Thinking About Ranges

by Andrew Brokos
This article originally appeared in Two Plus Two Magazine

If there is one lesson I have learned and re-learned as I’ve moved up the stakes in no limit hold ‘em, it’s that nearly everything comes down to hand ranges, both yours and your opponents’. The former may be grist for another article, but at the moment I want to address some of the myriad ways in which the hand ranges you assign your opponents should influence your decisions at the table.

Most readers of 2+2 Magazine will understand that they are supposed to be putting their opponents’ on a range of possible hands. However, many will be equally confused about what exactly to do with these ranges. That is, they will not necessarily understand how exactly the ranges they assign should influence their decision-making in virtually every situation.

There is a lot more to it than thinking, “I beat that range, so I’ll call,” or “I don’t have the right equity versus that range, so I’ll fold.” Your perception of an opponent’s possible holdings should influence everything from whether you bluff to how you size your value bets, sometimes in rather subtle ways.

This article will move quickly through the basics of calculating your equity versus a range of hands and then examine some of the more complicated ways in which the ranges you assign should influence your play.

Assigning a Range and Calculating Equity

You are on the button with a pair of Jacks in a $5/$10 full ring no-limit hold ‘em game. Tighty McNuts raises UTG to $50, and only you call. The flop is AJ2, and Tighty moves all in for $115. You have played with Mr. McNuts many times and are confident that he would never move all in without at least a set. Since you are looking at three of the Jacks, then his range must consist of 50% sets of Aces and 50% sets of deuces, in which case we have a clear call getting 2:1 pot odds, right?

Wrong. The range you assign to an opponent should evolve from street to street, growing narrower as you gain more information based on what your opponent does. An absurdly tight player is much less likely to raise 22 than to raise AA when he is first to act at a full table. In fact, Tighty will make this raise with 22 only 10% of the time, whereas he will do it with AA 90% of the time. Pre-flop, 22 and AA are only a few of the hands that we put in his range, but once we see him move all in, they are the only two we care about.

There are two important concepts to note from this example. First, you must consider all of your opponent’s actions in the hand, not just the current street, in your analysis of his range. Second, a range consists not only of a set of possible hands but also of the probability that your opponent holds each of these hands. This is sometimes called a weighted range, though that’s a bit redundant: every range ought to be weighted.

In this case, our range for Tighty McNuts is 10% 22 and 90% AA. To calculate our equity versus this range, we multiply our equity versus each hand times the probability that our opponent has that hand and then sum these products. In this instance, 90% of the time our opponent has AA and according to Poker Stove (a very handy, free tool available at www.pokerstove.com), we have 4% equity. The other 10% of the time, he has 22 and we have 96% equity. That makes our total equity (0.9)(0.04) + (0.1)(.96) = 0.132, or roughly 13%. Even given pot odds of 2:1, this is a clear fold.

Note that if we had not considered the pre-flop action and weighted Tighty’s range appropriately, we would have calculated 50% equity and quickly but incorrectly called his all in.

This is the most basic application of range-based decision making, and it may be obvious to some. But as we’ll soon see, assigning a range is useful for a lot more than calculating showdown equity.

Bluffing

There is a lot more to bluffing than betting because you don’t have anything but are sure your opponent will fold. In fact, if you are only bluffing when you are sure your opponent will fold, then you are not bluffing nearly often enough.

The decision to bluff should be based on the range you assign your opponent. When contemplating a bluff, you should be able to articulate which specific hands in your opponent’s range you expect him to fold. You can then compare his folding frequency to the size of the pot and the size of the bet you are considering to decide whether the bluff will be profitable.

Suppose that at a $5/$10 NLHE table, you open for $30 with 4 :spade: 3 :spade: in the CO and are called only by the SB, a tight aggressive regular in the game. The flop comes 9 :heart: 8 :heart: 7 :diamond:. Because you have nothing, you are tempted to take one shot at stealing with a half-pot bet and then give up the pot. But don’t bet automatically just because you read somewhere that you are supposed to bet at the flop after raising pre-flop. That’s generally good advice, but like most things in poker, it is situational and your decision must ultimately be based on how you expect your opponent to play each hand in his range.

Many solid, tight aggressive players will have a surprisingly narrow range for cold calling a raise from out of position. They will fold the vast majority of the time, usually re-raise with their strongest hands, and call almost exclusively with speculative hands like pocket pairs and suited connectors. So let’s assign this one a range of pairs 22-99, suited connectors 76s-KQs, and gap suited connectors J9s-KJs.

