Math Activity Turned Social Experiement

In the college course that I am teaching, one of the big units we cover is probability.  We talk multiplication counting principle, permutations, combinations, theoretical probability, empirical probability, independent events, and all that good stuff.  It's a hard unit; students struggle with many of these concepts, mostly the counting piece.  I wanted to add in something that was a little lighter but very related.  I was struggling to think of something at first, but then, at the very last minute (which tends to be where my best ideas come from)  I decided to create a lottery system that we would play throughout the course of the unit.  Every student was given $20 to start the unit and could spend it the best way they thought they could with the goal of having the most money at the end of the unit to get some extra credit on their unit test.  The drawings and payout rules we followed are below.  

It was a fascinating experiment to watch.  You learn a lot about students and their spending habits.  There were students who dove right in and thought they would surely win big, and there were others that sat back quietly and held tight to their money, hoping others would spend and they would win with their original $20.  

The best part was the last day.  

On the last day, there were a few students who still had their original $20, one who had a questionable $22 (some were accusing him of stealing someone else's $2) and the rest were all less than $20.  So, most with less than $20 went all in, they knew their only chance at the extra credit was to win the lottery.   I say most went all in because not all of them did.  There was an interesting turn of events that changed their minds for how they wanted to use their money.  

One student in the class received a pretty low score on the test and at first in jest, requested that everyone donate their money to him because he needed the extra credit the most.  (Note he had saved his money, and hadn't spent it gambling in the lotto in hopes he would have the most.)  Quickly questions came to me about whether that was legal or not for our game.  I said, it's your money, it's up to you how you spend it.  Suddenly this student had himself about $100 and would easily win the extra credit as long as no one won the last drawing.  Not surprisingly, no one won the last drawing and this student bought his extra credit.  The lesson we wrapped up the class with outside of the probabilities of lotteries was if you are going to give your money away, which made you feel better, giving it to the lottery or giving it to charity?  Some students were glad to give it to the lottery because it upped their own chances of winnings, and others were more happy to give it to someone else who they knew would benefit from their funds.  

I do have to say that there was yet another lesson learned in all of this.  After this charity student got his money collected from his kind peers, he came over to me and asked if he could buy tickets with all the money.  Really buddy?  You just got that money donated to you and you are going to toss it at the lotto?  His donors were not pleased and he decided that perhaps that wasn't the best idea and held onto his money, but I appreciated that he gave us yet another social experiment to discuss.  If you are donating to charity, it doesn't feel as good if the funds aren't going to where you were led to believe they would be going.  

All in all, this was an awesome class activity.  After going through the entire process once now, I am so excited to do this in the future.  The discussions that took place about probability were good, but the discussions that took place about real-life, gambling, saving, donating were unexpected and meaningful.  

I love it when something turns out really good and students feel good about it and got more than just a math concept from it.  

Here were our lottery rules:  

Lottery Rules: 

Each student will start with $20. 

There will be 5 lottery drawings, students can buy any number of lottery tickets they can afford on any of the days there are drawings. 

Drawings: 

#1:  4 numbers will be randomly selected from 0-9, numbers will be replaced after each draw, must match the order the numbers are drawn

#2:  4 numbers will be randomly selected from 1-20, no replacement, order does not matter

#3:  4 numbers will be randomly selected from 0-9, numbers will be replaced after each draw, order does not matter

#4:  4 numbers will be randomly selected from 1-15, numbers will be replaced after each draw, and then one PowerNumber will be selected from numbers 1-10

#5:  4 numbers will be randomly selected from 1-15, no replacement, and then one PowerNumber will be selected from numbers 1-30

Winnings: 

For 4 number drawings:    

1 out of 4 numbers right:  $0

                2 out of 4 numbers right:  $1

                3 out of 4 numbers right:  $2

                4 out of 4 numbers right:  Jackpot (Shared equally among all Jackpot winners)

For games with a PowerNumber: 

                PowerNumber right:  $3

1 out of 4 numbers right:  $0

                2 out of 4 numbers right:  $1

                3 out of 4 numbers right:  $2

                4 out of 4 numbers right:  $10

                4 out of 4 numbers right AND PowerNumber:  Jackpot