One of the things that a lot of people have a big misunderstanding about is the difference between equity and expected value. We’re going to look at a few examples in this week’s article that should help players to develop some clarity on this issue. We’ll start with some very basic, conceptual scenarios and back up into some larger issues dealing with common situations.
Equity and Bet Sizes
Expected value is a function of three major pieces of information: the size of a range, the equity that range has and the size of the bet being made or called. The relationship between equity and bet size is what we’re going to look at first.
Consider the following. If you put in a bet of $10 that is always called when you have 60 percent equity against a single opponent, then your expected value from that bet in a vacuum will be (0.60)(10) + (0.40)(-10) = $2.00. You have a 20 percent advantage in equity (60 percent vs. 40 percent), so you’ll be picking up 20 percent of the bet size in a vacuum. Being aware of your equity advantage on a single bet is often more useful than knowing your actual equity in heads-up situations.
Now consider what the scenario looks like when you have 70 percent equity with a bet size of $5. Your equity advantage is 70 percent – 30 percent = 40 percent, and 40 percent of $5 is $2.00. It’s not intuitive to think that having 70 percent equity with a bet size of $5 has the same expected value in a vacuum as a bet where you have 60 percent equity with a bet size of $10 because you’ve been trained to think of your own equity instead of your equity advantage.
The point of looking at these two examples is to help you to understand the anti-intuitive nature of equity as one of the variables that determines expected value.
When Bet Sizes Change
Another issue that a lot of players have a problem with is thinking that an equity advantage in a given situation means a lot more than it does. For example, suppose that you are betting a flush draw on the turn against an opponent who probably has a medium-strength made hand when he calls. You probably have about 16 percent equity. However, because the river action will differ greatly based on your future equity, that 16 percent doesn’t tell a complete story.
Implied odds and reverse implied odds are two of the concepts that are closely related to this idea. The point is that even though you’re making a bet with 16 percent equity, you can still have an overall expected value because of the future betting (ie: implied odds when you hit). This is an underestimated aspect of figuring out exactly what’s going on with your range and your equity in a given situation. A great example of this is how we looked at draws in your range last week. While they might slightly bring down the overall equity of your range, they usually increase your expected value because of the effects of future betting.
Breaking Your Range into Equity-Based Sections
One of the ways that you can start to account for future betting is to break your range up into sections with the idea that each section will have a similar type of equity. All of the hands in each section will usually be played the same, but this isn’t necessarily the same as breaking up your range according to hand strength. Instead, with these sections we’re interested in how our equity will change over the course of a hand. While we would normally call parts of our range things like “strong hands,” “our value betting range” or “our B range,” with these sections we’re going to be looking at how dynamic or static our equity is.
In the context of our overall goal of getting better with hand equities, these sections and their relative sizes can be used to quickly get a feel for what our equity is like in a particular spot as well as what our equity is going to look like on future streets and how betting will affect our overall expected value.
The most dynamic hands that we can have will be draws that will usually either be a total lock to win on the river or complete trash when we miss. These hands will typically bring down our total equity in the present because they miss more often than they hit. However, because future betting usually favors us in terms of implied odds, we more than make up for that decreased equity. Obviously, these draws will range in strength based on how likely they are to hit, how likely they are to hit the nuts and how likely our opponents are to pay us off.
Made hands that are vulnerable to draws are only marginally dynamic. For example, a hand like top pair on the flop is a hand that can be vulnerable to draws or someone catching two pair with their kicker. Barring these instances (ie: a dry flop), their value stays pretty consistent throughout the hand. These hands add to your equity in the present, but you have to think about the future betting when you might be building a big pot with them. This might seem like common sense for people who are aware of the ideal pot sizes to play with certain types of hands, but it’s still important to understand in the context of whether your ranges are dynamic or static.
How to Practice With Example Ranges
While learning about this kind of stuff on a conceptual level can help you to speed up your understanding of what’s going on, the only way to really learn it on a deep level is to practice. I recommend that players break down ranges in terms of decision trees from the flop based on which cards will increase or decrease the value of their hands. From this point, you can add and subtract hands from ranges to see the dynamic aspects at work.