Jan 16, 2025 21:00:00

What are the 'gambler's fallacy' and the 'hot hand fallacy' that confuse people?

The world is full of random events such as 'Will tomorrow's stock prices rise or fall?', 'Will the ball be kicked left or right in a penalty kick?', and 'Will the lottery ticket I've been buying for years finally win or lose again?'

Millard Hagani , a senior lecturer at the University of New South Wales in Australia, explained two fallacies that confuse the brains of people who observe or experience these events: the gambler's fallacy and the hot hand fallacy.

The 'hot hand' and the gambler's fallacy: why our brains struggle to believe in randomness
https://theconversation.com/the-hot-hand-and-the-gamblers-fallacy-why-our-brains-struggle-to-believe-in-randomness-246244

The various events people encounter in their daily lives are independent and unrelated. However, people experience these events as 'part of the flow of life,' and the brain tries to read certainty and patterns into them. In other words, the human brain tends to find patterns behind random events that don't actually exist.

To avoid this fallacy, it is important to think about whether the outcome of one event affects the outcome of another event and not associate independent events with other events. People who do not understand the independence of these events are prone to fall into erroneous ideas such as the 'gambler's fallacy' and the 'hot hand fallacy.' Haghani explains these fallacies in detail.

Gambler's fallacy
On August 18, 1913, the most bizarre phenomenon in history occurred at the Monte Carlo Casino in the Principality of Monaco. The casino's

roulette wheel showed the number 'black' more than 10 times in a row. Many gamblers who saw this bet on 'red,' thinking that 'red will come up soon,' but the black numbers continued to come up, and by the 20th spin, the roulette table was full of gamblers betting on 'red.'

However, the roulette wheel continued to show 'black' 26 times in a row, and finally 'red' appeared on the 27th spin, but by that time many gamblers had lost a lot of money. This is a textbook example of the phenomenon known as the 'gambler's fallacy,' which refers to the fallacy of believing that 'independent events in the past affect the outcome of independent events in the future.'

In this case, gamblers thought, 'I've had enough black so far, so red will come out soon,' but in reality, each spin of roulette is an independent trial, so the probability of red, black, and green coming out in the next trial is the same every time. In other words, no matter how many times black has come out in a row, the probability of red coming out next does not change. However, people do not understand that these trials are random, and they tend to mistakenly think that red will come out soon because black has come out in a row so far.

Similar thinking is seen in many places other than gambling. For example, if a certain number has not come up in the lottery for a long time, you might think, 'Maybe this number will come up soon,' or if you keep giving birth to boys, you might think, 'Maybe girls will be born soon.' In fact,a study analyzing 37 penalty shootouts in the World Cup and European Cup showed that after three consecutive kicks to the same side, the goalkeeper will kick the ball in the opposite direction for the fourth kick. In other words, even though it is actually unknown which way the next penalty kick will be kicked, the goalkeeper tends to think, 'It will be a shot in the opposite direction soon.' The kicker was not able to predict this tendency of the goalkeeper, and the proportion of shots kicked in the opposite direction did not change.

◆Hot hand fallacy (hot hand phenomenon)
In some cases, it is difficult to say that consecutive attempts are completely independent random events, and previous results are likely to affect future results. For example, in a basketball game, it is natural to expect that a player who has made multiple shots will also make the next one. In basketball, a player who makes consecutive shots is called a 'hot hand,' so when a player who has made a shot once continues to make a good run, this is called the 'hot hand phenomenon.'

However, there is ongoing debate as to whether the hot hand phenomenon actually exists or is merely a biased pattern of random events. Cases in which the hot hand phenomenon is merely an illusion are also called the 'hot hand fallacy.' However, unlike roulette, which does not involve human conditions, in sports the psychological state of the players is involved, so the players' skill, confidence, momentum, etc. may affect the results.

Several studies have looked at the hot hand phenomenon, but the results have been mixed and context-dependent: some studies have observed mild effects in a few sports, including baseball , darts and tennis , but suggest that they are not as strong as many players, coaches and fans believe.

People are prone to the gambler's fallacy and hot hand fallacy because the human brain seeks to find patterns and trends to make decisions, but there is a limit to the number of events that humans can observe. To see the overall pattern, you need to observe many events and record the results, but this is difficult to achieve in the real world, so you end up reading trends and flows that don't actually exist from a small number of events.

However, events are not always independent and sometimes successes or failures occur in succession, influenced by skill, confidence, trends, etc. In this case, past results are the key to predicting future successes or failures.

'Going forward, whenever you encounter a series of events, good or bad, pause and think. If you have no reason to believe the events are connected, resist the urge to overinterpret them,' Haghani said. 'Understanding randomness can free you from unnecessary worry and false hope, allowing you to focus on down-to-earth decisions.'