# What are the odds?

Krazy Kaan

We have two similar but not identical puzzles to share.  We’ll discuss the solutions in an upcoming post, but we’ll give you a week to think about it on your own.

Both puzzles are about a game show we’ll call Krazy Kaan’s Extravaganza!

The premise of Krazy Kaan’s game is simple, there are three doors:

Behind one door is \$1,000,000.  Behind the other two doors there is no prize.  You get to pick any door you like (for example, Door 1), then Krazy Kaan opens one of the other two doors (for example, Door 3) and you see there is nothing behind it.  You now have the opportunity to either stick with your original door, or switch to the third door (in our example, Door 2).  Once you’ve made your choice, the door you’ve picked is opened and you get whatever is behind that door.

Simple, right?

The question, then, is after Krazy Kaan opens the door, should you switch doors or stick with the one you picked?  That is:

Does switching help, hurt, or not affect your odds of winning the million dollars?

Now we said at the beginning that there is two puzzles here.  As you might guess, the answer depends on how Krazy Kaan chose which door to open.  So really there are two scenarios here:

1. Say Krazy Kaan picked at random between the two doors and it just happened that he selected a door which doesn’t have the money behind it.
2. Say Krazy Kaan already knows which door hides the money and that he specifically choose a door which doesn’t have the million dollars behind it.  In the event that you picked the door hiding the money, Krazy Kaan picked one of the two other doors at random.