How to calculate the expected value

Every bettor who wants to be profitable in the long run should deeply understand what the Expected Value is. If you bet just for fun you do not have to know how to calculate the expected value, but if you want to make money on a regular basis then betting excludes fun and luck! What betting exactly includes is careful planning, calculations, math and the most important thing is Expected Value! Forget about how much money you will get here and now from a certain bet, it does not matter! All you need to think about the amount you can expect to win or lose if you were to place a bet on the same odds many times over. That’s the concept of Expected Value (hereinafter referred to as EV). The figure of EV will tell you how much you can expect to win or lose on average per bet. Actually you don’t need to try to win every time, that’s sounds crazy, but that’s the idea! What you really need is to maximize gains and minimize losses! Once again it doesn’t matter whether your bet win or lose today the only thing that is important is at what odds you bet.

To choose a bet you must understand which bets are profitable and which are not and Expected Value is the best indicator that guides you thought it! There are positive (+EV) and negative (-EV) indicators which show you whether or not to bet. The formula for calculating Expected Value is simple! You must multiply your probability of winning with the amount you could win per bet and subtract the probability of losing multiplied by the amount lost per bet.

Let’s look at this in practice and return to the coin-tossing experiment then everything will become absolutely clear. There are two options which both pay out at the same odds 2.00 as probability of each outcome is 50%. Imagine you bet £100 on these two outcomes and calculate Expected Value.

Expected Value (Heads) = (£100 x 50%) – (£100 x 50%) = £0

Expected Value (Tails) = (£100 x 50%) – (£100 x 50%) = £0

We have an Expected Value of 0 for either outcome, so there is no point in making bets in the long run; you will not win money and will not lose it. But this situation is possible only on a fair market; the bookmaker will offer even odds 1.95 – 1.95. Let’s calculate Expected Value again.

Expected Value (Heads) = (£95 x 50%) – (£100 x 50%) = – £2.5

Expected Value (Tails) = (£95 x 50%) – (£100 x 50%) = – £2.5

There are negative indicators (-EV) which suggesting that you will lose an average of £2.5 for every £100 staked. For example if your bankroll is £2 500 so you will lose it after 1000 stakes. Now imagine that bookmaker offer Heads at @2.10 and Tails at @1.90 and calculate Expected Value once again.

Expected Value (Heads) = (£110 x 50%) – (£100 x 50%) = +£5

Expected Value (Tails) = (£90 x 50%) – (£100 x 50%) = – £5

The negative indicator (-EV) means that you will lose an average of £5 for every £100 staked and positive indicator (+EV) means that you will win an average of £5 for every £100 staked. The same event, the same outcomes, the same probabilities, but different odds and as a result a different pay out ratio! How you can use this formula in betting?

Let’s take for example real betting lines when Liverpool (1.70) play Everton (5.50) with a draw at 4.10, a bet of £100 on Everton to win would provide potential winnings of £450 with the probability of this event happening is at 1 / 5.50 = 18.2%. The probability of opposite outcome (Liverpool or Draw) is 1 / 1.70 + 1 / 4.10 = 83.3%. So Expected Value formula looks like:

(£450 x 18.2%) – (£100 x 83.3%) = – £1.4

As we can see the Expected Value is negative and that means you will lose an average of £1.4 on every £100 bet. You should not place bet on this outcome, because there is no value in it.

But as we know, the estimation of probabilities is subjective! If you use your knowledge of sports and statistical analysis and think that Everton’s chances of winning are actually about 20% then the EV will be different. Let’s calculate this value according to your opinion on the match.

(£450 x 20%) – (£100 x 80%) = +£10

In this case Everton win will be a value bet and you must place it! The only question is whether you can correctly determine the likelihood of any outcome. But the main conclusion that should be drawn is that one need to ignore odds offered by bookmakers! You must calculate own probabilities and translate them into the odds. If your odds are lower than the bookmaker’s odds, you should place such bet; if they are higher you must skip such stake as it is not a value bet.

In other words, your decision for bet selection should not depend on the bookmaker’s odds. The best way to do it is not even look at the betting lines first, just drill down the statistics, analyse the current form of the rivals, examine H2H, learn about injuries and suspensions and only then make conclusions about the chances of rivals and express them in probabilities. For example, you think that the chances of home win are 55%, draw 20%, away win 30%. Then translate probabilities into decimal odds: 1 / 0.55 – 1 / 0.20 – 1 / 0.25, that is 1.82 – 5.00 – 4.00. It’s time to open the betting lines and compare your and bookmaker’s odds. Let’s say that the bookmaker offers for this match the following odds 2.00 – 3.80 – 3.10. As we see, in this match it makes sense to place bet only on home win, because this is a value bet (the bookmakers odds are higher than the odds calculated by you). So if you were going to bet on the hosts – do it, if you wanted to bet against them – skip this stake and keep looking for a value bet in another match! That’s the only way to be profitable punter; you do not need to seek winning stakes, what you need to do is to beat bookmakers odds!

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