I almost believed you, until I ran through this version of the problem, and realized that, if I know Monty always opens the lower-numbered goat door, it actuall

I almost believed you, until I ran through this version of the problem, and realized that, if I know Monty always opens the lower-numbered goat door, it actually gives a completely different result. In particular, if I pick door 2, and Monty picks door 3, this _guarantees_ that the car is behind door 1 under your version of the problem. Meanwhile, if I pick door 2, and Monty picks door 1, it is now 50/50 whether I should switch or not, instead of 2/3 to 1/3. Try the math yourself and see. So the reason the "fake math" quits working is that you've changed the problem; if you do the math using the method at the link, for your version of the problem, you _rightly_ get different results, and I believe they are correct.