[matsemann]

My interpretation of the host opening a single door and asking if you want to switch is equally valid when you expand it to 100 doors.

[joshuamorton]

Sure, it could be that the host only opens one door, or it could be that he opens all but one door. In every case, however, it is better to switch. The all-but-one example is hyperbolic but still follows precisely the same mathematical rules. Your interpretation is valid, but so is the all-but-one example, and they all lead to the same result, it's just more obvious when you open nearly all the doors.