Here's why I say it's better to be a 1 boxer then a 2 boxer (although I'm sticking with my 1.49999 box solution outline on the first page as being the best).
Two boxers seem to think that their choices are something special that comes out of their perfectly free minds. However, minds are merely complex physical processes, and there's no physical reason why one couldn't anticipate one's reaction with a high degree of success given good enough measurement and analytic tools. So it is possible that this alien could know what you were going to pick before you picked it. After the box is laid yes, it would be optimal given a free choice to pick both, but you don't have a free choice, you have the culmination of your personality, experience, knowledge, biology, whatever determining your choices for you! Your free choice is actually a fiction, brought about in your mind!
The question really isn't what should one choose, but whether one person is a two boxer or a one boxer (or a 1.49999 boxer)?
If you are a one (or 1.4999 boxer) like me you get the money
if you're a two boxer you don't.