Have you been to a casino?
My mom loves to play Mahjong. It's one of her very rare hobbies. When I asked her how the Mahjong was playing that afternoon, she often mentioned that she was on a "winning streak". She is the best Mahjong player I have ever known. But, she also would get a "losing streak" once for a while. My mom would also summarise the most recent Mahjong activities she joined and conclude that if she is on a lucky streak. If YES, she would keep going; if NOT, she would step back and take a break of several days to wait for the bad luck to go away (hot hand effect).
Did the decision-making of my mom make sense? No, she ignored the casual independence of each round of Mahjong. It is also called the gambler's fallacy. It occurs when an individual erroneously believes that a certain random event is less likely or more likely to happen based on the outcome of a previous event or series of events.
For example, if you flip a coin ten times, you get eight heads and two tails. What are the odds for each side? The correct answer is 50%. No matter how many heads you have got in the previous flips, the odds of getting a head in the next round will always be 50%.
Here is another real story to understand the gambler's fallacy. In 1913 August, at a roulette game at the Monte Carlo Casino, the ball fell on the colour black 26 times in a row since this was such a rare occurrence. Gamblers lost millions of dollars betting that the ball would fall on red throughout this streak, mistakenly believing that the ball was due to land on it soon.
The same phenomenon can also be found in the stock market. Investors may see the continual rise of a stock's value as an indication that it will soon crash, therefore deciding to sell. Likewise, if a stock has lost value, this can indicate that it is due to appreciation, so they choose to hold onto those stocks. Gambler's fallacy may work here, as investors make decisions based on the probability of a somewhat random event (the stock's price) based on the history of similar past events (the trend in its previous price points). The two are not necessarily related. A stock that has been appreciating may continue to appreciate, just as it could crash. Its past price trajectory in itself does not determine its future trajectory.
Then, why do we fall into the gambler's fallacy so often? As I mentioned in my previous blog, "The story-telling paradox", we are an animal of causal reasoning. And random events act as a thorn in the flesh to us. So, as a result, we try to make sense of the random events, leading us to the pitfall of cognitive bias.
Then, how to avoid the gambler's fallacy? Of course, being aware of the gambler's fallacy is always the first and most crucial step. But what else can we do? We can also keep the "law of large numbers" in mind. The law of large numbers in probability and statistics states that as a sample size grows, its mean gets closer to the average of the whole population. For example, you may get eight heads in 10 flips of the coin, but how about 10,000 flips? Research shows that the odds will get closer to the mean (50% in this case) when the sample size is large enough. Likewise, a small sample size tends to show an extreme result (80% in this case).
Casinos generate profits based on the "Law of large numbers". The house edge on an American roulette wheel, which contains a double zero, is 5.26%. So for every $1 million that's bet at the roulette tables in a casino, the management expects to pocket a profit of slightly more than $50,000. So naturally, casinos don't win. They just have greater odds.
Last but not least, recognising the independence of different events is also crucial for avoiding the gambler's fallacy. As complicated as the reality is, events aren't always independent. My mom has more wins because she is skilled at Mahjong and surrounded by many unskilled players.