[Retric]

> But instead of 3 doors, imagine 1000 doors. You pick 1. Monty shows you what's behind 998 that aren't the prize and asks you if you want to switch. By switching, your 1-of-1000 odds become 1-of-2.

No they should become 999 out of 1000. If your door is 1 in 1000 then the other door must have all other possibilities.

Also, the Monty haul problem is counter intuitive because it depends on the exact rules under which he operates. Suppose the classic 1 in 3 odds of a win, but an evil Monty haul where he only gives the option if you would win, now swapping is a guaranteed loss. Mathematically the answer is obvious when all the rules are guaranteed, but people’s internal heuristics don’t automatically trust rules as stated.