Simulated experience #2

There are 3 doors.

Behind one of them is a Ferrari of your favorite color.

You do not know which door is the winner.You don’t.

But I do!

I ask you to select a door and you make a choice.

Once you choose a door, I eliminate one of the two that you did not select, while making sure that there is NO Ferrari behind the door I eliminate.

Now…

Do you stay with your original choice, or given the option, would you change to the other remaining door?

This is the famous Monty Hall problem. And it confuses a lot of people.

The probabilistic structure, like in the birthday problem, is hard to understand.

Although one might be inclined to think that the odds are 50%-50% at the last stage, it turns out that if you change doors, your chances of getting that Ferrari is 67%, and if you stay, it is only 33%.

There is, of course, an analytic solution to this problem. But why bother? Use simulated experience. Just take 3 playing cards, 2 black and 1 red (Ferrari).

Put them upside down as you make a selection. Then, turn them over, take out a black card out of the ones that you did not select and make a note of the result. You’ll see that when you repeat this procedure over and over again, out of the remaining cards, the red one will mostly be the other card.

Or, play the game HERE.

Who is the killer?

I look at my card. It’s red. So, who is the killer?

I am in a train, together with three friends. We have tried playing several card games. This game beats them all. It is mind-boggling.

It is not even a card game. It’s simpler than that. You need only four cards: three reds and one black. Everybody gets one card at random. The owner of the black card is the killer.

Then you start talking with each other. The job is to find the killer, just by talking, discussing. Once three people agree that a fourth is the killer, the cards are opened, the scores are delivered; alea iacta est. Until then, you just talk and think and form conjectures.

Does this game have a solution? I doubt it. You get to know the other players first. How do they behave? What do they say? With each new game, you hope to improve your ability to predict.

The interesting thing is that, after some playing time, you start perceiving subtle changes in behavior and communication. You base your theories on them. However, the more you convince yourself of the validity of your theory, the more difficult becomes the task of convincing others. The better you express your opinions, the more the other players think that you are the killer, as you are trying to divert them to another target.

There is no easy fix. You just have to be patient, observant and cautious about what you communicate to others. The trick sometimes is to be even more cautious about what you communicate to yourself.

I look at my card. It’s red. Or is it?