That doesn't add up. Literally, 1/3 + 1/2 does not add up to 1. What third option exist that has a 1/6 chance of happening? The basic argument is. If you don't

That doesn't add up. Literally, 1/3 + 1/2 does not add up to 1. What third option exist that has a 1/6 chance of happening? The basic argument is. If you don't switch, you have 1/3 chance of winning. So if you do switch you have 1/3 chance of losing. Hence if you switch you have 2/3 chance of winning. How the door you switched too went from 1/3 chance to double is the hard part to explain. But it must be the case.