# Pocket Pairs

Last week I wrote an article about playing pocket pairs for setvalue , in which I talked about certain situations where you play for setvalue in a 3-bet pot. Of course this is not always the case. Often when playing a pocket pair (PP from now on), you are faced with 1 single raise. The following paragraph will sum up the points I will be discussing in this article.

When playing for setvalue, you need to focus on the following things: range of your opponent, his aggression, the stacksizes, cost of the call, money in the pot, and a few more factors. The last article talked about how these factors can influence your decision. We also calculated that you flop a set and win the pot 10% of the time, while we won't flop a set or will flop a set and lose the pot 90% of the time. We discussed the 5/10 rule and reached some mathematical conclusions. In this article I will try and fill the gaps and discuss the things that weren't discussed in my first article.

Playing as IR

If we are the initial raiser (IR), we don't have that many difficult decisions to make. We want to play our pocket pairs in an open pot, and since we don't like to open limp, we raise. Often we will pick up the pot preflop. If we do end up seeing a flop, we can always flop a set, a full house or even 4 of a kind, or we can miss the flop completely.

If we flop a strong hand we can either bet or check. This decision does not only depend on the board, but also on your opponent(s). Ask yourself: what range does my opponent have? Then ask yourself if he will call hands from that range, and how you can get the maximum value out of the situation. Imagine we have . On a flop like , it is often difficult to get value out of an opponent on all three streets, as he won't often have hit the board, and if he does hit, he can't be that happy with his hand to put his whole stack on the line. On a flop like , however, you can and must bet out straight away because far more hands will call. In a case like this, you don't only bet for value, but also for protection. By being aggressive you will often get your money in straight away while holding the best hand.

If we do miss the flop, we can often still pick up the pot with a continuation bet. How and when you can best C-bet will not be discussed in this article. If you do want to know more about continuation betting, check out this article.

Playing in raised pots.

Pairvalue, setvalue, bluffvalue

Lets just lay out all of our option in front of us. We don't always have to play our pocket pairs solely for setvalue, we can also play them simply for pairvalue. You can easily call a raise with 88 on a flop showing J73. Your opponent will often check the turn if he has nothing and you can think about how to best pick up the pot. You also have the possibility to bluff your pocket pairs, let's just call it bluffvalue to keep things simple. To sum that up; we play our pocket pairs for setvalue, pairvalue and bluffvalue, or a combination of these factors.

Classification of the pocket pairs

In the following table you can see how often you flop 1, 2, 3 or no overcards with your pocket pair. In the last column you see the heading "all the rest", which will be explained later on. I produced this table with the help of StoxEV.

First of all, you can see that the numbers in the "all the rest" column are all 12%. This means that 12% of the time, we will flop a set, a full house or quads. With full house I mean not only flopping JJ6 with pocket 6's, but also flopping JJJ with pocket 6's for example. The value of a full house when there are trips on the board increases as the higher your PP is.

I chose the following classification with PP: 22 up to 77 are small pairs, 88 up to JJ are medium pairs, and QQ up to AA are big pairs. This classification is based on my experience at the table playing PPs. 88, for example, is on the border between small pair and medium pair, while JJ can be said to be on the border between medium pair and big pair. The value of these border pairs depend a lot on who you are playing against. More information about this classification will follow later on.

But this classification is not only based on experience, it's also got a lot to do with math. You can see the situations highlighted in yellow that will occur most often on the flop for each PP. With pairs between 22 and 77, you will often flop 2 or 3 overcards, which makes it difficult to play for pairvalue. With pairs between 88 and JJ, you will often only see one overcard on the flop, so these hands can often be played for pairvalue, although in some situation we can only play them for setvalue. Pairs between QQ and AA will rarely see and overcard on the flop, which is why these hands are the best to play for pairvalue.

In general, we can say that:

- 22-77 is mainly played for setvalue, sometimes for pairvalue

- 88-JJ is played for pair- and/or setvalue, depending on the situation

- QQ-AA is mainly played for pairvalue, sometimes for setvalue.

The problem with the small pairs

The big problem with small pairs is the range of our opponents, and the effect that this range has on our implied odds. Imagine you get dealt 55 on the button and a TAG player in the cutoff raises to 4x BB. Many players will make a call here, but can we actually do that here? It's going to be very difficult to play for pair- or setvalue, as our pair will rarely be good with so many overcards. 71% of the time, you will see 2 or 3 overcards on the flop, in which case you can't do much with your hand unless you flop your set. If we do actually hit our set, we will rarely get paid off because of his wide range of hands. In order to not play this situation â€"EV, we need to take a closer look at our options.

