> Suppose there are a million doors,... This is a common way to explain it, but I always found it less intuitive; not sure why. My go to thought experiment al

> Suppose there are a million doors,... This is a common way to explain it, but I always found it less intuitive; not sure why. My go to thought experiment along these lines is rather this: Adjust the game to where both you and your friend are playing at the same time. You _NEVER_ switch doors, and your friend _ALWAYS_ does, when given the choice by Monty. Since you never switch, no matter what Monty does you know you're going to win 1/3 of the time. Since you both know Monty is always going to show a "goat" door, ONE of you must win, so your friend MUST WIN ALL THE TIMES YOU DO NOT. Since you win 1/3 of the time, the wins "left" is 2/3 of the time.