Survivorship Bias (Part 2/3): Warren Buffet’s illustration of coin-tossing:

I had come across an intriguing illustration by Warren Buffet some months back. It relates closely to the topic we are discussing (Survivorship Bias), and hence I will try to reconstruct it for us in Indian terms. Imagine a game of tossing a coin with participants betting 1 rupee at every stage. Supposing that every Indian citizen participates in this game by betting 1 rupee each, and calls (bets) for a head or a tail. As per laws of probability, roughly 50% will make a correct guess and get 2 rupees (their own one rupee and a rupee each from those who made a wrong call). Now, the rules of the game are such that it is compulsory to keep playing this game as long as you are winning. So, on the second day, we have 50% of India’s population betting with 2 rupees each (which they had won the previous day). That leaves us with only 25% of the population as winners with a game portfolio of 4 rupees each at the end of day two. The game goes on this way until only one participant finally wins.

Considering India’s population to be 136 crores, I have created the following excel sheet that shows the number of winners and the day wise earning per winner. It has some interesting observations:

It takes exactly 30 days to complete the game and declare a single person as the winner.

The winner will earn Rs. 53.68 crore as prize money (before the tax man comes calling).

Now, look at day 20. There are only 1297 people left in the game from entire India. These are the people who will start impressing their friends by bragging about their successful coin-tossing abilities. They will discuss their technique in great detail. There will always be people interested in listening to them with the hope that they too will apply these techniques, just in case there is a second season of the game coming up.

On the 21st day, there will be around 648 people surviving. They will be the ones who will project themselves as top-masters of the game and write books having titles similar to ‘Making ten lacs in 20 days just by flipping a coin correctly’, and ‘You too can be a million-er in 20 days like me’. The books will be bestsellers… Just in case, there is a second season of the game coming up, let’s read them and be better prepared this time.

On the 23rd day, there will be only 162 survivors. They will be all over the media giving interviews as experts and authorities discussing their unique coin-tossing skills and techniques. Some of them will be invited and paid in lacs by prestigious institutions to deliver lectures on “Wealth creation in less than 20 weeks”.

The fact of the game is that if we had 136 crore crows playing this game, the results would have been the same, and we would have 162 surviving crows at the end of the 23rd day with each of them earning a million rupees. This imaginary game example is an attempt to illustrate why we will not learn anything from books titled “How to convert 1 rupee into ten lacs in just 20 days”, and “How to earn ten lacs in just 30 seconds a day” even if they have sold a billion copies. It’s better to avoid books and videos having such types of titles. We might get some pointers but let’s forget about getting cutting edge insights from such books and videos. Let’s remember that Nothing succeeds (and sells) like success.

In the final part of this series of 3 posts on survivorship bias, we shall discuss how we can survive the survivorship bias. In case, you would like to read it now itself, just click the link below and start reading:
Survivorship Bias Part 3: They have no idea how they lucked-up!

And, if you haven’t yet read the first part of this 3 part series yet, you can read it by clicking below:
Survivorship Bias Part 1: The curious case armouring WW2 aeroplanes