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One of the things that I’ve seen people struggle with is getting a feel for how different ranges come together on boards to create equities. It’s one thing to be able to get a relatively good idea of what both you and your opponent’s ranges look like in a given scenario. However, you also have to be able to get at least a rough picture of what the relative equities look like. In this series, we’re going to look at some factors that play into figuring out what those equities are like.

### Why Hold’em Ranges Are Problematic

There are two reasons why getting a feel for hold’em ranges can be problematic. The first is that you can’t rely on the intuition you’ve already built by working with the real number system in your everyday life because hold’em range equities are not transitive. What that means is that just because range A beats range B, and range B beats range C, it doesn’t mean that range A beats range C. Here’s a quick example of that:

• JTs has 54% equity vs. 22
• 22 has 53% equity vs. AKo
• AKo has 59% vs. JTs

Note that in this example JTs beats 22, and 22 beats AKo, but it doesn’t mean that JTs beats AKo. This doesn’t come into play all that often, but it’s a real eye-opener for people to see how seriously you have to take learning this as a skill instead of relying on “common sense.”

The other reason why the equities for hold’em ranges can be a pain is that they depend on both your range and your opponent’s range. This means that you’re going to have to juggle a lot of information and be able to quickly break it down into the parts that matter a lot and the parts that don’t matter as much. We’re going to attack this problem with the Pareto Principle (or the 80/20 rule) by trying to work with the 20 percent of information that influences 80 percent of your feel for range equities.

### The Principle for Draws in Ranges

Normally, you think of adding size (or girth) to a range as decreasing that range’s overall strength. The reasoning behind this is that there are only so many good hands that you can have in a given situation, and once those are in your range, you have to start adding hands that aren’t as good. Naturally, you think of this as bringing down the overall strength of the range. Draws, however, do not influence the equity of your range as much as you might think, and this is the principle that we’re focusing on with this part of the series:

Strong draws do not decrease the equity of our range as much as we tend to think.

With that principle out there, let’s look at a couple of examples that will help to cement the idea.

### Good Hands vs. Better Hands and Draws

Suppose we have {A8+} against {A2+} on a board of As Qh Jh 2c. Because of the superior kickers, it’s obvious that we will have the advantage here, and that advantage is shown with our equity of about 64 percent in this scenario. The question we want to think about here is what will happen to the equity of our range if we add a whole lot of draws. Specifically, we’re going to look at what happens when we add a lot of eight-out straight draws in this particular situation.

First, consider the current size of our range. With {AK, AT-A8}, we have four hands that have 12 possible combinations each which gives us 48 combinations. For {AQ-AJ}, we have two hands that have nine combinations each, and that’s another 18. Overall, we have 66 combinations to start with. If we add both T9 and T8 to our range, we’ll be adding an additional 32 combinations which is close to a 50 percent increase in the size of our range.

So if we increase the size of our range so much with draws when we only have one card to come, what will happen to our equity? Note that with an OESD on this turn against a hand like A4, we only have about 18 percent equity. Shouldn’t adding hands this weak just kill our equity? As it turns out, and according to our principle above, it doesn’t really put us in a terrible situation after all. We are only a 45/55 underdog after increasing our range by a factor 50 percent with hands that have 18 percent equity or less against our opponent’s range.

If we were to just add total air, consider what would happen if we just added 65 to our range instead of {T9-T8}. With 16 hand combinations of 65 added, our equity becomes 48 percent. Essentially, we drop about the same amount of equity by adding half as many hands of air in this example. This really illustrates how much stronger these hands are than air and how adding them to our range does not move our equity as much as a lot of people would initially think.

### Going Back to the Flop

If we back up to the flop and look at {A8+} against {A2+} on a board of As Qh Jh, we’ll find something that you probably would suspect. Because the value of OESDs increases on the flop when compared to the turn, we’ll have a higher equity when we add them to our range. If we add {T9-T8} to our range, our equity only drops to about 50 percent. If you added 65 instead, the equity would tank to about 48 percent again. Notice that air in this case doesn’t benefit much from being added on the flop when compared to the turn like the stronger draws do.

### Conclusions to Draw

The point we’re looking at here is that we have to accurately consider how draws change the equities shared between two ranges. When we add draws to our range, we lose less equity on the flop than on the turn. However, because we’ll have implied odds with draws, a lot of that decrease in equity is compensated for by the fact that we won’t put in as much money overall when we miss with draws as when we hit. Pay close attention to how this affects the ranges and their equities in the hands you play, and next week we’ll get into another aspect of range equities in no-limit hold’em.