What Investors (and Their Advisors) Can Learn from Monty Hall

The recent death of Monty Hall, host of “Let’s Make a Deal,” is a reminder of a famous logic problem. The Chicago Tribune’s Eric Zorn has a nice article trying for “an airtight explanation of the solution that will forever put an end to the controversy surrounding the poser that bears his name”. Here is his description of the problem:

You are a contestant on the old “Let’s Make a Deal.” Hall tells you there is a new car behind one of three doors, and a goat behind each of the other two doors. You choose door No. 1. Hall, who knows where the car is hidden, opens door No. 3 and reveals a goat behind it. Then, as Hall often did on the show, he offers you the opportunity to switch and choose door No. 2 instead.

Does it improve your odds of winning the car if you accept his offer and switch? Or does it not matter?


Most people intuitively think that the choice is 50-50. Actually, the odds in favor of switching are 2-1. Many intelligent people got this wrong and were stubborn and aggressive in asserting their opinions.

A New Problem

Did the world learning anything? Here is one distressing example.

A source asserting authoritative expertise on probability and statistics claims to have “proved” that a random process can predict market moves better than experts. This source, who has gotten hired by government and teaches some university classes, presents great “paper” credentials. His claims to fame include the following:

Former two-time Obama Admin executive.  This is the leading educational probability site in the world, with over 150 thousand followers, including celebrities, and 28 million reads.  It’s also integral to the curriculum of at least five leading universities and also followed by central banks.

The article in question got a big play in a variety of media sources. The key point? He asserts that flipping a coin with a 2/3 chance of a market increase would generate a better result than analysts who are consistently bullish. Put another way, you should make your forecasts match the overall odds. Just like the Monty Hall problem, this has intuitive appeal. It also provides confirmation for the existing bias against analysts and forecasters of any stripe.

But it is demonstrably wrong!

Let us suppose you rolled a single die, predicting a down market if it came up 1 or 2 and up if it were 3 through 6. The dice rolling would give you a down prediction for number 1 or 2, each correct 1/3 of the time (1/3*1/6*2). That is 1/9 in your win column. When you predicted an up market, on rolls 3-6, you would be correct 2/3 of the time. That is another 4/9 in your win column. The total is 5/9 or 55.6%.

If you simply predicted an up market, you would be correct 2/3 of the time, or 66.7%, much better than the dice rolling. This is a simple analysis which most people don’t think about. Like the Monty Hall problem, it does not confirm their intuition.

I briefly attempted refutation with some media sources, but it was a hopeless task. (More explanation here).


First, the real lesson of the Monty Hall story is that probability questions – even simple ones – mystify most people who have not studied the subject.

Second, the media publish stories that will be popular, usually confirming biases.

Third, publishers use superficial criteria for determining experts, generating many who are famous for being famous. They are unable to determine truth, even when there is no question about the solution.

And finally, since few can recognize the actual experts, we cannot objectively evaluate their performance.

Investors and Advisors

Any time there is a widespread misperception it provides an opportunity for astute investors. The biggest current error about probability is that amateurs expect certainty instead of favorable odds. But that is a subject for another day.

And I hope the central banks who supposedly follow him do not take this guy too seriously!!

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