I definitely don't think it is the only point of confusion, but I definitely think it is a big one. We discussed the problem in my discrete math class and the professor had stated the problem without the constraint. Many in the class, being far too young to even know who Monty Hall is, were confused, and several had their 'aha!' moment once that constraint was mentioned.
> According to Wikipedia, even Paul Erdős remained unconvinced until he was shown a computer simulation.
Interestingly, coding up my own simulation took me from understanding the problem to grokking it. I'd definitely suggest anyone who has programming ability but doesn't grok the problem to write up a simulation.
If anyone reading this uses this example in a class, or is thinking of doing so, perhaps it could be set up as an experiment to see how much the phrasing influences the result?
> According to Wikipedia, even Paul Erdős remained unconvinced until he was shown a computer simulation.
Interestingly, coding up my own simulation took me from understanding the problem to grokking it. I'd definitely suggest anyone who has programming ability but doesn't grok the problem to write up a simulation.