Tambola | The Law of Large Numbers

The lockdown has hit us hard. Now that it has been extended for another 15 days, people are going crazy sitting at their homes (soye bhi toh kitna soye, khumbkaran thodi hain :P)

Well, all of us decided to schedule out the first 21 days with the most productive outlook initially, good for those who have been able to stick to it, Hi5 to those who still have to decide everyday what to do next ;) People have found their ventures to spent time in – books/online courses/work from home/kite flying(me)/online series/ and what not. My mother too, has found her way to engage herself – Tambola!

I kid you not, she is not the only one in family, there are about 4-5 different groups with Tambola games going on every day in her circle. And yes, these traditional games turned digital are actually on a high these days.

So, okay. You too would have played Tambola at least once (lets not be sexist) or you must know how to play it.

Basically, there are tickets with people with some random numbers on them, ranging from 1-90. One person calls out numbers, on a random basis, and the people with the tickets strike off these numbers on their tickets. There points (money prizes) based on pre-defined criteria such as on striking off all odd/even numbers or smallest and largest numbers. You pay for the ticket, and the sum of ticket prices from all members, gets divided into small amounts of monetary prizes attached with each criteria.

Every day, at the end of the game, a tally was done w.r.t. which person won how much amount, and what balances are due. I was intrigued by the numbers and decided to put them in a spreadsheet and see what comes out.

This is how the sheet with 15 days data looks like. Obviously, there were inconsistencies (varying number of members and varying total prize amount, varying criteria), which were overlooked while preparing this sheet.

Now, what is law of large numbers? And, what does it show in the game of Tambola?

As per this law, when large number of trails are conducted, the average tends to be closer to the expected value, and gets closer as more and more trials are conducted.

The last column of the sheet tells us the same thing. The maximum loss = -50, and maximum profit = 100. Almost everyone had no profit/loss, and with those having any profit/loss was within a range of -50 to 100.

The green cells represent continuous winning streaks, while cells in yellow represent continuous losing streaks. These represent the extremes of our data, when you continuously lose and win. But when you total the amounts won (or average them), you will see, they all are close to zero. Even though someone kept winning/losing, in the end, they are all equal (approximately).

So, the next time you play Tambola, or any other game (which doesn't involve any skill), and you happen to be continuously losing/winning, don't be too sad/happy. Chances are, you will win or lose.

P.s. I have been reading this book Freakonomics which prompted me to put those numbers in excel. The book deals with various never thought of, unanswered questions and takes the help of data to answer them. A must read, even if you don’t understand anything about economics.