Expected Value For Discrete Events

[!def] Expected Value
Expected value for discrete events is the summation of outcome and the probability of that outcome.

[!def] Formula of Expected Value (Discrete Events)
$$
E(x) = \sum x P(x)
$$

For example, lets say, the probability of Argentina wins is 90% and France wins is 10%.
And if Argentina wins I get $1000 and if France wins I have to give $2000.
Then my Expected win will be,

$$
\begin{align*}
E(bet) &= 1000 * 0.9 + (-2000) * 0.1 \\&= 900 - 200 \\&= 700
\end{align*}
$$