## Pages

### Expected Value

Anyone who is serious about their betting will need a measure to determine profitability.

Expected value is a measure of the return expected over the long run. We cannot emphasis "the long run" enough.

An expected value does not tell you how much profit each bet will make. Simply, that over many bets the EV will tend towards its expected value.

Expected value is given by the formula

EV = Decimal Odds * Probability of Success

The value returned will consist of the total return on a 1 unit bet, including the bet itself. Values over 1 show profitable returns and values below 1 are unprofitable returns, in the long run.

Examples

You see a bet on a horse being offered at 2.12 and you believe the probability of that horse winning is 0.485

The EV is 2.12 * 0.485 = 1.028

If the probability estimation is correct then the profit from betting in this situation over time will be 2.8%

A football team is quoted odds of 3.3 for winning the match. You believe the probability of winning is 0.284

The EV is 3.3 * 0.284 = 0.937

Again, if the probability estimation is correct then the net loss over time will be 6.3%. In other words, for every 1 unit bet, you will only receive 0.937 units back. A losing proposition.

Remember, EV tells you the expected return in the long run. Your first few bets could all be losing ones, especially if they are of low probability of success. Likewise your initial bets could all be winners and your EV is far higher than expected.

Expected EV is dependent on being able to accurately determine the odds of success. If your estimation is wrong then your EV will be a different value. If you have overestimated the probability of success then the EV will be lower and may actually be negative.

Determination of true odds is the single most important task of the winning bettor.