The formula to calculate expected value for betting is fairly simple:
(Amount won per bet * probability of winning) – (Amount lost per bet * probability of losing)
Let’s use a coin toss as an example of calculating expected value. Assuming the coin and the toss are fair, each outcome (heads or tails) has an equal probability of 50% - therefore the odds offered on a fair market would be 2.0.
This would result in an EV of 0 for either a Head or Tail - because the probability of the two outcomes is the same, so if you tossed a coin infinitely it would theoretically end up all square.
If however you were offered odds of 2.15 for the coin to land on heads, this is a value bet.
If you placed $10 on the coin landing on heads at 2.15, the EV is calculated likewise:
(11.50 X 0.5) – (10 X 0.5) = 0.75
This shows an EV of 0.75. Therefore you would expect to make an average profit of 75p for each $10 bet, because the odds received are better than the implied odds of the coin toss.