Size matters to people in games of chance

Study uncovers bias that can lead to poor predictions

Lotto 649 tickets are shown in Toronto in a recent photo. Photo: THE CANADIAN PRESS/Richard Plume
Published: March 7, 2014, 2:18 pm
Updated: 3 years ago

After purchasing lotto tickets with friends, you notice that the majority of the group has, like you, selected the number 11. Sensing that this improves the chances of 11 turning up, you buy even more tickets that include that “lucky” number.

It’s completely illogical. Foolish, even. Yet, in games of chance, sporting events, and risk assessments alike, a forthcoming study in the Journal of Consumer Research finds people are consistently biased toward large groupings when making probability judgments.

In one experiment, for instance, people estimated that a basketball team’s odds of winning a tournament were significantly better when the mascot shared similar features with the mascots of many other teams. In another, people assumed their chances of winning a lottery were higher if their ticket colour was the same as many fellow gamblers’ stubs – and they were willing to wager nearly 25 per cent more because of this.

“You would correctly conclude that the winning ticket is more likely to be blue than yellow (if more blue were printed). However, you might also incorrectly conclude that if your ticket is blue you are more likely to win, and that if your ticket is yellow you are less likely to win,” said study co-author Aaron Brough, assistant professor of marketing at Utah State University.

“Even though every ticket, in reality, provides an equal chance of winning, people act as though their ticket somehow inherits the probability of its entire group. I like to think of it as a case when bunches change hunches.”

Co-author Mathew Isaac, an assistant professor of marketing at Seattle University’s Albers School of Business and Economics, said it’s likely this effect occurs unconsciously, as people naturally group things in order to simplify their lives. This just happens to be a context in which it isn’t helpful.

To wit, in one of the paper’s five experiments, which collectively involved more than 700 people, participants judged the probability of rolling an “A” or a “T” on a 26-sided die featuring every letter of the alphabet. When researchers emphasized that “A” was one of just five vowels and “T” was one of 21 consonants – irrelevant information, given that the odds are one in 26 of rolling any individual letter – people predicted a significantly greater likelihood of landing a “T.”

Fortunately, there’s an upside to our belief that size matters, with Isaac noting that “policymakers can use this bias to influence behaviour” and potentially save lives.

A patient’s odds of getting a diphtheria vaccine, for instance, could be greatly improved by listing it in a health brochure alongside other serious conditions for which immunization is available, as it may inflate the perceived risk of contracting diphtheria. Similarly, a campaign promoting seatbelts would likely be more effective if related fatality stats were grouped with other preventable causes of death among road users.

“When people see many causes of vehicular death listed together, they may think that not only is the risk greater of getting into a car accident but that each of the causes is also more likely,” said Isaac.