[dllthomas]

"If the host picks randomly, and the host picks a goat, and you switch, your odds of a car are 1/3, just as if you'd stuck. There's no point."

1/2, once you see the goat. One of 1/3, 2/3, and 1/2 beforehand, depending on what happens when Monty shows a car: whether you automatically win, automatically lose, or start over from the top, respectively.

[Cushman]

Right, to be clear, that's your total chance of walking away from the show with a car. Switching doesn't change it.

[dllthomas]

Right.