The Monty Hall Problem

If you’re inclined to learn about statistics or have watched the movie “21”, you would have heard about the Monty Hall Problem.

So what exactly is this? It goes something like this. Imagine you’re on a game show, where you have to choose from 3 doors. Behind two doors are two goats, and behind the third one is a car. If you choose the wrong door, you’ve lost the car.

So at the start, the probability of a car being behind each door is 33.33% or 1/3rd. So let’s say you choose Door 1. After you do so, the show host (who knows by the way where the car is) opens Door 3 to reveal a goat, and then asks you if you would like to switch. You may be inclined to say no, but mathematically, you should switch.

That’s because after taking Door 3 out of the equation, the probability of Door 2 having the car goes to 66.66% (1/3rd + 1/3rd) while it stays at 33.33% for Door 1. You can imagine the same thing for 1000 doors: when we take out 998 other doors, it might make more sense intuitively to switch to the other door left. Here’s the clip from the movie “21”.

Now what application does this statistical problem have in finance? In the world of trading, the implications of decisions made by high-stakes traders are profits or losses in the millions. The main lesson which we can take from the Monty Hall problem is that there is value in re-evaluating your strategy when new information comes out, even if it seems contrary to the initial plan.

To show this, we can take an example from the famous businessman George Soros’ famous currency trades in 1992. At that time, he was betting against the British Pound, believing it to be overvalued. He had chosen his ‘door’, so to say. But then, new information came up — the Bank of England (the central bank) struggled to keep its currency strong, indicating that the pound’s devaluation was imminent.

With this new information, Soros would have had his Monty Hall moment. He could stick with his initial door, or he could “switch doors” - reassess and add to his position against the pound. Soros chose to switch, significantly increasing his short against the pound. When the pound did collapse, Soros reportedly profited by $1 billion. And he’s famously dubbed “The Man Who Broke the Bank of England” due to this episode.

On the face of it, the Monty Hall problem seems more like a party trick than a strategy guide. Yet, it holds substantial implications for the world of finance, trading and even other areas of life where you need to make decisions. It presents a lesson in decision-making based on additional factors and the significance of probabilities. And you don’t need to change the decision every time, you could be right with the original choice even after new information has been given to you. After all, life is not as objective as the field of statistics is.

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