HAH! That's a great UK reference, but the Monty Hall Problem relates to a US game show (hosted by, yes, Monty Hall) called Let's Make A Deal, a feature of which at one point involved a player winning whatever was behind one of three curtains. One had a car, two had goats (yes). The contestant would choose a curtain, and then Monty Hall would reveal one of the other two... to contain a goat. Because he does so in full knowledge this will happen (if only you could do that with DoND and blues eh?) the probability of your initial choice of curtain having the car is not 1/2, it is 1/3 - because that is the probability you chose the car in the first place, and if you choose one curtain with a goat the host must reveal the other and the swap is guaranteed to work!)...
...this doesn't apply in DoND though because the reveals up to two-box are done fairly. (We believe, assume and fervently hope!
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The Monty Hall problem works perfectly if the host always offered the switch. Monty Hall himself conceeded that there was a 2/3 probability of winning the car with the switch if that was the case. The problem is that most times he didn't offer the switch. As a result you can't use simple mathematical probability, but a more intuitive solution based upon the host's behaviour. Monty talks about it here
FAQ
Posted: Wed Feb 11, 2009 10:06 am Author: DanJudge Post subject: Re: 10/02 Ash - Love Week Special
