Gambler’s fallacy & Regression towards the means

Gambler’s fallacy

Humans are not good at handling probability. Suppose we have a fair coin, which has the same probability of getting heads and tails on every single toss. If we got 3 heads already, what will we get in the next toss?

If your answer is tail, then you fall into the gambler’s fallacy. The correct answer is we have the same chance on getting head or tail. The coin has no memory, it will not “balance” the results. Every toss is independent.

Regression towards the means

Regression towards the means is a less common know statistic phenomenon. It states that “when an extreme was measured, the next measurement will tend to be closer to average”.

It sounds like Gambler’s fallacy: We got 3 heads already (an extreme case), it is not likely to have 4 heads in a row (another extreme case), we will get a tail in next toss (a common case). What’s wrong?

Probability and Statistic can only predict trends but not specific events

The scope of regression toward the means is different from gambler’s fallacy. Gambler’s fallacy is predicting what is the result of the next event, but regression toward the means is talking about the trend of future events.

Let’s go back to the coin example, having a tail in the next toss is a specific event. Regression towards the means only stated that “In upcoming tosses, it is more likely to have tails, so that the number of heads and tails are almost the same in the long run”. “In the long runs” is really long, can be the next millions or billions of tosses, there is a high level of uncertainty on the next toss.

Regression towards the means tells nothing to gamblers, never count on it in games.



Software Engineer from Hong Kong, living in Luxembourg

Love podcasts or audiobooks? Learn on the go with our new app.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Ku Lok Sun

Ku Lok Sun

Software Engineer from Hong Kong, living in Luxembourg