Do you like being wrong? What the Monty Hall problem tells us about ourselves

The Monty Hall problem is a brilliant way to start a fight with someone.

Now, I’m not advocating violence but when Marilyn Vos Savant published Steve Selvin’s idea in 1990, it provoked an uproar.  Thousands of Professors and Phd’s waded into a debate that raged for years. And even after a computer model demonstrated it to be true, many still refused to believe it. And as I have discovered twice in the last few weeks, this seems to really fire people up.

The scenario is simple. You are in a game-show. There are three doors behind which there are two goats and a car. You indicate one door at random that you believe has the car behind it. Without opening that door, the host opens one of the other two doors, and reveals one of the goats. You are now faced with two shut doors and he asks if you want to switch your choice or stick to your original choice. Should you switch?

When posing this question, it’s a good idea to take cover around now.  The second thing to do is to be ready with a clear explanation, stand well back and watch the fireworks begin. Because the answer, as Steve, Marilyn and many others went onto show, was, contrary to what we believe to be correct, ‘Yes’, it is better to switch.

Everything in one’s mind says there is no reason to do this. I have a 1/3 chance before he opened the door and a 1/2 chance afterwards. But there is no logical reason to switch, is there? How can there be? There are two choices and just because a door has been opened doesn’t mean I should change my mind.

The reason is breathtakingly simple to demonstrate.

There are 3 permutations of what’s behind the three doors:

1. Car Goat Goat
2. Goat Car Goat
3. Goat Goat Car

Let’s say you chose door 1 initially (so the first of each of the permutation above). Another door is opened and  now there are only two doors remaining, your one and one other hiding either  a car or a goat.

1. In permutation 1, door 1 hides the car. If you’d switched, you’d end up with a goat
2. In permutation 2, door 1 hides a goat. So if you’d switched, you’d get the car
3. In permutation 3, door 1 hides a goat. If you’d switched, you’d get the car.

So you have a 2/3 chance of winning a car if you switch and a 1/3 chance if you stick.Pretty simple huh.

What I find most interesting isn’t the problem itself but the reaction it gets from people. You can set out the problem and show the answer but every-time, people want to fight you all the way.

I suspect the reason is this: the Monty Hall problem stirs much emotion because we simply do not like being told we’re wrong. And we hate smart-arse’s leading us down a path and watch us make the choice and then tell us we’re wrong. And we hate it more after allowing them to allow us to fight them tooth and nail, even when faced with incontrovertible evidence to the contrary, we try to hold on to our original position, based on whatever flawed logic and not realising until later, sometimes years later, that we were wrong all the time.

It’s uncomfortable being faced with truths that conflict with our view of the world. Most organisations do all the time but do little about it because their world view conflicts with reality. Take RIM and Blackberry as a stunning recent example – their market research told them Apple’s i-phone was just not good enough. The mistake they made was that they started this research with a view of what their customers valued not what non-customers might value. Big mistake

The minority of organisations that do face up to reality, tend to have  reflective people,  prepared to confront the real issues and then deal with them; they’re the ones who are more likely to improve their chances of success (and get into fewer fights on the way).

Follow