CORRECT.
I still havent found a good mathematical solution to this. most of them involve Bayes law (is that spelt right?). And i still dont understand why it ALWAYS works out to switching=2/3 chance of winning, and not switching=1/3 chance.
however, I've tried repetitions of this many times, and it ALWAYS works out that way...
i always see it as a 50/50 chance either way, since at that moment, you have a choice of two, and only one is a winner....weird...