What does Expected Value (EV) mean?

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As it’s has been a little while since our last blog, we thought we’d make this entry an educational one. A number of our members on the Heads&Heads forum have been asking about Expected Value (EV) and what this means exactly. For once, this blog topic will be relevant to both matched bettors and traditional gamblers. So even if you are not a matched bettor, this will still be worth your time.

In most cases, you’ll read the term EV in reference to Poker. This is unsurprising, as EV is an important mathematical probability concept that can be applied to gambling. Often, this term will crop up a lot in movies about counting cards - ‘21’ being our favourite example.

So, what exactly 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 is about the mechanics of gambling, the numbers behind the numbers. In essence this is what matched betting is built on – numbers, not chance.

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 results in different outcomes based on the option chosen. The concept of expected value (EV) is used precisely to evaluate which option you should choose to maximize gains and minimize losses. It excludes variables like fun or personal satisfaction. Expected Value is essentially a positive (+EV) or negative (-EV) indicator that should guide you in making the best decision.

At this point, matched bettors may be thinking that this is all well and good, but if the Heads&Heads Oddsmatching software tells us what to bet on, why do we need EV? Well, understanding EV can be hugely beneficial to matched bettors, especially when it comes to accumulator offers. Such offers rely on the majority of your selections winning, as most will only offer a refund if one leg loses. So, with this in mind you need to be considering what is likely to win, as well as finding those good odds matches to minimise qualifying losses.

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’ll give him 0.98 pence 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, the expected outcome for you during the wagering of 1 unit of money is equal to 1.01……or an average profit of 0.01p per flip of the coin.

Applying this concept is what can give us an edge over the house. However, this is a lot easier to apply to Poker or Blackjack than Sports Betting. To apply it to Sports Betting, you need something other than this formula. That something is experience.

You’ll require experience to be able to identify when a bookie has undervalued or overvalued a particular selection. This is crucial, as for Sports Betting the above formula is turned on its head, because you’ll 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 and in this case you would turn £1 into £2.5 on average.

Some of you may think it overkill to understand all this because at the end of the day, you are still guessing the percentage chance of a winning or losing outcome. However, by the time you reach the stage where you are regularly attempting accumulator reload offers, you should be really very experienced in certain sports markets. Thus, applying this mathematical knowledge to that experience, will lead to greater overall profits.

For our members, we believe the best EV bookmakers out there are: Paddy Power, Coral, Bet Victor, William Hill and Ladbrokes.