Suppose there were 100 doors... and I allowed you to choose one of them, what's the odds you picked the right door? 1%

What's the odds that the prize is behind one of the other 99? 99%

So, if I gave you a choice of switching your choice from Door 1, and allowing you to pick all 99 of the other doors, which would you take? Obviously, the 99.

The torture is that I first open 98 of the goat doors (because I know where the prize is), leaving two... The one you picked, and the one remaining. None of that changes the fact that you're initial guess was only 1% chance of guessing right.

Therefore, switching from your initial choice at the last minute is effectively the same as changing to all 99 doors.

Occassionally this strategy would fail, but only about 1% of the time, since that was the likelihood you chose correctly to begin with.

Same is true with three doors. Your chance of picking correctly initially is 1/3rd... If you were allowed to switch to the other two doors, you'd have a 2/3rds chance of winning.

At least, that's how it was initially explained to me, and it seems pretty reasonable.

Trek