Instead of asking yourself "should I switch?", ask yourself "At the time of making my first guess, would I have bet that it got the car (1/3) or a goat (2/3)?"

Instead of asking yourself "should I switch?", ask yourself "At the time of making my first guess, would I have bet that it got the car (1/3) or a goat (2/3)?" Obviously the answer is that your first guess is more likely to have been a goat. So if you had to bet, you'd have bet on the car being in one of the ones you didn't choose. After the host reveals a goat, it's no longer "one of the ones you didn't choose", but rather "the one you didn't choose" (since the host has taken the other out of consideration). So the choice is easy now (as is the probability calculation).