Say that you are told that one of the boxes contain $a and the other contains twice of that $2a. Consider the example where you open a box and find $100 in it. Now you aren't sure whether this is equal to 2a or a (i.e if you picked the $a box then the other contains $200, or if you picked the $2a box then the other contains only $50.).

The expected value is $5/4a if you decide to switch ($125).

Say that you are told that one of the boxes contain $a and the other contains twice of that $2a. Consider the example where you open a box and find $100 in it. Now you aren't sure whether this is equal to 2a or a (i.e if you picked the $a box then the other contains $200, or if you picked the $2a box then the other contains only $50.).

The expected value is $5/4a if you decide to switch ($125).