Intuitively, you may notice how well this flop connects with your opponent’s range. Assuming that he’ll call or raise your bet with bottom pair or better or a draw with eight or more outs, he’ll be folding 22-55 100% of the time and QJs, KJs, KQs 75% of the time (the other 25% he has a heart draw). Even without calculating the exact percentage of his range that these hands represent, it should be obvious that a one-street bluff will succeed too infrequently to be profitable.

So you check. The turn is the 2 :spade:, and your opponent checks again. Even though you were prepared to give up on the flop, you can’t stop thinking about his range, because a profitable opportunity may have just presented itself.

You are confident that your opponent wouldn’t have passed up a second opportunity to bet his stronger hands or to semi-bluff most of his draws. You believe his calling standards remain the same but can now narrow his range to 33-66, 76s, 86s, T8s, and his non-heart QJs, KJs, and KQs. That makes 18 combinations of pocket pairs (remember that you are holding a 4 and a 5), 12 of which (all but the 66’s) are folding, 9 pair and draw combinations that are not folding, and 9 combinations of unpaired cards that are folding. Your opponent will fold 21 of his 36 possible hands, making a half-pot bluff profitable.

Note that you can get away with this relatively small bluff only because a decent portion of what you need your opponent to fold is, from his perspective, air. If you had something like AK, your would have a lot less to gain by folding out hands like QJs, then this bluff might not make sense.

Value Betting

Like bluffs, value bets should target specific hands in your opponent’s range. Assuming that he is capable of some basic hand reading, then your full thought process when betting for value in position on the river should go something like this: “I want him to call with X, so I’ll bet $Y, hoping he’ll put me on Z.”

Suppose you raise A5 to $30 on the Button in a $5/$10 head up no-limit hold ‘em match. At this point, his range is still be too wide to enumerate, though you should already be discounting certain hands. He probably does not have T2o (you’d expect him to fold that) or KK (you’d expect him to re-raise that, at least most of the time). Your opponent calls, and you see a KTT rainbow flop. He checks, you bet $45, and he calls.

Now we’re getting some worthwhile information. Although your opponent is very capable of bluff-raising, you have never seen him call with the sole intention of bluffing a later street, and you think he is particularly unlikely to do this out of position. So his range most likely consists of Ax (he knows you make a lot of continuation bets and correctly assumes that Ace-high is ahead of your betting range), Kx, QJ, Q9, T8-AT (you expect him to fold worse Tx pre-flop), pocket pairs 22-88, and occasionally higher pocket pairs, though you believe he would usually re-raise these pre-flop.

The turn is another K, which is a great card for you: it counterfeits most of your opponent’s pocket pairs, makes it less likely that he has a K in his hand, and gives you a tie against most of his Ax holdings that previously had you outkicked. He checks, which tells you very little, and you are happy to check behind.

The river is a deuce, and your opponent checks again, enabling you to narrow his range even further. You are fairly sure that he would have bet any full house or quads and would have bluffed with a counterfeited pair. This leaves only Ax, QJ, Q9, and the rare AA/QQ/JJ in his range.

Looks like a good situation to value bet, since you are almost never beat. The question now is how much to bet. To determine this, you need to consider which hands you are targeting. In this case, you are looking to get value from QJ and Q9. What would cause your opponent call a river bet with Q high? If he thinks you are bluffing. Thus, you have to make a bet that your opponent will interpret as a bluff.

This is an important point, because many players make the mistake of betting an amount commensurate to the strength of their hand. They bet a lot when they are bluffing or value betting a big hand and make tiny “suck bets” when value betting thinly. This is a very obvious, intuitive betting pattern, and your opponents can and do take exploit it.

I am not saying that you should always make a big value bet here; that depends on your opponent. What I am saying is that your opponent’s calling range, not the absolute strength of your hand, should determine your bet sizing. If your opponent will call a half-pot bet with Q-high three times as often as he would call a pot-sized bet, then you should bet the smaller amount. If he will call the smaller bet less than twice as often, then the bigger bet is better. You must first decide which hands you want to call you and then determine how to maximize your equity against those hands.

Conclusion

Although many players have a vague sense that they are supposed to be thinking about their opponent’s ranges, most do not seem to understand what exactly to do with that information. Hopefully these examples illustrate the importance of keeping a running tally of your opponent’s possible holdings and demonstrate some of the ways in which you can use these reads in your decision-making.