In last week’s article, we looked at the basic components of EV calculations. We made two very important points that we’re going to use this week:

  1. The EV of an event is equal to the EVs of each possible outcome added together.
  2. The EV of an individual outcome is the chance it happens multiplied by the profit when it happens.

We also broke down how to find the EV of any event into a three-step process. If you aren’t familiar with that process, then go back and read last week’s article because that’s the process that we’re going to use to evaluate the expected values of some poker situations this week.

For the time being, we aren’t going to be concerned with factoring in the rake for these calculations. Once you learn how to do these calculations on a basic level, it’s easy to compensate for the rake, and we’ll do just that once we get into more in-depth problems.

A Basic Bluffing Scenario

Suppose we’re on the river with the nut low against a single opponent who has us covered. The pot is $15, and we make a bet of $10. If our opponent folds, then we win the hand. If our opponent does anything besides fold, then we lose. What is the EV of our bluff if we estimate that our opponent will fold 35 percent of the time?

The first thing we need to do is identify all of the possible outcomes. In this scenario, there are really only two possible outcomes. Our opponent can fold, or our opponent will not fold. This gives us the following EV equation for the value of our bluff:

EV of our bluff = EV of opponent folding + EV of opponent not folding

Now we need to find the EV of the outcome of our opponent folding. To do this, we need to know our profit when our opponent folds and the chance of our opponent folding. We will profit the $15 pot when our opponent mucks his hand, and it will happen 35 percent of the time. We multiply these values together to get the EV of the outcome.

EV of opponent folding = $15 * 0.35 = $5.25

Next, we have to find the EV of our opponent not folding. This will happen 65 percent of the time, and our profit will be a loss of $10 since we lose our bet.

EV of opponent not folding = -$10 * 0.65 = -$6.50

Finally, we add the EV of each outcome together to get our overall EV of our bluff.

EV of our bluff = EV of opponent folding + EV of opponent not folding
EV of our bluff = $5.25 + (-$6.50) = -$1.25

So on average, we will lose $1.25 each time that we make this bluff.

A Basic Calling Scenario

In a $0.05/0.10 game with $2.25 stacks before the blinds are posted, it folds to the small blind who goes all-in. We’re in the big blind and decide to call. If we have 55 percent equity against our opponent’s range, then what is the EV of our call?

First thing’s first: We have to figure out all of the possible outcomes. For our purposes, we can say that we’ll either win or lose. That gives us the following EV equation:

EV of calling = EV of winning + EV of losing

Like before, we have to find the EV of each of these outcomes to find the overall EV of calling. The chance of winning is 55 percent since that’s our equity, and we’ll profit $2.35 because we’ll get our opponent’s entire starting stack plus our $0.10 blind that was posted. That makes the EV of the winning outcome the following:

EV of winning = $2.35 * 0.55 = $1.29

Now let’s find the EV of losing. We know that we’ll lose 45 percent of the time because we have 55 percent equity. When we call, we’ll actually be calling $2.15 since our starting stack was $2.25 and we posted a $0.10 blind. That means that if we lose, we’re losing $2.15.

EV of losing = -$2.15 * 0.45 = -$0.97

Like always, we’ll add together the EVs of each individual outcome to get the total overall EV of the betting option.

EV of calling = EV of winning + EV of losing
EV of calling = $1.29 + (-$0.97) = $0.32

From our quick calculation, we see that we’ll be making about $0.32 each time we make this call, on average.

The Principles in Action

What we want to see from these two examples is that if we follow the basic principles that we have outlined so far, then the calculations themselves are not very difficult at all. This approach is great for people who aren’t particularly comfortable with math because it gives them a very straight-forward way of doing EV calculations for basic scenarios without having to really learn a lot of algebra or get in over their head when it comes to the math side of things.

The first principle that you have to know is that the EV of an event or betting action is found by adding up each individual EV of each of the possible outcomes. While both of our examples this week only had two possible outcomes, we’re going to look at some more complicated scenarios next week that have three or more.

The second principle that you have to learn is that the EV of an outcome is found by multiplying the profit of that outcome with the chance of that outcome happening. As you can see in the examples above, your profit can be positive or negative, and the chance of an outcome happening can be found with either a fraction or a percentage.

Next week, we’re very specifically going to look at semi-bluffing against a single opponent and pure bluffing against multiple opponents. These are two very good situations for learning a lot about the principles of poker with a very minimal amount of math.

One More Thing

I just want to point out that FTR has a chat room that’s easy to access. I’m in there pretty often, so click here and follow the easy instructions to come chat about poker with us. We don’t care if you’re a complete beginner or a seasoned veteran — we would love to have you either way!

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EV Calculations Tutorial 2: Basic Poker Scenarios
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