Monty Hall

Have you ever had a night of dreams that just go around in circles? The other night I had one of those, and I woke up tired from it. And the issue I was circling was as unresolved in the morning as it had been the night before.

It had to do with a book I’m currently reading by Sam Harris called, “The Moral Landscape.” The following three paragraphs were taken from the book:

The same can be said, however, about our failures to reason effectively. Consider the Monty Hall Problem (based on the television game show “Let’s Make a Deal”). Imagine that you are a contestant on a game show and presented with three closed doors: behind one sits a new car; the other two conceal goats. Pick the correct door, and the car is yours.

The game proceeds this way. Assume that you have chosen Door #1. Your host then opens Door #2, revealing a goat. He now gives you a chance to switch your bet from Door #1 to the remaining Door #3. Should you switch? The correct answer is “yes.” But most people find this answer very perplexing, as it violates the common intuition that, with two unopened doors remaining, the odds must be 1 in 2 that the car will be behind either one of them. If you stick with your initial choice, however, your odds of winning are actually 1 in 3. If you switch, your odds increase to 2 in 3.

It would be fair to say that the Monty Hall problem leaves many of its victims “logically dumbfounded.” Even when people understand conceptually why they should switch doors, they can’t shake their initial intuition that each door represents a 1/2 chance of success. This reliable failure of human reasoning is just that… a failure of reasoning. It does not suggest that there is no correct answer to the Monty Hall problem.

Now Sam Harris is no slouch, so when he says when your’re confronted with the Monty Hall problem and if you switch doors, your odds of winning the car change from 1 in 3 to 2 in 3, I assumed he knew what he was talking about. That was the dilemma, because I clearly saw the odds of both remaining doors were 1 in 2. My mind went around and around all night, and in the morning, the odds were still 1 in 2. I had a Skype conversation with Steve the next day, and he agreed the odds were 1 in 2.

Later on that day, Steve Skyped me back, and said he’d looked the problem up in Wikipedia, and that he could explain it to me, which he proceeded to do. The scales fell from my eyes.

Perhaps you’ll have a poor night’s sleep as a result of reading the above. If you haven’t resolved it before you go to sleep, I’d recommend you read the Wiki article before you shut your eyes tonight, or you might be a little sleepy tomorrow.

One Response to “Monty Hall”

  1. Ryan says:

    The Monty Hall bit is one of the best examples of how poorly we’re equipped to handle that sort of problem intuitively. I love it, and after taking a while to get it myself seem to get stuck trying to explain it frequently. Now I can just use the wiki link.

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