# 2 boxes of money, unknown money inside, one is twice the amount of the other [duplicate]

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?

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