Town & Gown:
You Can Bet There's No Sure Thing
Reprinted here in its entirety.

Knowing something about statistics gives a person an almost magical ability to see into the future and predict with significant accuracy what may happen.

Jacksonville State University students study statistics because almost everyone has to interpret statistical reports at some point in their career and be able to assess risk. But some would say the best reason of all to study statistics is that it can be personally rewarding.

Dr. Jan Case, associate professor of mathematics, said, “Probability theory began with gambling problems in the 17th century, and statistics began around the same time with the compilation of mortuary tables. For some people, the subjects still seem to have that aura of deceit and death clinging to them. There are so many interesting examples from gambling that I have to be careful in class not to go overboard with the fun and games.”

Dr. Case grabs attention by presenting students a series of interesting games and examples to illustrate the principles behind statistics.

“One such class example is called the Martingale Strategy,” she said. “It’s my favorite because it’s a foolproof idea that is impossible to implement. Say you wanted to win $1 when playing a game that pays 1:1. First, bet $1 on the first trial. If you win, quit. You’ve won $1. If you lose, double the amount bet for the next trial. Stop as soon as you win a trial.

“Suppose you lose three bets and then win the fourth one. The amounts bet would’ve been $1, $2, $4, and $8. The last bet is a winner, so we stop and count our winnings. The payoff is $16 minus the $8, $4, $2, and $1 we bet when we lost, and so we’ve won 16 – 8 – 4 – 2 – 1 = $1, which was our goal. Sure thing, right? Well, not quite.

“The catch is the amount of money needed to play the strategy. Doubling the bet is an example of exponential growth, and it will bankrupt the bettor before the $1 is won. In class, I set up different games for the students to play and let them calculate the amount of money required before the strategy pays off. If the probability of winning is greater than ½, then there is a simple formula to determine the amount of money needed.

“Of course, it’s hard to find someone who offers a game paying 1:1 that you win over half the time. So, either you need an infinite amount of money before you start, or you have to find a very stupid casino. Those are substantial hurdles.

“Probability theorists have determined the impossibility of a successful betting strategy. So, for now, we’re sure there’s no such thing as a sure thing.”

In life, obviously some choices are higher risk than others. How is this measured?

According to Dr. Case, “In statistics we are concerned about central tendency and variability. In other words, what is most likely to happen and how far off are we likely to be in our estimate.

The standard deviation gives an average amount of spread around the mean of distribution. For example, if I say that my class average for a test was 75 with a standard deviation of 10, then it means that the majority of the class scored between 65 and 85, which is 75 give or take 10.

“The larger the standard deviation, the more risk is involved in the endeavor. Stocks are evaluated in the same way. A small standard deviation indicates low risk and also low return, while a high risk stock has a large standard deviation and the potential for much larger gain or loss. Taken together, measures of central tendency and variability give a lot of information about uncertain situations.”

To learn more about statistics and JSU’s statistics courses, please contact Dr. Case at 782-5119 or send e-mail to jcase@jsu.edu.