Probability Refresher
Expected value
The expected value is the sum of all possible values, weighted by their respective probabilities. Each thing that can happen will have both a probability and a value. To figure out the "expected value", you just multiply the value of the thing by its probability, then repeat for all things, and add the result.
Think about it starting with a fair coin toss. You win one dollar on heads, and zero dollars on tails. If you flipped the coin 100 times, on average how many winners would you expect? You'd expect 50, because that's the probability of heads (0.5) times the number of trials (100) - in other words, half of the time it works out in your favor. On those tosses, you get $1.00, so the whole deal would be worth $50.00 on average.
The expected value asks, "On average, how much is each coin toss worth?" You could take those 50 successes and divide by the total number of coin tosses to figure that out:
Exercise: If I earn $2 per heart, $1 per spade, and $-1 otherwise, what is the expected value of drawing a card?