re: Let's Find Out How Smart You Baws Are

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why would one of the two have better odds than the other?
the only difference between the two is that one is in my hand and one is on the table.

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The probability changes because he reveals one of the cups. This gives you more information.

There is a 1/3 chance of picking correctly. If you pick correctly and switch, you get no money.

There is a 2/3 chance of picking incorrectly. If you pick incorrectly and switch, you always get the money. This is because the dealer always reveals an empty shell, so the remaining shell must contain the money.

So, the probability of getting paid is the same as
the probability of choosing the wrong shell, which is 2/3.