Douwe Osinga's Blog: Should you switch?

Saturday, February 5, 2005

A couple of weeks ago, two friends of mine came over to visit from the Netherlands. It was great of course, but one of the things we ended up talking about mainly were a couple of riddles. I thought about it some more and now I have five variants. Some might seem familiar, some trivial, but I think the combination is very interesting.

  1. You have hundred dollars. I offer to throw a coin. If heads comes up, I half your money, if tails comes up, I double your money. Should you do this?

  2. There are two envelopes on the table. One contains twice as much money as the other. You take one. One hundred dollars. I offer you to switch envelopes. Should you?

  3. A quiz master has hidden a price behind one of three doors. You are a winning candidate. You'll have to guess which door has the price by lining up before it. You make your choice. The quiz master says, I'll help you a little, this door, and he points at one, does not have a price behind it. He then opens it to prove his point. You are now allowed to switch to the third door. Should you?

  4. A quiz master has hidden a price behind one of three doors. You are one of three winning candidates. You each choose a door. The quiz master says, we can't all win. Unfortunately you and he points at one of your competitors, didn't win. He opens the door of that person and there is nothing behind it. So your competitor leaves. Now the quiz master offers you to switch door with the other survivor. Should you?

Well, think about these for a little. Then continue reading this sentence. And a little more if you really thought about it. You're sure you thought about it and are not just continuing to read to get the answers? Ok, here is the answer. You should take the bet/switch in puzzle 1 and 3, but it doesn't matter in 2 or 4. I'm sure you can come up with some kind of explanation, but what is exactly the difference between them?