IPS - Day 27

Today we wrapped up our probability unit. The focus was to have students create probability models, calculate expected values, and simulate situations.

The class started by considering the game of roulette. What is the expected value of repeatedly placing a $1 bet on the number 29? If 29 comes up then you win $35. If any other number comes up you lose $1. The roulette wheel has 38 values on it, 1-36 plus zero and double-zero.

     E(29) = 35 x 1/38 - 1 x 37/38 = -2/38 or approximately -$0.05.

This represents the average amount of lose. So, if I were to play the game 100 times, on average I would lose approximately $5.00. In total, however, I would have lost $500.

What if you decide to place a bet on black numbers? In this case you win $1 if a black number comes up and you lose $1 otherwise. Students calculated the expected value and were questioning that the result of
-$0.05 was correct. That is the expected value.

I asked the class what if you bet on the red numbers instead? They thought briefly and decided that the expected value shouldn't change.

Suppose someone placed a bet on the last third of the numbers? In this case you win $2 if a number in the range of 25-36 appears and lose $1 otherwise. Students were amazed to see that the expected value in this situation was again -$0.05.

I asked about what would happen with a bet on even or odd numbers or betting a column of 12 numbers? They responded that the result would be -$0.05.

This is a fun but compelling example of expected value. Students start to grasp that no matter how you break down a bet on a roulette table that the expected value will be the same. As I tell my students, "They don't build those large hotels and casinos on generosity."

Next, I had students explore the games of craps, blackjack, and roulette. The later was for those who needed a bit more structure to help them absorb what was going on.

Students looked at these games from a simulation perspective and from a theoretical perspective. It provided the class another opportunity to determine probabilities of events and create simulations.

I concluded class by explaining that we will make use of probability models, expected value, and simulations to understand data that we collect. The concepts learned and skills developed so far will be applied within the context of data that we have collected and are trying to understand.

Visit the class summary for a student's perspective and to view the lesson slides.