Are Lotteries A Good Bet?

Submitted by George Bratton, University of Central Arkansas

It has been said that “the chances of winning the lottery are about the same, whether or not you buy a ticket.” Let’s examine what this means, particularly with respect to the relative odds of lottery winnings versus other gambling games. The vehicle that we’ll use for these comparisons is called the House Edge. The House Edge is generally accepted to be the expected loss divided by the initial bet. As an example, in roulette with a 00 wheel a color bet (“red” or “black”) wins with a probability of 9/19 and loses with a probability of 10/19. It is an even money bet, that is, if you risk $1 and win your pay back is $1. Hence the House Edge is computed as, Calculation .

According to the “Wizard of Odds” web site, here are the House Edge for some common casino games: Blackjack (liberal Vegas rules, skilled player) 0.28%, Caribbean Stud Poker (skilled player) 5.22%, Craps (Pass/Come) 1.41, Slots (manufacturer info) 2%-15%, Video Poker (Jacks/better/full pay, skilled player) 0.46%, and Keno 25% - 29%, depending on the pay table. The first observation is that the House Edge, no matter how small, is positive. The house always makes money in the long run and the more people are playing (even playing well), the more money the house takes in. The second observation is that Keno is a horrible game from the player’s perspective. You will lose 25% or so of your money on average.

Now, let’s examine the results for the various scratch off games that have been offered by the Arkansas Lottery. According to the Lottery Commission’s announced figures for the first twenty-eight days of operation (as reported in the Arkansas Democrat Gazette), the total amount wagered was $40 million and the total amount paid out was $25 million which means that the total losses were $15 million. Applying the House Edge formula, 15/40 = 37.5%!

Suppose that a person buys $20 worth of tickets per week which is obviously less than $3 per day. Over the course of a year that is $1040 and on average 37.5% of that or $390 will be lost. So, are lotteries a good bet? Another old quote sums up the discussion here. “In some towns the lottery is the only game in town and in other towns it’s not. But in any town, the lottery is the worst game in town.”

Resources: The American Statistical Association is developing a series titled “Statistical Significance” to highlight to policy makers the important contributions that statisticians make to society, from healthcare and economy to national security and the environment. For more information, see www.amstat.org/outreach/statsig.cfm.

2010 Statistics Exam: Once again, I will be authoring the ACTM Statistics Examination for our annual Math Contests. If you have any input regarding this test or if you have questions regarding its content, please contact me. My e-mail address is This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Arkansas Curriculum Conference 2009

Submitted by Leigh Price, Arkansas Department of Education

The 2009 ACC was filled with mathematics! The ticketed items included a Cognitively Guided Instruction mini-conference, Elementary and Middle School Math for Math Coaches with Dr. Jennifer Bay-Williams, and the ACTM Luncheon, at which Dr. Bay-Williams presented Quadrants of Questioning. With at least 30 other math sessions and more than 40 cross-curricular sessions, there was hopefully something for everyone.

The CGI mini-conference featured nineteen sessions that ranged all the way from What is CGI? to a panel discussion about Supporting CGI from a State, District, School and Classroom Perspective, and everything in between. Dr. Linda Levi, Director of CGI Initiatives for Teacher Development Group and co-author of Children’s Mathematics: Cognitively Guided Instruction, participated in the panel and presented Relational Thinking: Linking Arithmetic and Algebra in the Elementary School. The remaining sessions focused on both content and pedagogy and were presented by practitioners, state and district mathematics coaches, and other national experts: Tanya Blais, Olof Steinthorsdottir, and Dyanne Van Den Heuvel. There were 240 elementary mathematics teachers in the five room mini-conference. The great attendance exceeded everyone’s expectations.

We were very fortunate to have Dr. Jennifer Bay-Williams as a presenter and key note speaker at ACC this year. Dr. Bay-Williams is Associate Professor at the University of Louisville, immediate Past President of the Association of Mathematics Teacher Educators, and co-author of the book Elementary and Middle School Mathematics: Teaching Developmentally. She addressed mathematics coaches in a short course and led them through key points of the book. The session was full, with sixty teachers present. She also spoke to a record number of teachers, 345, attending the ACTM luncheon where she spoke about questioning practices. Her key points regarding questioning reminded us of the need to use questions to delve deeper into content, and that each of us can grow and refine our questioning skills over our entire career.

On Friday, the Joint Luncheon featured Arkansas Governor Mike Beebe and his Workforce Cabinet. Governor Beebe shared the compelling story of the challenges of his childhood and upbringing by a hard-working, smart, but uneducated mother and the value she, and thus he, placed on his need for an education. The esteemed panel included Dr. Tom Kimbrell, Commissioner, Arkansas Department of Education; Dr. Jim Purcell, Director, Arkansas Department of Higher Education; Dr. Ed Franklin, Director, Arkansas Association of Two-Year Colleges; Senator Bill Walker, Director, Arkansas Department of Career Education; Mr. Artee Williams, Director, Arkansas Department of Workforce Services; and Dr. John Ahlen, Director, Arkansas Science Technology Authority. Each panel member shared the perspective of his agency on the relationship between academics and the future careers of Arkansas students.

Most importantly, of course, were the many wonderful sessions presented by Arkansas’ best educators. Most of the sessions are presented by teachers, professors, and instructional facilitators from around the state sharing ideas they have developed to meet the needs of their students. ACC is not really about going to see an expert present a dynamite workshop, but instead it is about sharing. Not all of us are expert presenters, but each of us has the love of students and teaching, and the willingness to share ideas and learn from others.

ACC 2009 was a huge success with nearly 1,450 educators and pre-service teachers registered. “[The] conference was well put together and I enjoyed all the sessions I attended. I was able to bring a lot back. I am encouraged to use a new piece of technology and have a renewed focus,” says mathematics coach Linda Maples from Earle, Arkansas. Many others shared Ms. Maple’s sentiments. There was indeed a lot that went into the planning and organization of the conference. Thank you to all the presenters, presiders, committee members and volunteers for another great conference where teachers had the opportunity to learn, share, and renew their purpose.

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