Kate Butler

The Principle of Expected Value

by Lucie Knight-Santos

Earlier this year, when the Blue Sky Project first began, we took the opportunity in our cohort meetings to ask about the innovative methods our fellow “cohorters” were using in their classes. Ms. Kate Butler told me about the work she was doing with her Probability and Statistics class involving the game of Roulette and the Principle of Expected Value. As someone who is the farthest possible from being a math genius, I was fascinated and decided to take this opportunity to find out more about the unique methods that she uses to teach this class.

The Principle of Expected Value predicts what return a player can expect if they bet one dollar. For example, in the game of Roulette, you can expect to lose 5.3 cents on every dollar bet. Knowing this, students can then calculate what each bet is worth if the player wins. Since Roulette involves different kinds of bets, such as placing a bet on a single value or only even numbers, students have their work cut out for them calculating the expected return on dozens of different bets that a player can make in this particular game. In Ms. Butler’s class, the students first play an electronic version of the game on an app and then discuss the different types of bets possible, especially the riskier kinds of bets such as a bet placed on one number. They then go through the bets and calculate the probability of winning and the expected pay out. They receive one chip, place bets and keep a running tally of their winnings and losses to check the validity of their own calculations.

Ms. Butler has designed this Probability and Statistics class keeping the students, who tend to find math challenging, very much in mind. The classes focusing on the Principle of Expected Value and Roulette form part of a larger theme that has students learning how to calculate the expected value of games, varying from Blackjack to the Lottery and The Price is Right. The latter game forms an entire unit towards the end of the year that involves students creating simulations of their own games, that they then play and track the results to see if their data matches up with their own calculations. Last year, students created their own Plinko games that they took around campus and asked other students to play, betting - for example - hugs or high fives.

In creating these classes, Ms. Butler has successfully turned these games into an effective and fun teaching tool that engages even the most challenged and skeptical math learners (myself included)!