When you are talking about expected value in betting terms, you are talking about the expected amount you can expect to win on average for each bet you place. Of course, this can only be worked out as an average because every bet is different, with various odds in play, but it is there to give you a guide as to what you are doing and how successful your strategy is.
The expected value is the amount of money you will win or lose based on the odds you take, based on the probability of your bet winning. So, if you like to bet on football and place the same bet at roughly the same odds each week, by finding out your expected value, you can get a rough idea of the type of money you will win or lose on these bets, on average.
Expected value is readily available for you to look at, all you need to do is one simple mathematical sum to find out your expected value, and then you can use this and work out if your betting is heading in the right direction or if you need some assistance.
How to Calculate Expected Value
If you would like to work out the expected value of bets you are placing, then you need to do a simple sum to get the figure. This will either give you a win or loss figure, based on the success of your bets, combined with the odds you are taking, to give you what the bigger picture looks like for each bet you place.
Here is the expected value calculation:
(probability of winning) x (amount won per bet) – (probability of losing) x (amount lost per bet)
Probability of winning is the percentage chance that your bet has to win. For example, if your selection is 3/1, then your implied probability of winning is 25%.
Amount won per bet is the amount you would win for your £10 bet.
The probability of losing is the other outcomes added together, so if this is a football match, it would be the percentage chance of the other team winning and the draw.
Amount lost per bet would be your stake, so £10 as you use the same as the stake you enter in the amount won part of the calculation.
A Simple Example of Expected Value
Expected value is a complex area of gambling, so here we will try and offer a simple example of how it works and what it looks like when you are winning.
Let’s use a coin toss to explain this in the simplest terms.
A coin toss has a probability of winning of 50%, you should win half of your throws and lose the other half.
Let’s say if you place a £10 bet, you receive back £11 when you win, and if you lose, you will, of course, lose your £10 stake.
(0.50 x 11) – (0.50 x 10) is the calculation for this bet.
When you work it out, the EV for this is 0.50, or in monetary terms, £0.50.
For every £10 bet you place on this market at these odds, with this probability, you will win 50p, so the good news is that the bet is a profitable one in the long term.
To prove this works:
If you toss the coin 20 times, you should win ten and lose 10.
The ten victories give you returns, including a stake of £210, from £100 bets placed, so a £110 profit.
You will lose £100 from the ten losing bets you place, which means your actual profit overall is £10.
This is from £200 worth of bets, winning 50p per bet means that you win £10 for the 20 bets you have placed.
How to Use Expected Value to Your Advantage
When you are comfortable working with expected value, you can use it to your advantage and really get a long-term feel for your betting with it. Of course, everyone will have good runs and bad runs, don’t let these affect how you bet, the bigger picture should be what you base all your thinking on.
By knowing what your expected value is with certain bets, you can see if you are going to make a positive return on them over the long term and how much. Of course, if these bets point to a losing strategy in the long term, it is time to look at your betting and change around what you are doing.
There are occasions when you should and should not bet, and finding these and working out what to do will be vital to any success you have. It would help if you did all the planning and working out you can with this to give you the best big picture, and then use this to evaluate your betting and where you are at.