# Don't Expect the Expected Value

Tim Erickson, NCTM 2001

Hi all!

Eventually I should turn this in to a better handout, but this HTML document should be a good start. This is in response to the heartfelt request for step-by-step directions for how to do some of the simulations I showed at my talk on Thursday at NCTM.

We were studying what happens when we go to a roulette wheel, and always bet on red.

Let's break it down into steps...

Make a Roulette Wheel

Make a trip to the wheel (Sampling)

Make repeated trips (Collecting Measures)

By this time, we can see, as in the last graph...

...that while the expected value is -2/38 for every roll (and therefore -20/38 for ten rolls, or -.53), many people will win. So we can repeat the "Author's Message":

In a gambling game, you can use expected value to explain why the house wins.

But you have to understand variation to explain why people gamble at all.

That is, expected value is great, but it's focused on the mean. And measures of center are not enough to get the whole picture.

This is the main thrust of the ideas in this section of the talk. But there are a number of other things you can do:

• use Plot Value in the above graph so we can see where -.53 is.
• Create measures in the measures collection, and collect them. Here is a measures panel for that collection (pick which ones you care about):

• Go back to the sample collection and change the number of rolls in a sample, for example, from 10 to 20, and then to 40, and 100. Collect more measures in our ultimate Measures from Measures from Sample of wheel (whew!) collection (not emptying the collection) so you get a few (5-ish) cases at each sample size. You'll get to make graphs such as:

(This one shows how, as you get more spins of the wheel, you're likely to get farther from just breaking even -- both in a positive and a negative direction.)

Whew! Any questions or requests,

All the best,

Tim