Someone shows you two boxes and tells you that one of these boxes contains twice as much money as the other, but he does not tell you which one it is. He then lets you choose one of the boxes and opens it. It turns out to contain $10. Now he gives you the opportunity to choose the other box instead (and thus give up the ten dollars from the first box) because the second box could contain twice as much (i.e., $20).

The question: Should you choose the second box, or should you stick with your first choice to maximize the expected amount of money?

A hint : If you have $10 and could double it with a 50% chance or halve it with a 50% chance, you would expect an average of ½ × $20 + ½ × $5 = $12.50 (so you would expect to gain $2.50)!

The solution: Click here!