Assume I flip a fair coin n times until it comes up Heads. Now I take two large boxes, in one of which I place $3^n (3 to the power of n dollars) and in the other I place $3^(n+1) (3 to the power of n+1 dollars). I then give you the two closed seemingly identical boxes and allow you to open one box and count the money. At this point you can either take the money in the box you chose or take the unknown amount of money in the other box. Is there a strategy which you may employ in order to maximize your expected gain? For example, if you open a box and see $3 you should always switch because there will definitely be $9 in the other box. However, if you open a box and see $9, switching might get you $3 or might get you $27.