Thinking about thinking: the gambler’s fallacy
The sixth in a series of articles where Whitianga resident, Max Ross, is exploring the way we think.
On 8 August 1913, in a casino in Monte Carlo, the roulette wheel landed on black 26 times in a row. When the wheel landed on black for 25 times in a row, the probability of the next spin being black is still 50 percent.
When the wheel was black so many times, people furiously bet on red believing that the odds of red were now better than on any other spin. In fact the odds of red or black have not changed and these gamblers fell victim to the gambler’s fallacy. They continued to bet on red long after the streak had finished, believing that red was now more likely, as the blacks had been “used up”.
Thinking about probabilities is hard for us. There are lots of confusing and counterintuitive things that happen with probabilities. I have always maintained that Lotto is a tax on the mathematically stupid. The odds of winning are so small that it’s not worth playing the game. Others tell me, “Well someone has to win and that someone could be me.” After a big Lotto win, players select last week’s winning numbers less in the following week, believing that there is less chance of them coming up again. The gambler’s fallacy is a way that we incorrectly think about probability. The chance of a row of things happening is increasingly rare. The chance of getting black 26 times in a row is around one in 67 million. While this is really rare, the very next time we spin the wheel, there is still a 50/50 chance either way.
When I was teaching mathematics, I used to ask the students to generate some random numbers. They had homework of tossing a coin a hundred times and recording the results. We then used this data in some of our probability work. There was always someone who didn’t bother tossing the coin and making up the outcomes instead. These were easy to spot due to the gambler’s fallacy. When they made up the results, they avoided strings of heads or tails and these occur more regularly than you would expect when you toss a hundred coins.
The gambler’s fallacy keeps gamblers gambling. “I have now lost so many times, I must be due for a win soon.” The gambler’s fallacy is a deep-rooted bias that is really hard to overcome. Some experiments have shown that teaching people about probability doesn’t reduce their susceptibility to the gambler’s fallacy. Age reduces the susceptibility in other experiments. Older people are less influenced by unrelated past events.
This bias has more consequences than just for gamblers. When US asylum judges have granted asylum to the last two people, they are 5.5 percent less likely to approve the third person. The best way to counteract the gambler’s fallacy is to see each event as a new beginning. Training yourself to think of each random event as a new beginning can help you to avoid falling into the gambler’s fallacy.