This blog provides supplementary thoughts and ideas to the site. If you haven't seen the main site, there is a lot there including the Martel and Rodwell interviews, photos, and articles. This blog is focused on advancing bridge theory by discussing the application of new ideas. All original content is copyright 2009 Glen Ashton.

Tuesday, July 01, 2008

Let's modify the Monty Hall problem this way (no, this is not the Drew Carey problem):

On a game show you're given the choice of three doors: Behind one door is a car (low gas mileage) and behind the other two doors, a deck of cards.

You are told that there is a 50% chance the car is behind door 1, 25% each for the other doors.

So you pick door 1, and the host, who knows what's behind the doors, opens door 3, which has a deck. He then gives you the chance to switch to Door 2. Should you?

The starting odds of getting the car were:
Door 1: 50%
Door 2: 25%
Door 3: 25%

Now when the host opens door 2 or door 3, to reveal a deck, the odds now change to:
Door 1: 50%
Door 2 (if not shown): 50%
Door 3 (if not shown): 50%

Using the chart from the Wikipedia article:

Car location Door 1 (50%)
-- Host opens either other door --
Door 2 open (25%) - switching loses
Door 3 open (25%) - switching loses

Car location Door 2 (25%)
-- Host opens Door 3 --
Switching wins (25%)

Car location Door 3 (25%)
-- Host opens Door 2 --
Switching wins (25%)

Thus it is equal odds to switch or not, in this case since door 1 was 50% before you picked a door.

The point here is you need to know your beforehand ("a priori") odds (e.g. was each door equal probability or not?) and then use the additional information based on how it was discovered or given to you.


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