Another way to look at it... With your initial pick, there is a 1/3 chance you were right, and a 2/3 chance you were wrong. If you were right initially, the correct move is to stay where you are. If you were wrong initially, the right move is to switch to the correct box after the host removes one of the wrong ones. So 1 time out of 3, the right move is to pick a box and stay there. The other 2 times, the right move is to switch. So by the odds, you should always switch.







