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OK, so I pick a door, Monty randomly reveals a goat. Your claim is that this information should make me increase the odds that my initial pick was a car. That s
by furyofantares 6y ago
OK, so I pick a door, Monty randomly reveals a goat. Your claim is that this information should make me increase the odds that my initial pick was a car. That sounds right. In the normal Monty problem, Monty doesn't give me any information about my original pick, just about the remaining door.
Alright just working through your logic here. Let's say I pick the first door always. I'll write out all the possible configurationss with both possibilities for Monty.
CGG > Monty reveals mid (Goat)
CGG > Monty reveals right (Goat)
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GCG > Monty reveals mid (Car)
GCG > Monty reveals right (Goat)
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GGC > Monty reveals mid (Goat)
GGC > Monty reveals right (Car)
So there's 4 worlds where Monty reveals a goat. In two of them, I picked a car initially. In the other two, I get a car by switching.
My prior post is mistaken -- thank you!
- basch 6y agoThere are only three situations. Initial pick in parentheses. (C)GG - switch and lose (G)CG - switch and win (G)GC - switch and win
- furyofantares 6y agoBy the time you have the decision, yeah, that's true. There are other situations where the game is over before you get a decision. Both GCG and GGC are eliminated half the time before you get to make a decision. But CGG is never eliminated before you get to make a decision. Once you're making a decision and the game isn't already over, you can use this information -- that the game didn't end -- to assign a 50% chance of being in CGG, and 25% of each of the other two.