Sat, Oct 03, 2009
The Straits Times
The numbers game: Down a blind alley?

By Mabel C. Chou & Qingxia Kong, For The Straits Times

SEPT 9 this year - 09/09/09 - was a happy day. It was reported that 366 couples were married that day, compared with 64 couples on a normal day.

The reason? The belief that the auspicious number '999' will bring them eternal love. Slightly over a year ago, on Aug 8, 2008, the opening ceremony of the Beijing Olympics began at the auspicious time of 8pm. And when it comes to certain matters, such as car plate numbers, logic and reason may desert an otherwise rational person.

In Chinese culture, certain numbers are believed by some to be lucky, based on the similarity of their pronunciation to that of certain Chinese words. For instance, Chinese people usually associate the number eight with prosperity. Similarly, the number nine is viewed as lucky because it sounds like the Chinese word for 'long-lasting'.

How does this affect people's gambling behaviour? Certain numbers may be chosen more frequently than others because of their perceived auspiciousness.

At the National University of Singapore Business School, we developed a mathematical model that estimates the proportion of people who do not choose numbers 'uniformly' in lottery games and demonstrate that some people have the tendency to choose certain numbers over others.

With the integrated resorts expected to open early next year, there are some concerns about the social problems that gambling may cause. Our study may have implications for those trying to tackle these problems.

In Singapore, 4-D is the most popular lottery game, with more than half of the population taking part. It is a Pick-4 game, where punters bet on four digits from 0000 to 9999 to match winning numbers drawn every Wednesday, Saturday and Sunday. There are similar games around the world, such as Pick-3 games.

We studied the sales data on a particular draw of a Pick-3 game in the United States and found that players prefer smaller numbers. For example, numbers starting with one or two are generally more popular than those starting with eight or nine. This is called the small-number phenomenon in the numbers game.

Why does this phenomenon exist? One explanation is that people tend to select numbers associated with special dates (for example, birthdays and anniversaries), meaningful numbers (phone, car and address numbers), and special events (accidents and murders) - and these numbers tend to start with lower digits.

Benford's law captures this phenomenon. This states that in number listings, the first digit will be one about 30 per cent of the time. This proportion shrinks as the digit gets higher until it reaches about 4.5 per cent for nine as a first digit.

Many natural data sets (for example, accounting data) follow this law. So one of the most important applications of Benford's law is in fraud detection. Fake data is unlikely to follow this law and thus can be easily detected.

According to our study, about 40 per cent of gamblers choose numbers following Benford's law. That is, roughly 40 per cent of punters tend to believe in and select lucky numbers.

When people believe that they stand a larger chance of winning with certain numbers, instead of perceiving the lottery game as a pure game of chance, they are in fact assuming that they would have some control over the results if they chose these lucky numbers.

This helps to create an illusion of control which, in turn, makes gambling more attractive, sometimes to the point where the punter becomes addicted.

Problem gamblers are of concern to society. Gambling addictions can have vast social repercussions. They may result in divorce, poor physical and mental health, bankruptcy and even imprisonment. They have also been known to cause family tragedies where innocent people have been killed because of gambling losses incurred by a relative.

With the integrated resorts opening soon, problem gambling has become more of a concern than ever before, especially with regard to the younger generation.

Studies have shown that children tend to believe in certain betting strategies by the time they reach 11 or 12 years old. This means that as they get older, they become more specific in their beliefs that certain types of numbers are more likely to secure a win than others.

Tackling this erroneous belief is something that problem gambling prevention programmes can do. If the young do not have an illusion of control when it comes to gambling, they may be less tempted to take it up.

The writers are from the Department of Decision Sciences at the NUS Business School. Part of the research results mentioned in this article will appear in the Journal of Gambling Studies.

This article was first published in The Straits Times.

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