Does the Monty Hall Paradox effect Gambling Strategies?

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A look at the Monty Hall Paradox and its impact on gambling strategies.

Did you ever hear of the Monty Hall Paradox? Does the name Monty Hall even ring a bell? The millennial generation may not be familiar with Mr. Hall, but he was the original host of an immensely popular television game show, Let’s Make a Deal, that originated in the US in 1963.

Monty spent the next 23 years of his life hosting the show – long enough to be immortalized in what’s now known as the “Monty Hall Paradox”. The theory is based on a player’s odds of winning the best prize when given three options initially, then having one losing option removed. It’s a theory that’s altered otherwise sensible gambling strategies for decades.

Monty Hall Paradox Explained

In the game show, a player would often be given the choice of claiming a prize behind one of three doors. Behind one door, there might be a shiny new car. Behind another door, a shiny new toaster oven, or even something much less desirable like a pig, goat, chicken or other small farm animal.

Obviously, the new car would be the better of the three prize (unless you have an unnatural fascination with toast, or a budding farm to go home to). When given the option to choose Door #1, #2 or #3, you have a 33.33% chance of picking the car. At the same time, you have a 66.66% chance of selecting a lesser prize.

So, with confidence, the player selects a door, firm in their resolve that the car lies behind it. Then, Mr. Hall does something to throw a big old wrench into the whole plan. After selecting a door, he would reveal one of the doors containing a lesser prize, and ask the age-old question:

“Would you like to switch doors?”

Suddenly, the once oh-so-confident player is thrown into a state of deep confusion, self-doubt, panic! Should they switch doors or stick with the original door?

The real question is, are the odds of winning the best available prize any different at this point? Does switching or staying have any genuine effect on the player’s gambling strategies and odds of winning?

Gambling Strategies Say Always Switch

It would seem that switching doors would have absolutely no impact on the odds of winning. But mathematically speaking, one should always make the switch, doubling their odds of picking the car. Here’s why:

In the beginning, with three doors available, the odds that the player picked a WRONG door are 2-in-3, or 66.66%. That only leaves a 33.33% chance of winning the car.

Now that one of the losing doors has been revealed, the odds of picking correctly seem to increase to 50%. Yet we have to take into account that the player has already, more than likely, picked a wrong door. Remember, the player’s odds of a losing pick were 66.6% with three prizes hidden.

Thus switching to the other door would increase the player’s odds of winning from 33.33% to 66.66%.

Wait, What? That Can’t Be Right…

Yes, it’s true. Because now, of the three doors, you know one that is incorrect, which eliminates 33.33% of the chance of losing. Now there’s the remaining 33.33% chance of losing, plus a 33.33% chance of winning. Since we know the player didn’t pick the first 33.33% chance of losing, that element must be added to the chance of winning – but only if the player elects to switch doors.

So, switching doors results in a 66.66% chance of winning the car, while staying with the original door continues to provide a mere 33.33% chance of winning the car.

Mind blown? You’re welcome. From now on, when presented with any analogous scenario, alter your gambling strategies accordingly. And if you don’t believe me, check out this video presentation by Kahn Academy. The author explains it in much more detail, and with illustrations (yay, pictures!)