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 Originally Posted by MadMojoMonkey
Even if it's chosen at random, your odds are still the same as the original choice, so you can never be worse off than you were by switching.
Yeah but the answer to your initial question is different. If it is opened at random and is empty then your EV is the same whether you switch or not, so it doesn't matter.
3 cases:
1 you chose the $300, opened empty box
2 you chose empty box, opened empty box
3 you chose empty box, opened $300 box
Since #3 didn't happen, it's between #1 and #2 so 50/50 and your EV is $150.
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