Should I bet in limped pots?

2024-09-12

Let's talk about limped pots in heads up poker. You might think limped pots mostly just get checked down, and you should spend your time looking at bigger mistakes in single-raised and 3-bet pots instead. The truth is, you're about half right. It is true that limped pots mostly get checked down. But it's not correct to say that the mistakes pale in comparison to the mistakes in raised pots.

You may recall the 100,000 hand sample I've been working with, which I have divided into situations to see where in the game tree you (the humans of ActionFlop) are making mistakes. I first wrote about it in this post. Out of the top 25 situations sorted by EV lost to mistakes, unraised/limped pots show up three times. The #3 top mistake situation is actually when the BN makes preflop mistakes in limped pots. The BB preflop mistake situation is also in the top 25, coming in at #19. The third limped pot situation that shows up in the top 25 is when the limped pot gets checked all the way down to the river: preflop call-check, flop check-check, turn check-check, river check-check.

Let's dive right into a hand like this.

The preflop action looks standard. The human is the BN, playing against the GTO bot in the BB. The BN limps with 84o, which is a perfectly acceptable thing to do most of the time (although raise or fold are also possibilities). One should never limp or raise with 84o from any position other than the blinds in a 9-handed ring game, but this is heads up, so 84o is playable. The BB checks behind.

Before proceeding to the flop, let's consider what the players' ranges look like after limping preflop. The following two charts show the BN and the BB's ranges. These ranges are as wide and weak as ranges are going to get preflop. You should note that the BN's range is a bit stronger, since the BN has to mix some stronger hands into his calling range in case the BB raises. The BB's range is weaker since the BB would raise with the top portion of his range. Because of this, the BN does have a small amount of pocket pairs in his range, in addition to better Ax and Kx holdings, for example, and less of the low card holdings that dominate the BB's range.

On that note, let's see a flop.

In limped pots, checking is very common. Checking all the way down to the river is the most common action sequence. In a game where checking is so mainline, and the BB has the weaker range, it should be no surprise that the BB should check almost all of the time on virtually every flop. This is actually a decent flop for the BB. Nonetheless, even with trips, the BB should only bet 34% of the time. He should mix in a small amount of bluffs to bring his range's overall betting frequency to only 13%. In comparison, on most flops, the BB should bet less than 10% of the time, in some cases less than 5% of the time. Having said that, betting here wouldn't be an atrocious mistake; it costs only about 0.1 to 0.2 worth of EV for many of the hands in the BB's range, but 0.1 to 0.2 worth of EV is 5 to 10 BB per 100. Mistakes in limped pots are nothing to sneeze at. The BB takes the mainline with a check.

In raised pots, when the weaker range checks, the stronger range often decides whether to continuation bet. If the BN bets here, it wouldn't technically be a continuation bet, since it wouldn't be continuing a pattern of betting preflop. But the concept is similar. While checking is the mainline, the BN does get to do some amount of betting because of his range advantage. Non-monotone Ace high flops are some of the best flops for the BN's range here because his Ax holdings are so much stronger. For example, on an AhJd3d flop, the BN should bet 55% of the time, with his Ax holdings betting 82.7% of the time and the majority of hands in his range betting at least some of the time. Because the BB has more Threes in his range, this particular flop is one of the worst for the BN. He should only bet 29.2% of the time on this flop. Interestingly, 84o is one of the hands the BN should mix into his betting range as a bluff. The chart below shows the BN's range distribution for this decision (blue means check and orange means bet). The BN's bets includes primarily full houses (with those rare pocket Kings), trips, and a bunch of bluffs which the BN finds in the lower middle part of the range chart, where the offsuit low cards are.

The BN decides to take the mainline with a check, and we proceed to a turn.

On the turn, the mainline is again check-check, and it's what the players do. Nonetheless, both players have meaningful decisions to make as to whether to finally wake up and bet. On the flop, the BB was checking almost all of the time. On the turn, the BB gets to do some amount of betting. On this particular runout, the BB's range should bet 23.9% of the time. The chart below shows his range distribution for this turn decision (blue means check and orange means bet). Note that the board is paired, so the worst holding is just a pair using the Threes on the board. The chart shows that the BB should wake up and bet most of his trips, and bring along all of his inside straight draws. Nonetheless, the BB takes the mainline and checks.

As the range distribution chart below shows, the BN gets to do something similar. Nonetheless, the BN's range should still check most of the time here (67.2%), and the BN decides to do just that.

On that note, we proceed to a river, which is where the BN finally makes a real mistake.

On the river, the BB's range consists of the occasional full houses or trips which for some reason did not bet earlier, two pair, or one pair (which is on the board, so it's really nothing). The range distribution is shown below (blue means check and red means bet). The two pair part of his range should bet 36% of the time, with higher betting frequencies in the Kx holdings. He should also bet as a bluff 12% of the time, reserving some of his worst hands for this role. The BB again decides to take the mainline with a check.

The BN makes a mistake here by checking back on the river. Consider the BN's range distribution, which is shown below (blue means check and red means bet). With the two pair part of his range, he should bet 74.2% of the time, 100% of the time if he has Kx. He should also bluff 23.2% of the time when he has nothing other than the board pair. This bluff decision is worth unpacking.

Before the river, when it comes time to mix in some bluffs, you usually get to mix in some semi bluffs and call it a day, so it's harder to make a pure mistake. You might not mix in the right proportion, but you would be less likely to choose an action you should never take (a pure mistake). On a river like this, the bluffing range has some real hard edges that the BN should know and think about. In particular, in this situation, the BN should bet 100% of the time with Ten-high or worse. With Ace-high, Queen-high, and Jack-high, the BN should check almost 99% of the time. The reason for this is that Ace-high, Queen-high, and Jack-high do have showdown value against the BB's range, whereas the lower hands have little to none, so they should fill out the bluffing range.

It's possible the BN wasn't thinking about bluffing at all. It's worth looking back at the range distribution at this point. In a pot that checked all the way down from a limped preflop, the players' ranges are quite weak. If the BN bets here, he should realize that about two-thirds of the BB's range will have to fold, because he has nothing other than the pair on the board. Even his worst two pair holdings (6x) will have to fold some of the time because of the amount of higher two pairs in the BN's range. This fold equity alone, with no more streets to come, is something the BB should be considering here. It makes betting with the bottom part of his range, including this hand, all the more enticing.

Let's see a showdown.

As it turned out, the bluff wouldn't have made a difference since the BN's 8-high beat the BB's 5-high.

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