The Gambler's Fallacy: Why Streaks Lie (My Mom's Mahjong Lesson)
Can we predict the future by looking at the past?
Have you been to a casino?
My mom loves to play Mahjong. It's one of the very rare hobbies of hers. When I asked her how the Mahjong playing went that afternoon, she often mentioned that she was on a "winning streak". She is the best Mahjong player I ever know. But she also would get a "losing streak" once in a while. My mom would also summarise the most recent Mahjong activities she joined, and make a conclusion about whether she was 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.
Did the decision-making of my mom make sense? No, she ignored the causal 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 and you get eight heads and two tails. What are the odds of each side on the next flip? The right 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 August 1913, 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 francs betting that the ball would fall on red throughout this streak, in the mistaken belief 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 be taken as an indication that it is due to appreciate, and so they decide to hold onto those stocks. Gambler's fallacy may be at work here, as investors are making decisions about the probability of a fairly 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 well 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 on the narrative fallacy, we are an animal of causal reasoning. And random events act as a thorn in the flesh to us. As a result, we try to make sense of the random events, which leads us into the pitfall of cognitive bias.
Then, how to avoid the gambler's fallacy? Of course, being aware of the existence of the gambler's fallacy is always the first and most important 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 8 tails 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%. 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. Therefore, 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 reality is, events aren't always independent either. My mom has more wins because she is skilled at Mahjong and she is surrounded by many unskilled players.