I have to say that I am totally amazed by gnu's inability to grasp the essence of this problem.

I know from his postings on Mudcat over the years that he is intelligent, and has a well developed grasp of maths and engineering, so it is bizarre that an elementary probability problem such as the Monty Hall problem continues to elude him.

Then again, I got to grips with probability theory at a very young age, and since doing so have been aware that the vast majority of people have difficulty in reconciling the mathematical facts with their initial intuitive assessment.

You can test this by asking the average person, "How many people would you have to assemble in one room to make it more likely than not that at least two of them share the same birthday ?"

Once you understand factorials, the answer is devastatingly simple, but approached intuitively, the solution seems incredible.

( The answer is 23 btw)