One of the hardest concepts to add to your overall Texas Hold’em strategy arsenal, unless you are particularly well-suited for it, is mathematics. Very few players actually enjoy the process that goes into figuring out odds and any other math-related poker problems.

The last thing you want to worry about while already thinking about your hand selection and any tells the other players are giving off is having to do tricky calculations in your head. However, most elements of a math-based poker game plan, such as the use of expected value (EV), will become all but absolutely mandatory if you plan on making it to the top levels of the game.

If you haven’t heard of expected value before, it is commonly referred to as the positive or negative outcome that will most likely result from both an individual play and long-term strategy. For example, if you limp into an un-raised pot with a medium pair and get other limpers to come along for the ride, there are chances that this play will have a positive expected value. The difference between positive EV (+EV) and negative EV (-EV) is that +EV means that there is a good chance that the play will win money in the long run, while -EV brings the chances that it will most likely lose money in the long run.

How to Calculate your Expected Value

Essentially, plays with +EV are expected to win more often than they’ll lose, meaning that if you try the same play 10 times over the course of six months and it has +EV, it should win more than 50% of the time. A -EV means that even though a play may win the first, second or even third time you use it, mathematically it still stands to lose in the long run.

One of the reasons learning how to calculate your expected value is such a good idea for players to implement into their poker lives is that not only does it help you make a decision right there in the moment, but it also helps you refine your probable choices in the future as you start to run across scenarios that carry heavy negative expected value. Standard pot odds will only assist you one hand at a time, but when you accrue a lot of experience with figuring out expected value you’ll notice that your hand selection and post-flop decision making will have been affected in a positive way.

Expected value: hand example 1

Here’s an example to consider. Say you have A-J suited with clubs on the button and the blinds are $50-$100. The action is folded around to you and you limp in for $100. The small blind folds and the big blind checks, making it a total of $250 in the pot. The flop comes 4h-5c-10c, which completely misses the ace and jack but gives you a flush draw. The big blind acts first and bets $125, making the pot $375. Should you call the $125?

First you need to figure out your outs. There are 13 of each suit in a deck, and in this hand you have two and the board has two, meaning there are nine cards left that can give your flush, or roughly 47:9, which simplifies down to 5.2:1. What this tells you is that for every six times you make a call in this scenario you will lose around five times and win once. So obviously in the long run this hand has very heavy negative value. However, does that mean you should still fold in this exact situation? That’s where the amount of money in the pot and the pot odds come into play.

Your pot odds in this situation are 3:1 ($375:$125). To calculate immediate expected value, take the number of times you will lose this hand (5.2) and multiply it by the amount it will cost you to call ($125). On paper it looks like 5.2x$125, equalling $650. Compare that to the amount in the current hand’s pot, which is $375. That means you’ll lose $650 for every $375 you win, for a net loss of $275, making the call wrong both here and in the long run.

Hand example 2

You have 5-6 suited with spades and the flop comes 7s-8s-Ac. Your one opponent bets $10 into a $60. A five or six won’t help your hand, but you have both straight and flush draws. Your total amount of outs is 15, with 47 unknown cards left (15/45), so now your odds of getting a card that helps you is 3 to 1. Your pot odds are 7 to 1 since you have to call $10 to win a $70 pot.

Using the same math as above, you have an extremely high expected value since you have a lot of outs and only have to put in a relatively small call in order to see the next card.

By structuring your poker career around making mostly +EV decisions, you’re setting yourself up to be successful in the long run versus successful in the short run. It’ll take a lot of patience to get used to the math, but it will absolutely pay off.