Chance Has No Memory

“My luck is about to change. The trend will reverse.”

Assume India and Pakistan are playing a one-day international series of 10 matches. Today is the ninth match and the Indian captain Virat Kohli is tossing a fair coin. Pakistan won all the tosses in the previous eight matches. The series is currently tied at 4 – 4.

What is the probability of Kohli winning the toss today?

The answer is –

P (Kohli winning the toss) = No of favorable outcomes / Total no of outcomes = 1 / 2 = 0.5, or 50%

If you had answered that Kohli will 100% win the toss this time because he did not win it a single time in the previous eight instances, and that his luck would change today – and this is how we often predict – you are mistaken.

The iron rule of probability that you need to remember here is – chance has no memory.

This means that, in activities largely involving luck (like fair coin toss, gambling, investing), past outcomes have no effect on the current outcome. Chance occurrences do not have any relationship to things that happened before.

The probability of a child being a boy or girl is, theoretically 0.5. Since chance has no memory, that’s the same probability EVERY time. Even in a family of 10 daughters, the probability of the eleventh child being a son is, theoretically, 0.5. In a country like India, that’s an important thing to remember for parents with first 2-3 daughters but still wanting another child believing that would be a son.

Now, it may sound simple but a lot of us struggle with this idea.

People have a hard time remembering this when they invest in stocks. For example, when I see that my past 3-4 stocks have not earned me quick returns like what other stocks have earned for my friends, I am more inclined to bet on the next stock thinking, “It hasn’t happened in a while, so it’s bound to happen soon.”

It’s like Ranveer Singh singing in the movie Gully Boy, “Apna time aayega…” (my time will come).

In the India-Pakistan match, the fair coin does not know nor can it understand the results of tosses in the previous eight games, and so even it doesn’t know which side up will it fall the next time.

In his book Seeking Wisdom: From Darwin to Munger, Peter Bevelin writes –

We tend to believe that the probability of an independent event is lowered when it has happened recently or that the probability is increased when it hasn’t happened recently. For example, after a run of bad outcomes in independent events that appear randomly, we sometimes believe a good outcome is due. But previous outcomes neither influence nor have any predictive value to future outcomes. There is neither memory nor a sense of justice.

In short, it is foolish to believe that independent events influence or provide us any predictive power over future events. Chance does not have a sense of fairness or memory.

As a stock trader, which involves flipping one stock after the other for making quick returns, if you have lost money on the previous five stocks you picked, it does not mean that you will make money for sure in the next stock. The odds of gaining/losing are still the same – 50/50 – because in all the instances you had no idea what you were getting into.

However, as an investor, you can try to get the odds somewhat in your favour (at least that is what you think you are doing) by knowing what you are getting into and allocating your capital sensibly. But even here, you have no control on the consequences of your actions.

Anyways, that’s not the big idea I wish to leave you today with.

The big idea for today is that chance has no memory, and you must remember than when you are betting on your next stock to earn you great returns just because the last few didn’t.

* * *
Here are the best things I am reading and thinking about today –

• When Dollar Cost Averaging Matters the Most (Ben Carlson)
• The Art of Being Alone (Farnam Street)
• Platforms in an Aggregator World (Stratechery)
• The Art of Survival (Ian Cassel)
• Bruce Lee’s Four Idea Principles (James Clear)

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That’s about it from me for today.

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Please don’t take chances with Coronavirus. Stay safe.

With respect,
— Vishal