You are at a party with a friend and 10 people are present including you and the friend. Your friend makes you a wager that for every person you find that has the same birthday as you, you get £1; For every person that does not have the same birthday as you, he gets £2. Would you accept the wager?
How could you calculate the expected value for this?
The probability of one person having your birthday is $\frac{1}{365}$, which means the expected value of the wager is (assuming you're only comparing yourself against the other $8$ people at the party excluding the friend):
$$E = 8 \cdot \left(1 \cdot \frac{1}{365} + (-2) \cdot \frac{364}{365}\right) = -\frac{5816}{365} = -15.93$$