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This problem causes a lot of Internet arguments.
This poll is based on whether the reader assumes the problem is based on conditional statistics or unconditional statistics. If read in an unconditional manner (it appears that most read it this way), the answer IS 1/2 or that it doesn't matter if you switch or not. Conditional statistics problems are based upon a completely different set of mathematics and prove that the answer is that you should switch because of the 2/3 chance of winning.
So basically the answer is founded on which way you look at the problem. Saying that the answer is 2/3 for switching is true, but the answer is also "doesn't matter" or 1/2 if you consider it unconditional.
Wikipedia: "According to Morgan et al. (1991) "The distinction between the conditional and unconditional situations here seems to confound many." That is, they, and some others, interpret the usual wording of the problem statement as asking about the conditional probability of winning given which door is opened by the host, as opposed to the overall or unconditional probability. These are mathematically different questions and can have different answers depending on how the host chooses which door to open when the player's initial choice is the car (Morgan et al., 1991; Gillman 1992). For example, if the host opens Door 3 whenever possible then the probability of winning by switching for players initially choosing Door 1 is 2/3 overall, but only 1/2 if the host opens Door 3. In its usual form the problem statement does not specify this detail of the host's behavior, nor make clear whether a conditional or an unconditional answer is required, making the answer that switching wins the car with probability 2/3 equally vague. Many commonly presented solutions address the unconditional probability, ignoring which door was chosen by the player and which door opened by the host; Morgan et al. call these "false solutions" (1991). Others, such as Behrends (2008), conclude that "One must consider the matter with care to see that both analyses are correct.""
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"A Darwinian attacks his theory, seeking to find flaws. An ID believer defends his theory, seeking to conceal flaws." -Roger Ebert
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