April  UTC   Here is a little something that I came up with myself  Let the boxes equal the letters AV Let the prize that you want to win be behind box A It doesnt matter which box the prize you want to win is in also assume biggest prize Now if you pick box A then the probability of getting through to the end of the game with the prize you want still in the game is certain This occurs is  cases   If you dont pick box A then the probability of you getting to the end of the game without taking out the prize you want is      This can be rewritten as    There is one very important thing to note here In the sum you dont multiply by  because you dont need to eliminate all of the boxes just all but one plus yours This means that instead of dividing by  you must divide by  which is why there is a  on the top  The sum works out with a value of    This occurs is  cases so     Therefore you are twice as likely to be on the path where you didnt pick the prize you wanted ie grand first which means that you should swap Now there may be a flaw in my logic and if there is then please point it out