Gambling in the Classroom

I play all sorts of games with my students in the classroom. Here’s one of my favorite ones:

A pair of dice is thrown. If we don’t get a 12, I will pay you USD 1 million. If we do, you will pay me USD 50 million. Assume the pair of dice is fair and you have the financial capacity to make this bet.

Will you play? To make it easy for the students to answer the question, I put up this expected value computation.

Nobody wants to play this game. When I ask the reasons, I get replies like “it has negative expected value,” or that it’s “mathematically unintelligent” to play this game.

The game gets more interesting when I add a twist which is this: We play this game once a year. And I urge my students to contemplate over what happens if they do play the game, even if it’s mathematically unintelligent to play.

There’s a 97.2% chance of winning USD 1 million every year and only a 2.8% chance of a possible wipeout. I ask my students to compute how many years can go by before their “mathematical unintelligence” becomes evident?

They do the math.

Question: What’s the chance of not landing 12 for ten years in a row?

Answer: 97.2%^10 ≈ 75%

What does this mean? It means that if they play this game every year then there’s about a 75% chance that they will get to earn a million dollars each year and not end up going bust.

Question: What’s the chance of not landing 12 for twenty years in a row?

Answer: 97.2%^20 ≈ 57%

The implication is surprising to students, when they reflect upon the “functional equivalents” of this type of gambling behavior outside the classroom. I give them some examples which I will not reproduce here.

That implication is this: People in the world of business as well as investing can do all sorts of mathematically unintelligent things and look like geniuses for long periods of time. They can deliver wonderful earnings numbers and return numbers for years and years which will look very impressive to analysts and markets and clients even though they are lucky outcomes from “mathematical unintelligence.”

And it can take a long long time, before the odds catch up. More often than not, reckless behaviour won’t result in wrecks. And then, one day, it will.

Indeed, if you take a sample of 20 entrepreneurs or investors who love playing this type of a game, there will be five who are not expected to encounter a possible wipeout, even after 50 years. I can assure you, those five lucky survivors would be regarded by the world as geniuses.

Ponder over that when you evaluate the performance numbers of businesses as well as investors you study.

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Note: Adapted from an example cited by Warren Buffett in his letter to the shareholders of Berkshire Hathaway Inc. in the company’s annual report for 1997