Updated: Oct 17, 2021
Conventional wisdom states that bluffing with a pocket pair is a bad thing. Pocket pairs have only 2 outs, if they're behind in a hand it's very difficult to improve. The hands that your opponent calls with also have bundles of equity against your small pocket pair. So even though you could be ahead in hand value, you can still be behind in equity (% chance to win) when bluffing with such a small pocket pair.
However, poker solvers are addicted to bluffing with 22, 33 and other smaller pocket pairs. Is the conventional wisdom wrong? Do the solvers know something that we don't? or, is it time the we updated how we think about bluffs in poker?
Small pocket pairs do have a few tricks up their sleeve when played as a bluff and when you have an abundance of hands to choose from to bluff with, they make much more sense than a random hand to bluff with.
Bet then Fold.
One issue with selecting a hand such as a gut-shot straight draw to bluff with, is that the hand has a fair amount of equity still. It has 4 outs to the nuts to hit by the river and would benefit from realising this equity. If we were to be x/raised with a gut-shot straight draw after betting, we wouldn't quite have the implied odds to call (most of the time) and we are being denied the realisation of a large amount of equity.
Small pocket pairs don't have this problem, they have such little equity against a players raising range that a fold becomes easy. No issues with equity realisation or folding a good hand at all. When you start paring this fact with the following concepts like the unblocking of folding ranges and what exactly clean outs are, 22 starts to look like a much more appealing bluff.
Unblocking a Folding Range
The concept of blockers is a relatively advanced topic, made more complicated when we start talking about unblockers. In poker, you can block your opponents good hands by having specific cards in your own hand. For example, if you have the Ace of Hearts, then it would be impossible for you opponent to have the nut-flush in hearts.
On the flip side to this you can unblock certain hands by you not having that specific card. Now you not having the Ace of Hearts makes your opponent having the nut-flush more likely. This becomes especially important when thinking about bluffing combinations. While its good to block your opponent from having good hands, it's as good if not better to unblock hands that your opponent can fold.
This is the reason bluffing with missed flush draws is ill-advised. Ideally, your opponent had the flush draw and will be forced to fold to your bet. When you have said draw, you are increasing the chance that your opponent will have a hand that he can call with. In other words, you are blocking his folding range.
What Makes Small Pocket Pairs Such Good Unblockers?
The goal of a bluff is to make our opponent fold a better hand or fold hands that have a large amount of equity against us. We would prefer to increase the frequency at which we generate a fold with our bluffs. The main problem with picking random hands to bluff with is that they can block weak hands in your opponents range. These hands include our opponents 2nd, 3rd pairs, and hands that have good amounts of equity still such as weak draws.
On this board for example, it's showing the optimal strategy for our opponent on the Turn facing an overbet from us. If we selected a random Tx hand as a bluff, we would be reducing the combinations of AT, KT, JT, 9T etc. that our opponent could have by a significant amount. When we reduce the combinations of weak hands from our opponents range, we are slightly increasing the chance that they have a hand strong that they will call with. So when we are spoilt for choice for bluff options, picking a hand that makes it slightly more likely that your opponent will fold is ideal!
Because nearly none of the hands that our opponent will fold contain a 2, 3 or 4- we are increasing the likelihood that the hand they do have is one that will fold. That's exactly what pocket 22's, 33's and 44's do. Very few of the weak 2nd or 3rd pair hands that we want our opponent to fold contain a low card, therefore we are unblocking the folding range.
Clean Outs, Dirty Outs, and Cards That Kill Action
We know that 2 outs is not very many in poker. When bluffing, we typically want to chose hands that have a lot of equity- a lot of outs. This is so that we have a back-up should our opponent not fold, we still have a high chance of winning the hand. Sometimes though we also need to think about the quality of our outs. Doyle Brunson famously talked about "double belly-buster" straight draws and how deceptive they could be. The idea being that the straight you made would be so disguised, opponents would call down and often not factor you having such a draw into their calling decision. We can take some of that old wisdom with us to the modern game. Some outs will increase the chance that our opponents call, others will kill the action.
Outs that kill the action are quite common, even just making a flush will make your opponent more tentative when deciding to call, and often will lead them into playing much more passively. How often do you raise with 3-of-a-kind when there is a flush possible? These action killing rivers can lead you to lose some value, and it's why calling with a draw out of position is often a losing strategy.
Another issue that you can run into, is that some draws have "dirty outs". I define a dirty out as one that may improve your opponents hand more than it improves your own. A flush draw for example would have 9 outs, but at least one of them is a dirty out- as it will pair the board which could give your opponent full houses. The most obvious example is actually a straight draw on a board that also has flush draw possibilities. Sure you have 8 outs, but 2 of these can make a flush possible on the board, which would kill action and could leave you out of pocket.
Why is this relevant? Small pocket pairs almost always have pure outs if you choose the correct combinations.
How Small Pocket Pairs Have Pure Outs
If I asked you to describe a brick on the river, a card that didn't improve either players hand, you would no doubt say a 2, 3, 4 or even 5 that doesn't bring in a flush draw or straight draw. This brick on the river would increase the probability that a player had a missed draw and therefore increase the likelihood said player was bluffing. This means that you are likely to get called much lighter on the river should a brick come along.
The great thing about small pocket pairs is that despite having only 2 outs, on most board textures, both of theses outs are going to give you the best hand on the river- provided there are no straight or flushes already possible. We are also expecting opponents to raise with their own sets at some point in the hand. What this means is you are likely to get much more value if you do hit a set on the river than if you had some other bluff, a flush draw for instance.
This is another great thing about small pocket pairs and why they are included as one of the best bluffing combinations in a GTO strategy.
Why Do Solvers Choose Small Pocket Pairs To Bluff With?
Solvers choose smaller pocket pairs for a number of reasons. In a range that is filled with potential bluffing candidates the most important reason by far is that it's best to pick the hands that increase your opponents chances of folding. Small pocket pairs contain no blockers to all the trash that your opponents have and gets them to fold a had containing a bunch of equity against ours. Good pure bluffs also want to have no problem folding facing a 3bet, something that a gut-shot would be borderline with, a small pocket pair is a no-brainer fold.