1. MA 102 Statistical Controversies Wednesday, April 10, 2002 Today: Expected value The game of Quick Draw Reading (for Friday): Chapter 20 – The House Edge – Expected Value Exercises: 20.2, 20.3, 20.5, 20.8, 20.14, 20.16

2. Expected value The expected value of an event whose outcomes are numeric is the sum of each outcome multiplied by the probability of that outcome. The term expected winnings is often used when describing a gambling game of some sort. This can be gross winnings or net winnings.

3. An example: Quick Draw The NY State game Quick Draw (played in various bars and restaurants) goes as follows: A player picks between 1 and 10 numbers, chosen from between 1 and 80. A computer picks 20 numbers from the 80, which light up on a board. If some or all of the player’s numbers match the lighted-up numbers, the player wins – but how much??? See the card!

4. The Law of Large Numbers The law of large numbers says that in the long run, i.e., over many trials, the average outcome of a numerical event will be the expected value. This is, again, why individuals can win or lose in the short run, but “the house” will win in the long run if the game is set up in their favor.