You are on a game show. The host says he has hidden money under two cups,
one amount being double the other one. You pick one at random, he turns it
over, it's $100. He gives you a second chance (that he would do so was
determined before the game and not dependent on which cup you'd turn over):
You can switch, or take the $100.

You figure: If I switch, I will either get $50 or $200 with equal
probability. Expected return is thus $50*1/2 + $200*1/2 = $125, which is
larger than the $100 I'd spend to "play" this second game. Looks like a good
deal. Is it?

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