The options we have after his raise are folding, calling and raising. Folding is, as always, 0 EV. A call is â€"EV, how is this possible? First of all our opponent has a very wide range. On the flop we will hit 2 or 3 overcards roughly 70% of the time and will almost always have to fold to a C-bet. If we do hit a set at some point, we have to have the additional luck that our opponent also hits a hand strong enough for him to commit a lot of money into the pot. Is that going to happen often? Of course not. A call with 55 is therefore â€"EV. The one option left now is a 3bet. This 3bet would actually be a bluff, as he would never call with weaker hands, but might fold stronger hands. We know that he opens with a wide range, and will therefore have to fold a lot of hands when confronted with a 3bet. We also know that if he should call, we will be behind the majority of the time. A 3bet with 55 in this case is, therefore, nothing more than a bluff, but it is a +EV bluff, as long as we don't do it too often. If we end up doing it too often, our opponent will start playing back at us with his wide range. As a result, we find ourselves involved in a pot that we can only win with a postflop bluff or if we hit our set. Or it could end up even worse: he could 4bet us preflop, in which case we will have lost 10-15% of our stack with our PP (assuming we started with 100BB stack).

The solution for our problem with pocket 5's is therefore obvious: 3bet > fold > call, but only if we vary enough between folding and 3betting. 3bet just enough to make it a +EV move.

An analysis with StoxEV

With the help of StoxEV I constructed quite a complicated decision tree for this CO vs BTN battle. Preflop, the CO opens with the following range: 22+, A5s+, A8o+ and broadway cards. You call with 22-TT. JJ+ is not mentioned here as that is an obvious 3bet. I kept the postflop game fairly straightforward, without fancy moves. The CO bets middle pair or better, flushdraws, gutshots or better and a board with an A, K or Q. You only call with middle pair or a gutshot/OESD, raise with a set and fold the rest. If you flop a set and raise his C-bet, he will push with combodraws, TPTK, and with hands like AK and AQ. Using this information, StoxEV constructed a huge decision tree for the postflop game. We then calculate the EV from the tree and can find out what our EV is for our PP.

Pairs between 22 and 55 are â€"EV or breakeven if we call, and all higher pairs are +EV. This is because of the pairvalue that is present for hands 66+, as opposed to 22 up to 55. If your opponent is not willing to go all in every now and then with a hand like KQ, or a hand where he flopped top pair when you flop a set, then it is recommended to not call 66 preflop, but to either fold it or 3bet it.

What changes if we're on the button with 22-TT and want to call an UTG raise? Which pairs are then +EV. Our intuition tells us that we can now call out PP more often, because an UTG range is much tighter and we are more likely to get all out money into the middle if we hit. Let's assume that an UTG raise range lies between AJ+, 22+ and KQ. Now we suddenly get +EV when calling with PP between 22-TT. Surprising? Not really, because his tighter range increases our chance of winning big if we hit our set. If we don't hit our set, we can still find some +EV spots with our higher pairs in which our pair has enough showdown value to win without hitting a set. If your opponent can easily fold AJ or KQ after hitting top pair on the flop, then a call with 22 or 33 would also end up being â€"EV, so with these hands our options are again limited to folding or 3betting. 3betting is maybe not the best idea against an UTG range, and therefore you should probably fold them against a strong player raising UTG. With 44+ you can start calling his UTG raises.

So, the question we ask ourselves is: how tight does the opening range of our opponent need to be before we can start calling pairs between 22-TT and make profit in the long run? In the table below you can find the answer for different ranges (calculated using StoxEV)

This table does not suggest that you should fold hands like 55 against a wide opening range. The exact opposite is the case! In situations like these, a whole new world unfolds: 3betting. Because their opening range is so wide and they will hardly be able to call or raise anything after you 3bet (in other words, you have fold equity), a 3bet in this situation would be +EV. You also don't always have to call your pocket 7's against the last range just because it's +EV. Often you can simply 3bet here as well, although you might run into a strong hand every now and then against which it will be very hard to play without hitting your set. When 3betting pocket 7's against a wide range, it's almost always a bluff, as your opponent will not call with weaker hands. So make sure to have enough fold equity against a player like that.

As you can see, the tighter the range of your opponent, the more you can call with PPs. The looser a range, the more you have to fold your PPs or 3bet them, as calling with them is no longer +EV. 3betting against a tight range is not always the best idea, as your setvalue increases against a tight range and you are scaring worse hands out of the pot. These are all reasons why a call might be the best idea when we're up against a tight range player.

