An easy way to word this exact problem in a way that makes clear the reason you should always change your choice is: I have 52 playing cards. I know which one

An easy way to word this exact problem in a way that makes clear the reason you should always change your choice is: I have 52 playing cards. I know which one is the Ace of Spades. Point to one of the cards and leave your finger on it. Okay, without telling you whether you are right or not, I'm going to remove every card, leaving only yours and one other on the table, that is the right card if the one you picked is not, or an indifferent card if your choice was right. Do you wish to choose the card I left on the table, or do you still think your 1/52 choice was correct? Notice that I followed the exact rules of the game, but changed the wording and used a lot more "doors." There was a 1/52 chance you would pick the right card, and even after I remove all but one of the remaining cards, it is still a 1/52 chance you originally picked the right card, and a 51/52 chance that the one I left behind is the right card. Now just make it 3 cards, and use the traditional script, performing the exact same steps, and you'll understand why you should always change from your original choice.