# Expected Value Calculator

Expected Value, or EV, is at the core of everything we do in **matched betting**. It is how we know that we have an edge over the bookies and will make money in the long-term.

**What is Expected Value?**

In mathematical terms, the expected value of a bet is the sum of each potential outcome multiplied by it’s probability. Here is an example that might make it easier for non-mathematicians…

If I bet $1 on the toss of a coin, with fair odds, there are two potential outcomes. Either I win $1 or I lose $1. Each of these outcomes has a 50% chance of happening.

The expected value for this bet is therefore (1*0.5)+(-1*0.5), which becomes (0.5)+(-0.5), which becomes zero.

A fair bet on the toss of a coin has zero expected value because, over the long term, i should win as many times as i lose and break even.

But what if it’s not fair?

Bookies regularly have ‘To win the toss’ markets on sports where a coin toss determines which team starts with the ball. However, the odds on these markets are usually around $1.90.

My chance of winning on these markets is still 50%, but now my potential outcomes are +$0.90 and -$1.00.

The EV calculation therefore becomes (0.9*0.5)+(-1*0.5), which becomes (0.45)+(-0.50), which becomes -$0.05.

This is a negative EV bet and the more i place it, the more i should expect to lose.

Almost every bet that you place at a bookmaker will have a negative expected value, but not all. When bookies offer **promotions** it shifts the odds in our favour and let’s us place bets with a positive expected value.

The more +EV bets we place, the higher our profits will be.

### Calculating Expected Value

Our coin toss example was pretty simple but things can get a bit more complicated once you start looking at other markets and adding in things like bonus bets.

Fortunately, our EV calculator simplifies the process…

By entering the applicable stakes and odds you can quickly figure out the expected value of your bet, and also the probability of the bonus bet triggering.

Once you have confirmed that a bet has a positive expected value you can place it with confidence that the odds are in your favour. Do this over and over again and **watch your bankroll grow**.

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