**Probability**: the chance of a particular outcome.

More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)

The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 1 is favorable in this case.

The probability of randomly chosen card from a deck being an Ace is exactly 4/52 because every card looks exactly the same from the back, you have 52 of them and only an Ace (of which it has **4**) is favorable.

**Expected value** is simply the product of the probability of something happenning AND the 'value' of that something. ( **probability * value** )

If i say I'll give you 100€ every time you manage to pick an Ace from a deck of cards, then your expected value is 4/52 * 100 = 7,69€. Why?
Because you are **virtually winning the 4/52nd part of the 100€s every time you pick a card**.

You could say that probability is just theoretical, but the law of large numbers says (in plain english) that the more you try (approaching infinity, that is), the **closer your results will get to your theoretical probability**, or **expected value** if you will. That is quite mindblowing if you think about it, but also makes a lot of sense.

Just thought of something even more simple:
Let's say there is only one card, face down: an Ace.
Now I tell you that if you flip it over and it's an ace, then you get 100€. 
How much is your expected value? Of course it's 100€. Why?
Because the probability of it being an ace is **1 (or 100%)** your potential winning is 100€ so 1 * 100€.
Now what if you had two cards face down, and only one is an Ace? Three cards face down? Four? Seventeen? What is your expected value in each case?