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Comment by moffkalast | Hacker News Reader

Any explanation that doesn't involve scaling up the number of doors to a arbitrarily large amount where the probability becomes obvious is really lacking if you ask me. The only reason this is so confusing in the first place is because it's only 3 doors.

With an infinite amount of doors, the chance of picking the right one at first is zero. When the host opens all doors except one other, it's almost certain that it's the door with the car.

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It’s good for the aha intuition moment for some people. It’s the thing that made me get it as a kid. There’s something unsatisfying about it though. You can have 100 doors, and open 98 to leave the initial guess and 1 more. But this is scaling up the rule as “all but one”. I don’t see an obvious reason that the rule shouldn’t scale up as “open one more door”. Then you have 99 closed and 1 open and the result isn’t nearly as obvious, even though switching is the better move.

Yeah I thought about that, both +1 door and infinity-1 door options are both equally unfaithful to the original I suppose. Keeping the 50% door opening ratio would make more direct sense if you wanted to scale it up for other reasons, but isn't nearly as clear in intuitively showing the concept.

I agree that it feels weird at first, but thinking about it this way fixed that for me:

The whole reason for the apparent paradox is having the "50/50" choice at the end. You either keep the door you picked, or swap with the other door, so it feels like no advantage.

If they only revealed a single door, then you would have multiple doors to swap to, so you wouldn't have the "50/50" choice. The only way to keep the "50/50" choice at the end is to reveal all but one door and give you the option to switch to it.

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