The Monty Hall problem.

[Tiberius]

Did you read what I wrote? In the ACTUAL game no one switched. The apparent paradox has been scientifically tested, but the doors were switched and yes, the switchers did win a disproportionate number of times. What I am saying is that this would never happen in a REAL game where the contestants were completely unaware of the Monty Hall problem. Do you not see something else going on here? Can anyone cite a similar situation where the seeming anomaly could be proven in its 'natural' form?

It is completely irrelevant if players are aware of the Monty Hall problem or not. Even if all contestants refuse to switch, they would on average win 1/3 of the time. Since a switch negates the outcome (i.e. switching from a winning door will always result in a lose, and vice-versa), it is a simple calculation to show that if people switched, they would have won 2/3 of the time.

In other words, if all the people switched rather than stayed with their original choice, the 1/3 who originally won would have lost, and the 2/3 who would have originally lost would have won.

But it doesn't tell you if they would have won 66% of the time if they had switched, because almost no one switched.

It actually does tell you that, because switching negates the outcome absolutely.