HCOL 196, January 31, 2011

First, we are having a snowstorm on Wednesday. Although I haven’t missed a class because of snow, it could happen. I will tweet from BAYESRULEZ if I have to cancel the class because of snow. If you want this tweet, follow me (I promise not to tweet much!)

Here are the whiteboard snaps from today. I’ll add comments later

#1: Monty Spreadsheet: This is the spreadsheet version of the standard Monty Hall problem. Should be self-explanatory

#2: Ignorant Monty. In this version, Monty doesn’t know where the prize is, and always opens a door. That means he will sometimes (by accident) open the door with the prize. The result is that it no longer matters whether you switch doors if he shows you a goat; the prize is equally likely to be behind the door you originally chose and the door he didn’t open.

We then discussed Angelic Monty and Monty From Hell. Angelic Monty opens your door if you chose the door with the prize, and opens a door with a goat if you didn’t. Obviously, if Angelic Monty shows you a goat, you should switch since the prize is behind the other door for sure. Monty From Hell opens your door if you chose a goat, so you lose, and if you chose the prize he opens a door with a goat and offers you the chance to switch, which you obviously should not do.

#3: Mixture Monty: Off stage, Monty flips a coin. If it comes up heads, he behaves like Angelic Monty. If it comes up tails, he behaves like Monty From Hell. You choose door #1 and Monty opens door #2, showing you a goat. Should you switch? Here’s the spreadsheet we came up with:

As we see here, there’s a two-thirds posterior probability that it is Angelic Monty offering you a chance to get the prize by switching, and a one-third chance that it is Monty From Hell trying to tempt you away from the prize door to a door with a goat. So it is advantageous to switch.

I also handed out next Monday’s assignment.

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