The thing that makes this old chestnut confusing and interesting is the decision on whether the odds are based on two individual events or a combined event.
It's in a similar being to the odds of tossing two heads in a row, is it 1/2 + 1/2 or 1/2 X 1/2...if you understand the maths behind that then the Monty Hall Problem should be less confusing albeit with one additional choice.