4 ms·
I think, canonically, Monty always knows where the prize is, and will always eliminate all doors except for one, and will never eliminate a door with the prize,
by LargeWu 2y ago
I think, canonically, Monty always knows where the prize is, and will always eliminate all doors except for one, and will never eliminate a door with the prize, and will always give you a choice to switch. There's no room for Monty's motivation.
- btilly 2y agoThose assumptions are required for the usual explanation. But they are very rarely stated. And so the usual explanation is not logically solid. You can't just sneak in the assumptions. You have to state them somewhere.
- 8note 2y agothe assumption is told to you in that the game is expected to continue after monty opens a door. if he could open the prize door, the game would describe what happens when he does that
- btilly 2y agoNo. That condition holds in all three of the scenarios that I stated. And yet you have 3 different answers. Switching 2/3 win, 1/2 win, and 0/1 win respectively. You specifically need information that we haven't been given about the counterfactuals. What might Monty have done in other scenarios that we have not yet observed? We don't know. And we're not actually told. That makes that an implicit assumption that wasn't specified.
- LargeWu 2y agowell, they are part of the original, canonical problem. it's not the original problem's fault if re-tellers omit key information.
- foxglacier 2y agoThey're not. It says he "opens another door, say No. 3, which has a goat". That could mean he deliberately chose a door with a goat or he chose one by some unstated process and it happened to have a goat by chance. It says he "knows what's behind the doors" but that statement means nothing because it doesn't say how he uses that knowledge, if at all. It's full of language ambiguity.