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Suppose, I have two boxes. A host is telling me to pick one. I see the money inside of this one - say 100 \$. Now, I need to decide if I want to swap, given the information that the other box has twice less or more money - say 50\$ or 200\$. Thereofre, expected value of the second box is clearly 125 \$.

Question 1: Does this apply that I need to always swap?

Question 2: If I repeat the experiment 1000 times, where the money inside of the boxes is some random $N>0$, does it matter if I swap? Does it have to do something with the law of large numbers?

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  • $\begingroup$ Is the amount of money in the other box always double/half the amount of money in your box? $\endgroup$
    – Dave
    Mar 20 at 12:41
  • $\begingroup$ Yet, this is always the case $\endgroup$
    – II K
    Mar 20 at 13:31