It seems that as was the case when Marilyn vos Savant published the correct answer in the New York Times back in 1990, my entry is causing some (seemingly) intelligent people to blunder. (I have to be somewhat polite here, as one of the blunderers is my hosting provider.)
The rationale in the post below is pretty straightforward, as highlighted by the friend who originally sought my help:
"Perfect ... even I understand that!"
Nonetheless, it seems some people need some further evidence. What better way to help than via the powers of Excel. Here's a spreadsheet that takes you through the logic behind both the no switching option and the switching option. Each row in each of the sheets represents a unique experiment, with each element that is up to chance being driven by an independent random number.
In the no switching option, the only things that are random are the prize-winning door and the door originally chosen by the contestant. In the switching option, both of these elements are still random, as is the door that Monty opens, although this is sometimes forced.
The spreadsheet contains 50 rows of experiments, although you can copy a row down as far as your computer's memory will allow to see where your odds settle. Using all 65,536 rows (65,532 experiments of each type), I recorded a 33.15% win rate for games in which I stuck, and a 66.72% rate for games in which I switched.
