Who is Monty Hall?
The story behind the Monty Hall Problem starts with the basic workings of the 'Lets Make A Deal' game show that Monty Hall hosted in the mid '70s (??). The idea of the game was for contestants to dress up in creative and often overly ridiculous costumes so as to draw as much attention to themselves. The belief being the more absurd or creative costumes got into the screened section of the audience. Monty would walk thru the selected section of the audience, pick someone to participate, and offer them something for a trivial item they might be carrying. Monty would then often offer the contestant to 'deal up' for one of a number of curtains or doors. These choices always involved a count of three curtains or doors.

The idea is that the contestant is offered the choice of three doors. A generally desirable and typically valuable prize was said to be behind one of the doors (ie. a new car) ... with the other two doors hiding a 'loser' prize (a goat or some other obviously non-valuable item). What the prizes or 'loser' offers would be were never disclosed in advance to the contestant. Once the contestant would make their selection for which door they believe has the valuable prize, Monty would open one of the doors that the contestant did NOT select. This would always disclose one of the two 'loser' prizes to the contestant.

At this point the contestant is made an offer by Monty. They can change their mind about the door they picked ... and select the other unopened door ... or they can stick with their intial choice and not change their mind. This option provided by Monty Hall now produces a question for the wary contestant ... is it better to stay with your first choice ... or is it better to switch your selection to the other unopened door?

So What's the 'Problem'?
So here's the problem ... at least for some it's a problem. It turns out that the odds are in your favor to switch your selection and pick the other unopened door. For some ... this isn't really the intuitive response that feels like the right choice. It's for this reason that this is worth reading about at all ... for it wouldn't be interesting if it were obvious. This whole thing started in 1991 when a reader of Marilyn Vos Savant's Sunday Parade column wrote in to ask the following question:

"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?"

Interestingly, Marilyn's response was that the contestant should switch his selection (thereby increasing their odds). This produced a flood of thousands of letters and responses from readers complaining that her answer was incorrect. Many of these letters were from quite learned types that have more than a casual understanding of mathematics or probability theory.

The History
The history goes way back beyond Marilyn Vos Savant ... and includes references to this logical paradox from Martin Gardner as far back as 1959 in his Mathematical Games column, Steve Selvin's discussion of this logical problem in two letters he wrote to American Statistician in 1975, a cover story in the New York Time in 1991, and to date over 40 stories have been published about this problem in academic and press mediums.

Confused? Are You Ready For The Explanation?
I'm going to warn you ... this stuff will make your head hurt. This problem has confounded career mathemeticians, physicists, and other sundry scientific types. Now's your chance to take this nice nostaligic 'walk down memory lane' with Monty Hall and his wacky game show ... and hit the road ... maybe go watch me do a trick in the Let's See A Trick section (much more passive and not as thought provoking).

This is really a mathematical problem ... and that math is really ugly! See the Credits & References section below for a eyefull of how really ugly it is (ie. Baye's Theorem). The best way to make sense of this is to show it visually. Below are the two scenarios that could occur for any given contestant in the game. They are:

    - Player picks the door w/ the valuable prize on first selection.
    - Player picks the door w/ the 'goat' on the first selection.