Comment on Jigsaw Trolley Problem
TauZero@mander.xyz 1 week agoKnowing that the ball was gold gives you Bayesian knowledge about the boxes behind the door, since the prior probability of the host pulling a gold ball from a 6-gold door is different than from the 3/3 door. So you have to multiply Monty Hall probabilities and Bayesian probabilities together.
That assumes the host pulled a ball at random, of course, and not a deliberately gold ball.
apotheotic@beehaw.org 1 week ago
Hmm, you’re quite right. My intuition is that the Bayesian portion would exactly offset the Monty hall portion. I think, at a glance, Bayes would give door 1 a 2/3 probability of having 6 gold, but Monty Hall would give door 2 the same probability, so we can effectively cancel these out and just consider a raw probability
You either have 5 gold or 2 gold 3 silver behind door 1, and 6 gold or 3 and 3 behind door 2, which gives door 2 a very slight edge. Does that check out?
TauZero@mander.xyz 1 week ago
Yes! Cancels out, leaving only a very slight edge on door 2. All that work for only… 2.77% edge over picking at random. What a troll problem, huh?
apotheotic@beehaw.org 1 week ago
Heh what a trolly problem indeed
sem@lemmy.blahaj.zone 1 week ago
Speaking of trolls I assume the madman has perfect knowledge of the layout, hence did not pick a ball out at random.