I know this one! It’s conditional probability. You have 33.33% of selecting right the first pick. When you are shown an empty box of one of the ones you didn’t pick, you add the value of that box to your next pick, for 66.67% chance the second box will have the money. Your first choice retains the 33.33% the entire time. So you favorably increase your odds to switch boxes.I like this paradox: A gamesman shows you three covered boxes. Two are empty and one contains a million dollars. You can keep the contents of the box you pick. You make your pick. Now you know that at least one of the other boxes is empty. The gamesman shows you an empty box. Now you are left with an empty box and one with a million dollars. The gamesman now asks you if you would like to switch boxes. Here most people would say that it makes no difference if the player switches boxes because the odds are even. However you would be wrong. It would be better to switch boxes since that would improve your odds. Try to figure it out.


