Because it really centers on the initial premise: Monty will always open a goat door after your choice, no matter what. So, you make a totally random choice. T

Because it really centers on the initial premise: Monty will always open a goat door after your choice, no matter what. So, you make a totally random choice. That choice must be 1/3 right, right? Now the thing that you already knew would definitely happen happens: Monty opens a goat door. How can your odds suddenly jump to 1/2? Are you saying every single time you play the game, you always have a 1/2 chance of getting it right first time?