hands to speak of. Although she could turn her smallest pairs into bluffs, and that would be bad for my TT specifically, it probably would not be an overall appealing strategy for her simply because of how often those hands can check and win the pot.
As an aside, it's worth pointing out that if she folds so often before the river, then my flop and/or turn bluffs will likely be very profitable. Her range for reaching the river is not entirely arbitrary or a question of style. Just as on the river, her flop and turn calling ranges ought to be determined in part by the desire to prevent me from bluffing profitably.
The worst scenario for my TT is if I put more big pairs into my opponent's call-down range. The more that she flats QQ+ pre-flop, the more weak hands she can fold after the flop without fear of exploitation by bluffs. Of course she has a lot of incentive to four-bet these hands pre-flop for other reasons, but it's not at all inconceivable that she would call with some of them. If she reaches the river with such a range, then checking with the intention of folding TT would be preferable.
What Keeps You From Shoving?
In game, I had some additional information based on my opponent's demeanor as she called my flop and turn bets to indicate that I had the best hand. This made my decision to shove the river easier.
I suspect, though, that even if we were to give the Hero a slightly stronger holding, such as QQ, many people would still be reluctant to shove. Why is this?
I believe the overriding cause to be classic loss aversion: at some level; most human brains are more concerned about not-losing than they are about winning. Even when we can expect to win at a favorable, very profitable frequency, our guts may very well tell us to be careful.
But how, exactly, can we be careful? Pocket Queens is much too strong of a hand to fold on a board like this one, which means that if your opponent has AA or a set, you're going to end up paying her off one way or the other. She may accidentally bet a few hands that you can beat, but overall she has much more incentive to call a bet with such hands than to make a bet herself. Checking also gives her some incentive to bluff, but again, her incentive to call with bluff-catchers that you beat will be greater than her incentive to bluff with hands that you beat.
The second argument I tend to hear is that players don't believe their opponents will call such a large bet with worse hands. Although I often suspect that this is an ex post facto justification for an underlying loss-aversion, it's not inconceivable. Some players really will fold far too often to a river shove.
If you believe you have such a player in your game, then you should be three-betting and triple barreling that player quite aggressively even when you miss. There really are players against whom this is a profitable strategy, but in my experience the same people who, when they hold QQ, tell me that their opponents won't call a shove with worse also tell me, when they hold JTs, that their opponents never fold and it's not worth trying to push them off of a pocket pair. In other words, these players seem to find an excuse to play neither an exploitably value- or bluff-heavy shoving strategy nor a balanced shoving strategy. They simply check often for reasons that, again, I ascribe to an underlying loss aversion.I learned a lot from my analysis of this hand, but if all of this talk of Expected Value and exploitability is going over your head, there's probably a simpler lesson for you to learn: don't put money on the poker table that you aren't fully prepared to put at risk.