More on the Monty Hall paradox. This written on April 7 2003.

Monty Redux

Recall, the Monty Hall paradox from “Let’s Make a Deal” an old game show. The last step in the game show was guess which of 3 boxes contains a big prize. There are three large boxes, box 1, box 2 and box 3, one contains a very valuable prize, the other two contain prizes of small value. The contestant guessed a box. The assistant (Carol Marol or was she on truth and consequences) opened one of the other two boxes showing that it didn’t contain the big prize. Monte Hall offered the contestant the chance to switch to pick the remaining unopened unselected box.

Now all contestants must have noticed the pattern that the assistant always opened one of the boxes which had not been chosen and that box always contained a small prize. I am going to add another assumption to make the assistant follow a well defined rule. I assume that the assistant opens the box which 1) has not been chosen by the contestant 2) does not contain the big prize and 3) has the lowest number of boxes satisfying 1 and 2.

Now consider a case of the game. Contestant guesses box 2. The assistant opens box 1 showing that it contains a small prize ? The contestant is allowed to switch and guess that the prize is in box 3. Should the contestant switch ? Does it make any difference for the probability of winning ?

How about another case of the game. Contestant guesses box 2. The assistant opens box 3 showing that it contains a small prize ? The contestant is allowed to switch and guess that the prize is in box 1. Should the contestant switch ? Does it make any difference for the probability of winning ?

Now I stress, I think this is a change from the standard problem. Please send proposed answers to rjw88@hotmail.com. If someone convinces me they got the right answer (whether or not it is the same as what I think now) they get applause here in front of an audience of 5 or 6 visits a day.