Expected Value: How To Find Value Bets

It is always important to gain as much value from your bets as you can. Making bets that aren’t profitable over time is a sure way to lose money. 

How do you know whether a bet is good value or not? We can perform a simple calculation to work out the expected value for any bet. This will help us to be profitable over the long term.

What Is Expected Value?

Often shortened to EV, Expected Value is the amount of profit or loss we would expect to make if we could make the same bet an infinite number of times. It eliminates luck and short-term variance so that you can understand the true value of a gambling decision.

For example, in poker you might lose a hand with aces when going all-in pre-flop. But just because you lost, it doesn’t mean it was the wrong decision at the time — it was still +EV in all circumstances, and if you could re-run the hand an infinite number of times then you would end up with a substantial profit.

If we work out the Expected Value as a positive number (+EV) then we would expect to make money on the bet on the long term, but not necessarily in the short term. The higher the value the better. 

If the calculated Expected Value is negative (-EV), then likewise we would expect to be losing money on the bet if we made it an infinite number of times. 

We can use this Expected Value to work out which bets will be the most likely to be profitable in the long term for us. We can also use this value to work out which bookmaker promotions are in our favour and which are not in our favour.

How Do I Calculate Expected Value?

There is a simple mathematical calculation to figure out the Expected Value of any wager. 

EV = [(Probability event 1) x (Profit/Loss if event 1 happens)] + [(Probability event 2) x (Profit/Loss if event 2 happens)] + [(Probability event 3) x (Profit/Loss if event 3 happens)]… and so on and so forth.

The probability of an outcome happening can be calculated by doing 1 divided by your lay odds then multiply by 100. If the lay odds on Liverpool are 1.25, the chance of them winning are 1 / 1.25 = 0.8, then 0.8 x 100 = 80% probability.

An easy way to picture this is with a simple coin toss.

There is a 50/50 chance of a coin landing on heads or tails in a fair coin toss. If we bet £10 that the coin will land on heads, our expected value is calculated as follows:

EV = (0.5 x £10) + (0.5 x -£10) = £5 – £5 = £0

The expected value in the long term would therefore be £0 (no value, but at least it’s not negative value). 

Now, a bookmaker will naturally build their commission into the odds they offer you. If a bookmaker was offering odds on a coin toss, they might offer you odds of 1.90 instead of the actual fair long-term odds (2.00).

This means your profit for the coin landing on heads falls to £9 instead of £10. The EV for this new wager is worked out as follows:

EV = (0.5 x £9) + (0.5 x -£10) = £4.50 – £5 = -£0.50

Therefore the Expected Value of this bet is negative, meaning we would lose money in the long term. The rate at which we would lose money depends on the size of the value of EV, and the frequency of wagers.

The worse the odds are for us, the more negative the EV will become, and the rate at which we lose money increases.

Clearly, we want to find wagers that have as positive an EV as possible for us to make as much profit as we can.

How To Find Value Bets

It is important to realise that Expected Value is not fixed, it is only ‘expected’, and may differ, especially in the short term. If you have inside information or tips on an event, you may find that the odds you calculate differ to the odds offered by a bookmaker.

Let’s work out the Expected Value for the Euro Qualifiers match between Spain and Sweden.

There are three outcomes, a Spain win, a Sweden win, or a draw. We bet £10 on a Spain win.

Spain win: 2.00 or 50%

Sweden win: 4.00 or 25%

The Draw: 3.60 or 27.78%

EV = (10.00*0.5) – (10*0.53) = 5.00 – 5.30 = -£0.30

This shows the negative value for EV we can expect when placing a bet with a bookmaker. This negative value is built into all bookmaker odds as their way of making profit. There are still situations where we can create positive EV through certain promotions.

This is the case for bookmakers, but what about betting exchanges? With exchanges like Betfair, the price of the odds fluctuates but always creates either a neutral or negative implied EV after commission. If the EV becomes positive, the market reacts to shift the value back to 0.

If we had some insider information or other details that led you to believe that the chance of a Spain win was actually greater than 50%, then you could have a Positive EV bet. The higher the positive EV, the higher the likelihood of long-term profit.

It is important to bear in mind that the figures used in these calculations are implied odds.

This simply means that the odds of each outcome are determined by the odds offered by the market. This does not mean they are the True Odds of each likelihood occurring. 

The odds have been arrived at because the market has decided them. You may have a more efficient way of calculating the actual odds.

You may have your own method of calculating the odds of an event occurring. This is sometimes done by calculating the Poisson Distribution Model. In this case, you should work out your own odds, and then compare them to the offered odds.

You may have read about an ‘arbitrage strategy’ which is simply finding odds from different bookmakers, and combining them into an Expected Value calculation to create a positive outcome for your bet.

When betting with a bookmaker, they will include their commission when setting their fixed odds. The calculation becomes simple. However, this changes with a betting exchange. Betfair takes a 5% commission on winnings from new customers. 

This commission can decrease over time. You must input the commission rate into any EV calculation made for betting exchange websites. This is as easy as working out the commission on a win and then taking it away from your net profit for a win.

There are a few different ways you can become more adept at finding Value Bets. This also happens over time, as you become more experienced. It is useful to stick to the same market, as you will naturally start to see patterns.

Expected Value From Bookmaker Promotions

In terms of matched betting, certain promotions will have a positive EV built-in and others which turn out to have a negative EV.

One of the easiest ways to find promotions that provide Value Bets is with sign-up promotions. When you first start matched betting, you will mostly be completing sign-up offers with various bookmakers.

These sign-up offers vary in their Value, but overall they should get you around a 70% profit! Obviously, once you have signed up with the majority of bookmakers, you will no longer be able to take advantage of this Expected Value resulting from sign-up offers.

After completing all available sign-up offers, there are other kinds of offers that you can take advantage of. Some of these promotions will have a positive EV, but not all of them! 

Sometimes bookmakers run promotions that seem enticing, but after calculating the EV, it actually turns out to be negative in the long term.

You can calculate the EV for promotions the same way as with a standard bet, except you must take into account the likelihood of triggering bonuses. The formula for this is as follows:

EV = (Profit if promotion triggers * Probability of triggering) – (Qualifying cost * Probability of not triggering)

As before, if the EV turns out positive, you will likely make a profit in the long term by repeating this offer over and over again. Likewise, if the EV turns out negative, you will probably lose money in the long term. 

What Are The Benefits Of Finding Value Bets?

It is important to note that just because a certain bet has a positive EV does not mean you are guaranteed to make a profit every time. It simply implies that if the odds are correct, then over time your outcome will tend to the positive.

Clearly, if you are consistently making bets with a positive EV, your bank should increase over time. 

It is important to try and stay away from bets with a negative EV most of the time. There may be occasions where even though the calculated EV is negative, you still make a profit in the short term, or for one-off bets.

The whole idea with Expected Value is that it is a long-term average. It is ok to make bets with a negative EV now and then, but it would defy mathematics to do this consistently and make long-term profits.

Final Thoughts

You should always try and calculate the Expected Value for any bets you place. It is ok to make a few bets with a negative EV, but if you do this over the long term, you will almost certainly not be making money!