Monty Hall/Take A Deal
Posted: Tue Jan 29, 2008 3:49 pm
"Take a Deal" (also known as "Monty Hall") was mentioned in the Mathmo test.
The traditional game goes thus: There are three doors: A, B & C. Behind only one of these doors is the star prize - the car, behind the other two doors - nothing. You select a door (let's say A), and then the host, Monty (who knows the location of the prize) always opens one of the other two doors (let's say B) to reveal that it is empty. He then offers you the opportunity to either stick with your initial choice (A), or switch to the other remaining unopened door (C). Is it a straight 50/50 shot, or can you employ a strategy to maximise your chance of winning the prize?
Once you've thought about that, consider if this situation is different:
You select your door (let's say door A). After some initial banter ("are you sure?") etc, Monty is about to walk over and do his door-opening bit. Suddenly, one of the doors swings open (let's call it door B). Monty hadn't touched it, nor given any indication he was about to open it, the lock just broke and the door came open. There's nothing behind it. There's stunned silence, then some laughter, and the director yells "cut!". He comes over and says "well that was lucky, it wasn't your door, and it also wasn't the car. It would have been a pain to have had to take you out back while we moved the car around. Okay, we're gonna start filming again with Monty walking over - obviously Monty you'll have to open door B, and we'll carry on from there..."
Is this different? What would you do in this situation?
The traditional game goes thus: There are three doors: A, B & C. Behind only one of these doors is the star prize - the car, behind the other two doors - nothing. You select a door (let's say A), and then the host, Monty (who knows the location of the prize) always opens one of the other two doors (let's say B) to reveal that it is empty. He then offers you the opportunity to either stick with your initial choice (A), or switch to the other remaining unopened door (C). Is it a straight 50/50 shot, or can you employ a strategy to maximise your chance of winning the prize?
Once you've thought about that, consider if this situation is different:
You select your door (let's say door A). After some initial banter ("are you sure?") etc, Monty is about to walk over and do his door-opening bit. Suddenly, one of the doors swings open (let's call it door B). Monty hadn't touched it, nor given any indication he was about to open it, the lock just broke and the door came open. There's nothing behind it. There's stunned silence, then some laughter, and the director yells "cut!". He comes over and says "well that was lucky, it wasn't your door, and it also wasn't the car. It would have been a pain to have had to take you out back while we moved the car around. Okay, we're gonna start filming again with Monty walking over - obviously Monty you'll have to open door B, and we'll carry on from there..."
Is this different? What would you do in this situation?