you have the choice of a million doors, with one having a prize in it. after you pick, but before you open it, i will open 999,998 of them that do not have the prize in them.
should you switch or stay with the door you picked?
@KitRedgrave I would just stay with the one I chose. If I have a 50/50 chance, it is really no dmmfferent from the 1/10000
@berserkx33 not so! the odds of you having chosen the correct door with no additional information is 1/1,000,000. if you chose the wrong door at first, then i remove the 999,998 wrong choices, leaving you with your choice and the door containing the prize, which would happen 999,999 times out of 1,000,000.
@KitRedgrave But it is from the standpoint that elimination of null options affect the amount of correct choices. It being a single correct choice from the 1000000 doors is not really affected by telling me that 999998 where empty, because it was already info I was informed before taking the decision. So it becomes 2 choices in 1000000, where it is still only a single correct one.
@berserkx33 the thing is i told you *which* doors were empty, and i will never open the door with the prize in it. so if you chose an incorrect door, i have no choice to open every door except the right one. and it's very very likely you did, so you'll see which door has the prize by the pigeonhole principle.
@KitRedgrave You are right on that. Considering the possibility of picking the correct one first, it really makes sense you would have only correct choice remaining as the other door. You got me. I was thinking along the lines of 2 1/1000000 choices, but it is as you said