Imagine you and a friend decided to play a simple game of heads and tails, starting with 30 rupees each. The rules are as simple: Heads, you win 1 rupee, and if it is tails, you lose 1 rupee.

Now mathematically, if you play some 50-60 odd rounds, you’d both end up with the same money since the odds are 50-50 for each of you. However, try tossing a coin 50 times to see how many heads or tails you get actually.

Now in the situation, after playing 70 rounds, you win 20 times and lose 50 rounds, the game is over for you as you have no more money left. You conclude that when you toss a coin, the chances of heads are 29% and tails are 71%, so the next time you play such a game, you would be inclined to choose tails.

However, if you had more money and could play say another 300-400 rounds, you would see the odds are close to 50-50, not 29-71. You arrived at the wrong conclusions as you couldn’t afford to play more rounds.

We can see similar trends in success and failure rates we observe as we are not sure if it was based on multiple independent observations across a long timeframe or just based on observations from a single event.

So next time, you see a probability score, it’s important we understand how it was measured rather than accepting it at face value