In probability theory, the **expected value (EV)In probability theory, the expected value (EV) of a random... More** of a random variable is the weighted average of all possible values a random variable can take on.

The expected value may be intuitively understood by the law of large numbers: It can be interpreted as the long-run average of the results of many independent repetitions of an experiment (e.g. a dice roll).

Example: If you roll a dice, the possible outcomes are 1, 2, 3, 4, 5 or 6 – all with equal probability of 1/6. The expected value of a dice roll is 3.5.

This example shows that the “expected value” is not a result that may be “expected” in the ordinary sense. Rolling a 3.5 with a dice (or having 2.5 children) is impossible.

In trading, we can speak of EV as the estimated value of an

with an unknown return.### A simple example on EV in trading

We can buy an apple for $10. We expect the following (based on analysis or on our experience):

- A likelihood of 50% that we can sell the apple for $16.
- A likelihood of 25% that we can sell the apple for $12.
- A likelihood of 25% that we will not be able to sell the apple and it goes bad.

The expected revenue of the “apple deal” would be:

(50% x $16) + (25% x $12) + (25% x $0) = $8 + $3 + $0 = $11.

Thus, the expected value of the transaction would be $11 minus the $10 that we spend for the apple. The resulting EV of $1 is positive, indicating that doing the deal would be profitable, or “+EV”.

The

In many situations, the expected value of an investmentInvestment is the commitment of money or capital to purchase... More can be estimated with thorough analysis.

## Positive result versus positive expected value

Differentiating between a positive result and a positive expected result is a key skill needed for every

.A trade that made you profit might, in fact, have had a negative expected value. And a trade that made you a loss might, in fact, have had a positive expected value.

Coming back to the dice example: you bet $100 on the result of a single dice roll being larger than 2. Obviously, this is a good bet. Still, the result might be a 1 – and you lose the bet.

## EV and money management

It also is obvious that you should not bet your life on the dice roll, even if your bet has a positive expected value. The potential loss simply is far too big. This is a good example that shows that you should not take any trade or bet, even if you have a positive expected value.

This is one of the fundamental ideas behind money managementMoney management refers to one of the most important concep... More. Do trades with a positive expected value, but do not invest more than 1-2% into a single trade. Otherwise, the risk of going broke despite making the right decisions simply is too large.

MoneyMoney is a generally accepted medium of exchange to buy and... More management is one of the most important skills for every traderWhat is a trader? A trader is a person who buys and sells... More. Read more about it here: