Lotto’s Secret: Probability or Psychology?


Dear Abbey: My husband and I had an eighth child. Another girl and I are really one disappointed woman. I think she should thank God that she was healthy. But Abby, this was supposed to be a boy. Even doctors have told me that the law of averages has a 100 to 1 advantage for us.
— Disappointed woman

From the Roman philosopher Cicero through the Renaissance to the present day, priests, mathematicians and scientists have devoted themselves to revealing the law of probability. Still, opportunities, risks and odds remain strangely opaque to many.

Consider a doctor who told a disappointed woman that the odds of being a boy with the eighth child are 100 to 1. The actual odds were one-to-one, as there were only two likely outcomes for girls or boys.

Why did the doctor make such a mistake? The answer to this seemingly simple question tells us a lot about how people think about risk and probability.

Doctors seemed to believe that the next child of the disappointed woman would be a boy because she gave birth to seven girls in a row. He resorted to the so-called “law of averages” to support his view.

A roulette player who bets on red after running black follows a similar logic. Unfortunately, I don’t remember the roulette wheel. Each spin is independent. The probability of red is the same regardless of how many times the ball has landed on black before. Similarly, the gender of the previous 7 children is independent of the gender of the 8th child.

Not being able to recognize this is known as the gambler’s fallacy. It is also known as the Monte Carlo fallacy because it is the reason why the city-state of casinos is so rich.

Epoch Times Photo
An overview of the Monte Carlo Casino in Monte Carlo, Monaco, May 19, 2021. (Brin Lennon / Getty Images)

For a simple event, it only takes one minute to estimate the odds and probabilities. But one minute is a long time and hard to think of. To deal with our limited cognitive abilities, we rely on a strategy called heuristics. This is a mental shortcut that allows you to make quick and efficient decisions. These rules of thumb are like intuition. They allow us to work in our daily lives without stopping thinking of all the problems from first principles.

Nobel laureate psychologist Daniel Kahneman gives an example of such a heuristic. He calls it “representative”. According to this rule of thumb, sights, sounds, and events that are in line with (“represent”) our normal experience appear to be more likely than those that are rarely encountered. For example, if all she knows about someone is that she has blonde hair naturally, the representative heuristic is that the person is more likely to be Scandinavian than Chinese. I suggest.

Representative heuristics are usually useful, but they can also be misleading. For disappointed female doctors, seven girls in a row do not represent a distribution of 50 to 50 percent of boys and girls in the general population. Relying on representative heuristics, doctors mistakenly predicted that the next baby of a disappointed woman would somehow even have odds by being a boy.

Representativeness is very convincing and can cause a health panic. This process begins when someone observes that the workplace (school, hospital, factory) suffers from a large number of certain types of cancer. The usual response to such “cancer clusters” is to look for the origin of the environment. That is, high voltage lines, poor air quality, cell phone tower radiation, etc. Most cancer clusters are fantastic, so this strategy is rarely successful. They are just a collection of random cases that happen to pop up in the same place.

Expecting the same distribution of cancer cases as the general population in all workplaces is a drawback of representative heuristics. It causes unnecessary panic and wastes better applicable resources to solve real problems rather than imaginary ones.

Doctors who expect the same number of boys and girls in every family, or gamblers who believe that roulette wheels should always produce the same number of red and black results, have become victims of representative heuristics. rice field.

Representativeness is not the only heuristic decision. Since COVID-19 arrived in town, the disease has dominated the daily news. As a result, people are significantly overestimating the risks associated with the disease, according to studies conducted around the world.

Kahneman attributed these overestimations to “availability” heuristics. Events that are widely covered in the media (airplane crashes, tornadoes, pandemics) are perceived to be more common than most neglected events. That may not seem true, but there are hundreds of times more chances of dying from asthma than a plane crash.

Determining relative risk seems to be especially difficult for politicians and health authorities. In Australia, fans are advised that it is safe to take part in a soccer match with thousands of other people. However, a contaminated soccer ball can infect COVID-19, so if the ball lands nearby, you will be warned not to touch it.

A senior Australian government official claimed that he was more likely to win the lottery than to get a blood clot from the COVID-19 vaccine. This is terribly untrue. Vaccine-related blood clots, which are rare, can be eight times higher than winning a lottery.

The organizer of the Spanish Christmas lottery “El Gordo”, which will be drawn at the Royal Theater in Madrid on December 22, 2018. (Curto De La Torre / AFP / Getty Images)

Understanding heuristics is very important for anyone playing Lotto. But before explaining why, let’s clarify one thing. Lotto numbers are randomly selected, so there is no way to ensure that the numbers are selected other than playing all possible combinations. Moreover, as already mentioned, there is little chance of winning.

There are 8,145,060 ways to choose from 45 to 6 numbers. Due to the large number of combinations, the probability of choosing all six correct numbers is 0.00000012. You don’t have to be a mathematician to understand that the odds of winning if you don’t buy a ticket are 0.00000000.

In other words, the odds of winning are about the same whether you buy a ticket or not. The situation is even worse for lottery games where you have to choose the correct numbers from 47 to 7. The odds of winning are 62,891,499 to 1 (don’t believe my words about this, get a piece of paper and a pencil, write out all the combinations)

If you are still keen on playing lottery, representative heuristics hold the key to maximizing your winnings. The advice I’m trying to give you is the legacy of three Polish mathematicians hired by Polish authorities to investigate the potential corruption of their national lottery games.

Officials said there were many winners in some cases, but none or very few in others. To the authorities, the big fluctuations in the number of winners didn’t look random. They were worried that a group of people would get internal advice and accidentally bring more winners than expected.

Authorities hired three mathematicians to investigate. They examined the results of the lottery for several years and concluded that there was no corruption. Instead, they found a working cognitive heuristic.

Like Polish authorities, Lotto players believe that randomly selected numbers should always look unplanned. For them, consecutive numbers (1,2,3,4,5,6) or other regular sequences (10,12,14,16,18,20) do not “represent” the concept of randomness. When an orderly set of numbers is drawn, no one plays such a sequence, so there is often no winner.

So here is a way to make cognitive psychology rewarded. If you need to play lottery and want to maximize your winnings, choose a serial number or other regular pattern. They have the same probability as other sequences, but almost no one plays them. If your number is selected, you will maximize your winnings as you do not have to share your winnings with anyone.

Who said that psychology wouldn’t pay off?

The views expressed in this article are those of the author and do not necessarily reflect the views of The Epoch Times.

Stephen Schwartz


Professor Emeritus Stephen Schwartz is Vice President of Macquarie University in Australia, Murdoch University, and Brunel University in the United Kingdom. He has advised and chaired many educational institutions, including the Australian Curriculum Evaluation and Reporting Agency (ACARA). As a scholar, Schwartz’s research extends to clinical psychology, psychiatry, and public health. He has also published over 100 articles in scientific journals and 13 books.