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Members
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Join Date: Oct 2002
Posts: 8,059
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Into two boxes I have placed a sum of money. The amount in one box is exactly twice what is in the other. I allow you to look into one box and there is $100 in there. This means that there must be either $50 or $200 in the other box. You are permitted to either keep the $100 from the box you looked in or switch.
If you switch, you will either lose $50 or gain $100. In other words, you can bet $50 to win $100 and it is an even bet. Betting $50 to win $100 is extraordinary. Lose $50, gain $100, lose $50, gain $100. Makes sense to switch. On the other hand, switching can't make sense no matter which envelope you choose. Otherwise, you would just choose the other envelope and not switch. But the logic above says it would be better to switch. Does it make sense to switch?
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