Against a looser range it's a different story, as calling becomes â€"EV here. Whether or not you will then 3bet against a loose range depends on your hand and your opponents' tendency to call 3bets. With small pairs you can easily 3bet if he folds a lot, and fold them if he calls a lot of 3bets. With medium pairs you can often +EV call and think about 3betting when sitting OOP, a call would be â€"EV and your hand is too good to fold. If you think your opponent might call your 3bet with a worse hand, you can start 3betting for value. A very general guideline is: call against EP raisers and fold/3bet against LP raisers. But of course every situation is different, so don't feel bound by this rule.

Now we have completed a kind of general analysis on the situation of PPs and how to play them preflop, choosing between folding, calling or 3betting. Now we'll take a more in depth look at setvalue itself.

Playing for setvalue

So when can we make a call now? If you only play for setvalue and forget about pairvalue, you can, principally, call with hands between 22 and 66 (and sometimes 77), but you need to make sure that you can win something postflop after you hit your set, in other words, you need implied odds. Often you won't hit and you will have to fold, the pot gets checked down, or your opponent C-bets the turn instead of the flop. The bottom line is: More often than not, your small pair won't win without flopping a set.

Everything you've read so far was based on you having the option between folding, calling or 3betting. Calling is favorable against tight ranges. The question is whether you should call against a tight range all the time. No! There are things you need to watch out for. These things include: the effective stacks and the costs of the call.

We will flop a set 11.76% of the time and will win on average 85% of these situations. That means that we will flop a set and win the hand 10% of the time (11.76% x 85%). The following equation clarifies our EV in such a call-situation.

EV = (0.10 * (current pot + X)) â€" (0.90 * cost of the call)

where X = implied odds

Let's try using an example. We get dealt 88 on the big blind. A 16/14 player raises UTG to 4xBB and everyone folds around to us. Folding and 3betting are incorrect against a tight range, so a call is the best option. Then again, a call is only correct if we get enough implied odds postflop. In other words, we need to win enough if we hit our set.

In this situation the equation will look the following:

EV = (0.10 * (5.5 BB + X)) â€" (0.90 * 3 BB)

How much do we need to win postflop to break even? We find this out by putting EV equal to 0 to solve for X.

0 = (0.10 * (5.5 BB + X)) â€" (0.90 * 3 BB)

0 = (0.10 * (5.5 BB + X)) â€" 2.7 BB

0 = 0.55 BB + 0.10X â€" 2.7 BB

-0.10 X = -2.15 BB

X = -2.15 BB / -0.10

X = 21.5 BB

From this we can see that our implied odds need to be 21,5BB. This number has an important characteristic, namely that it is an average. Sometimes you will hit your set and get no money what so ever out of your opponent(s), while other times you might win his entire stack. What is important is to win an average of 21,5BB every time you hit your set.

Let's imagine a situation where we flop a set and repeat this hand 5 times. 2 out of 5 times we win an extra 10 BB postflop, 1 time we win nothing, 1 time we win 25 BB and 1 time we win 100BB. What's our average here? Well, it's (10 + 10 + 0 + 25 + 100)/5 = 29 BB. That means that on average, we win 29 BB when we flop a set. And since 29 BB > 21,5 BB, we can see that we made a +EV call. Now imagine that we're playing against a better opponent, who will not just through all of his chips into the middle. Again we flop a set and repeat the hand 5 times. 1 time we win nothing, 2 times we win 10 BB, 1 time we 25 BB and 1 time we win 50BB. The average here ends up being 19 BB, and since 19 < 21,5, we can see that a call against this player is â€"EV.

A general rule you can follow is the following: You can call for setvalue if you, after you flop your set, can win back 9 times the cost of your call, minus the money that is already in the pot when you call preflop. In this situation, we had to call 3 BB to see a flop. 3 x 9 = 27 BB. There's already 0.5 + 1 + 4 = 5,5 BB in the pot, so you need to win 27 â€" 5,5 = 21,5 BB. Not that difficult is it?

One more example: we have to call 5 BB with our PP on the button. You think that both of the blinds are going to fold to the UTG raise. The pot is now 0,5 + 1 + 5 = 6,5 BB. So, postflop, you need to win 9 x 5 = 45, minus the money already in the pot. 45 BB â€" 6,5 BB = 38,5 BB. Whether or not you can win that amount on average is a decision you will have to make yourself by focusing on the effective stacks (are they big enough) and your opponent (will he pay me off when I hit?).

Conclusion

So, this article ended up being pretty long, nut I'm sure you've learned a thing or two about playing pocket pairs. I hope you enjoyed the article.

Kurt Verstegen (Riverdale27)