In this morning’s Globe I read this article on the newly introduced $30 Mass Lottery scratch ticket, atwww.bostonglobe.com/business/2014/04/28/lottery-introduces-scratch-ticket/vhQ94q6oeaGrm03uyafShK/story.html.
That’s a three page article (when printed) with lots of numbers. I cut it down to one page (including all the numbers, in context) and asked the class to “make sense of them” working in small groups. (I gave out just one copy of the text per group). My hope was that they could apply skills learned in the course to make sense of the numbers in an actual article, rather than the numbers as Maura and I have organized them in the text and its exercises.
I was wary and worried. In the end I think the effort was successful. I’m not sure how to use the material in the text – quoting the full article (or even one third of it) would raise permissions problems. For the record, here are the relevant numbers:
Since the new game was launched last Tuesday, bettors have snapped up more than $8 million in tickets, hoping to win one of the four $15 million instant jackpots or at least take home one of the 36 $1 million prizes. … The game also has smaller payouts starting at $30.
The chance of winning a prize is about 1 in 3, higher than any previous lottery game in the state. But with 25.2 million tickets printed, the chances of winning one of the four top prizes is 1 in 6.3 million.
Later on, these paragraphs put the new $30 ticket in a historical context.
Scratch tickets, first introduced in the state in 1974, are at the heart of the state lottery, consistently generating more than two-thirds of the system’s annual revenue. The lottery’s profits — $956 million in fiscal 2013 — are distributed as local aid to the state’s cities and towns.
The state has steadily added higher-priced games over the years, introducing the $5 scratch ticket in 1992, the $10 in 1999, and the $20 ticket, with a top prize of $10 million, in 2007. Even though the lottery generated a record $3.3 billion in sales last year, officials decided to introduce the $30 game — with bigger jackpots — as a way to keep players interested.
That’s enough information to answer the following question – but my asking them here is just part of what the class was about. What I really wanted was for the students to decide that this was a good questionsto ask.
What was the average value of the “smaller payouts starting at $30″? With coaching from me and from Tom most understood (eventually) that you needed the total number of smaller payouts (about 1/3 of the 25 million tickets) and the total paid to those winners. That’s the total paid to all winners less the 4*15+36*1 = 96 million dollars for the forty big winners. The total paid to all winners is the fair price of a $1 bet times the $30*25 million collected by selling all the tickets. (The 8 million tickets sold so far is a red herring.) To find the fair price of a $1 ticket you need the historical information in the second extract. The lottery profits are about 1/3 of the total bet, so the return on a dollar is about 65 cents.
One group of two students had another interesting thought: use the history of scratch ticket prices to predict the future price.
I asked the students to add to their homework due next time a writeup of today’s class in a form suitable for inclusion as an exercise in the text. I’m curious about how it will work.
In any case I think I will write this up for the instructor’s manual, in place of the section there now on an ancient attempt to build an exercise from a not very useful Globe graphic.
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