For a thorough understanding you can do some reading about the topic of Bayes theorem and some of the famous discussions on the Monty Hall problem also know as the prisoners dilemma.  It important to point out a few key ideas about this problem.  First, the problem as stated involves 3 doors not 2.  The car is behind one of the three doors.  Second, if you simulate all the possibilities you will see that the 2/3 of the time you win and 1/3 of the time you loose by switching.  At no time was there a choice between 2 doors.  In being asked if you want to switch, you forget momentarily the conditions of the experiment.  Remember to use Bayes rule here where you are given ptior information.  That is, the goat is in door 3 and there are still 3 doors not 2.
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