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You are one of many who don't get it.
Don't take it personal - many smart people don't get it.
Maybe you just don't want to believe there can be a 2/3 chance.
Something makes you read, yet refute, the truth.
You throw in an assumption "the only way to have a 2/3s chance is if there is a possibility for the host to show you the car"...
What is that based on?
The point is that the host shows you where the car is not, while he knows where it is.
His choice of which door to open is NOT random.
That changes the odds.
If you choose A and the car is behind B he'll show C. Swap and you get a car.
If you choose A and the car is behind C he'll show B. Swap and you get a car.
Only if the car is behind door A (1/3 chance) can he choose which one to open as none has a car. If you swap you don't get the car.
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2011 Honda Insight + HID, LEDs, tiny PV panel, extra brake pad return springs, neutral wheel alignment, 44/42 PSI (air), PHEV light (inop), tightened wheel nut.
  lifetime FE over 0.2 Gmeter or 0.13 Mmile.
For confirmation go to people just like you.
For education go to people unlike yourself.
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