A Strange Coincidence

Our weekly explainer on economics using lessons from popular culture. In Installment 28, Salman Khan and Kareena Kapoor hook up thanks to the Law of Truly Large Numbers.

“Ajeeb ittefaq hai, Kya mulakaat hai, Mil gaye aaj phir/ Koi tho baat hai.”

“What a strange coincidence. What a meeting this is. Once again, we’ve met today. Something’s up!” Salman Khan woos Kareena Kapoor in the film Main Aur Mrs Khanna by pointing out that their bumping into each other again is an unlikely coincidence, therefore implying that it is destiny and they should hook up now. Kareena — WATCH OUT! SPOILER ALERT! — falls for him, presumably because she knows no statistics. The actual reason this charming couple has met is the Law of Truly Large Numbers.

Now, this is different from the Law of Large Numbers, which we discussed in the previous installment of Housefull Economics. The Law of Truly Large Numbers states that “with a sample size large enough, any outrageous thing is likely to happen.” I had once written about this in the context of poker, and the headline I gave for that piece sums it up: ‘Unlikely is Inevitable’.

Naive poker-playing friends, losing their money just as Kareena lost her heart here, would call me up with bad-beat stories like their aces getting busted by sevens after a preflop all-in. I’d tell them that AA beats 77 around 80% of the time, and while it was unlikely over one iteration, if he got into that spot 1000 times, he should expect to lose about 200 of those. All bad beats, assuming one played enough hands, were not merely likely, but even inevitable.

Another way of thinking about this: there might be a billion events right now that are a million to one to take place. That means that many of them will. We’ll notice them, and not the others that didn’t happen, and go Wow, what a coincidence! There must be a divine plan! Come to my arms!

Many conspiracy theories are based on ‘unlikely’ coincidences, and even most of us who are not conspiracy theorists tend to take coincidences too seriously. Humans are prone to the Narrative Fallacy — the tendency to try and build a story around everything — so this is no surprise. We’ll see a black cat walk under a ladder, and notice that someone falls ill, and then see a black cat walk under a ladder, and someone dies, and boom, we build a superstition out of it. And from then on, we don’t notice all the times black cats walk under ladders and nothing happens. (Confirmation Bias, anyone?)

Indeed, it is actually inevitable that whenever a black cat walks under a ladder, something bad will happen, because bad things happen all the time. So do good things. So does everything, given enough iterations. There might be a trillion parallel universes right now where different ‘destinies’ are unfolding. You happen to be in this one, as do I. Such a coincidence!