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Silentiea@lemm.ee 7 months agoThe important thing is that the host will always show you a goat, meaning the only way the other door has the car is if you just so happened to pick it the first time.
Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?
Iamdanno@lemmynsfw.com 7 months ago
The host’s intentions are irrelevant. Numerically, there are only two choices. That makes it fifty-fifty.
Silentiea@lemm.ee 7 months ago
You think that even in the hundred-door case? Test it. Hell, even test it in the 3 door case. It is empirically not 50%.
If the host had an even chance to show you either door, you’d be right, but since the host always shows you a goat, the two events (picking a door and choosing whether to switch) are no longer independent, since if you pick a goat it forces the host to pick the other goat.