OK, smarty-pants, what's the best move?

[MadMojoMonkey]

You had a 3/1 shot the first time. now its 2/1.

It is not 50/50 on the 2nd choice; it's 33/67. This is a common mis-assessment of the effect of the revealed information.

In this case, the revealed box is ALWAYS empty. There is 0% chance the revealed box contains the money.

And in the example of 300 boxes, you go from 1/300 to 299/300 chance.

This is correct. You do NOT go to 50/50 on the 2nd choice.