> By switching, your 1-of-1000 odds become 1-of-2.
It's not 50/50. That means you had a 50% chance to get the door correct on the first guess out of 1000. By showing the non-winning doors, the odds collapse into the remaining door. You had a 1/1000 chance of getting it right the first time, after the reveal all 998 are now assigned to the remaining door.
It's not 50/50. That means you had a 50% chance to get the door correct on the first guess out of 1000. By showing the non-winning doors, the odds collapse into the remaining door. You had a 1/1000 chance of getting it right the first time, after the reveal all 998 are now assigned to the remaining door.