Expected Value (EV), +EV, -EV, Bets

Expected Value (EV)

You may have heard of the EV concept (expected value) in the past, especially if you play poker. It is a very important probability mathematics concept that applies to all gambling games, and even most real life situations. But what is it? In short, EV is the expected value returned on any wager. You can use the expected value concept in Poker, sports betting, casino games like Blackjack, slot machines, roulette... you name it.

This article targets players who want to understand the mechanics of gambling. If you are a player that just likes to have fun, such a concept will be pretty boring for you. It will explain in more details what expected value is, why you should care, how it works and how to use it in gambling. I will explore its use in Poker, Casino games and Sportsbetting. After getting this basic knowledge, you will be able to read more and understand what people are talking about.

Note that since most readers aren’t math fiends, and I am not either, the article aims to teach the basics of expected value, the tools we can all use easily while playing. You can even use what you learn in this article in your real life everyday situations.

What is EV (expected value) and why should I care?

In gambling, you are constantly faced with situations where you have multiple options, the first of which is to decide which game you’re going to play. Each choice you encounter causes different outcomes based on the option chosen. The concept of expected value (EV) is precisely used to evaluate which option you should choose to maximize gains and minimize losses. It excludes variables like fun or personal satisfaction. Expected Value (EV) is essentially a positive (+EV) or negative (-EV) indicator that should guide you in making the best decision.

Before getting into the details, let’s use an example that will demonstrate how expected values work. Say you and a friend are flipping a coin and decide to bet on the outcome. All things being equal, each face of the coin should be randomly selected 50% of the time. But you’re a wise entrepreneur and you manage to convince your friend that each time he wins, you give him 0.98 cents while when he loses, you earn the full amount. Here is what the formula would look like:

Expected value (EV) = wager + (expected win – expected loss)

In this scenario, on your point of view, it would look like this:

Expected value (EV) = 1 + ((0.5 x 1) – (0.5 x 0.98)) => 1.01

In other words, for you the expected value of wagering 1 unit of money is equal to 1.01, an average profit of 0.01 per coin flip. The EV of this wager is positive and favorable. Of course, in this case the profit is negligible. Similarly, the loss for your friend would be small since statistically, he would get 0.99 back on every coin flip. But when it comes to real gambling, expected value matters because it is the difference between winning and losing. This was a very simple example.

Since you will be playing more than 1 coin per wager, and the house / player edge will be more than 1% (compounded by the number of times you make this wager), it can amount to thousands of dollars. I hope this convinces you of the importance of the Expected Value (EV) concept. When the expected value of a bet is positive, then it means that statistically, in the long run you should make money. If it’s negative, then it means that you will lose money.

When does Expected Value (EV) matter?

The concept doesn’t matter much when you play a game for fun and you don’t mind losing. If you like playing American Roulette, the one with 0 and 00, then you have approximately 0.95 EV (expected value) on any given wager you can make. That is, on average, for every 1 unit of currency wagered, 0.95 will come back.

It is the house advantage. This edge varies from game to game but it is always in the casino’s advantage, and this is why there is a saying that the casinos always win. The longer you play, like in the coin flip example, the more money they make. Or if you were on a lucky streak in the first flips, the longer you play and the more likely you will lose what you had gained.

Can the Expected Value ever be in the player’s favor? Indeed, it can be in games involving not only luck but also skill. There are 4 occurrences where this is the case:

1. Poker, where an experienced player can and should win in the long run.
2. Sports betting, where a good handicapper can also have an edge over the house.
3. Blackjack, where card-counting can increase your expected value to about 1.02 but it is considered cheating.
4. Games in which there is a jackpot, such as progressive slot machines.

Those are to my knowledge the only games where skill can be used to increase Expected Value (EV) above 1, making every dollar played an investment instead of a loss. The other games are for fun. I will now give very basic examples on how this applies to Poker and Sportsbetting.

Sportsbetting Expected Value (EV)

Expected value in sports betting involves the same sort of calculations, with a twist: you know the house edge but don’t know your real odds of winning and losing. This is where knowledge and experience come into play. You have to estimate them adequately. If you manage to do this, you can beat the odds.

Say that in the Premier League, team A is playing team B. The odds given by the bookie for team A is 4/1 (4.0 in decimal, +300 in american). But you know both teams really well and you estimate that team A will win 50% of the time. Your expected value (EV) in betting on team A would be positive. In fact, it would be a great wager. Let’s see how. Note that I merge a tie result in the expected loss equation for simplicity.

Expected value (EV) = wager + (expected win – expected loss)

In this scenario, on your point of view, it would look like this:

Expected value (EV) = 1 + ((0.5 x 4) – (0.5 x 1)) => 2.5

This means that betting on team A in such a game would be extremely favourable. It would be like turning water into wine, except that in this case you would turn 1£ into 2.5£ on average.

Conclusions on Expected Value

I hope to have convinced you about the usefulness of the concept of Expected Value. It is one of the numerous tools in any gambler’s arsenal. It allows us to estimate what bets are profitable and which ones are not. Of course, it is not the end all be all. There are some games that we like and will continue to play even though in the long run we know that the house has an advantage. But it is a great concept that can be used to maximize wins and limit losses.

Courtesy of poster millionjack from Forumcasinos