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But Monty's only being helpful if I guessed wrong. If it actually was behind door #1, Monty's trying to entice me into picking a goat, and basically being a di

But Monty's only being helpful if I guessed wrong. If it actually was behind door #1, Monty's trying to entice me into picking a goat, and basically being a dick. This is also assuming he could've just opened door #1 right away if it was the correct answer and obviated this whole mess. Monty's free will (an unknown) underpins this entire argument- what choices does he have, and why does he even make me choose a door instead of giving me the car (and the goats) outright? Maybe from a statistical point of view it's better to have Monty pull this shtick, but something that's helpful 2/3 of the time and harmful 1/3 of the time doesn't make the cutoff for helpful.

ModernMech 8y ago
I feel like you're still missing something. The probabilities come out of a table. It's just math. There's no need to bring "free will" into the explanation.
- username90 8y ago
  No, it is you who are wrong. You can't write down a table if you don't have a proper explanation of the possible event chains, and in this case you don't. Instead when people write down these event chain they add information that isn't there and then think they actually solved the problem. But all you really know is that this one time the host opened a door with a goat, you have no idea if the host always does this since the problem statement doesn't actually say it outright. It might be a good assumption to make, but it isn't in the description so it isn't a mathematically rigorous answer.
  - ModernMech 8y ago
    But once you do have a proper explanation of the possible event chains, free will still doesn't play a part of it. It's a game with rules. You seem to be keyed in on some aspect of the rules being unclear, but even with the rules perfectly clear or not clear at all, the probabilities are the same regardless of the psychological state of the contestant.
indigodaddy 8y ago
But the odds of you guessing wrong are 2/3, so you should switch.

ModernMech 8y ago

I feel like you're still missing something. The probabilities come out of a table. It's just math. There's no need to bring "free will" into the explanation.

username90 8y ago
No, it is you who are wrong. You can't write down a table if you don't have a proper explanation of the possible event chains, and in this case you don't. Instead when people write down these event chain they add information that isn't there and then think they actually solved the problem. But all you really know is that this one time the host opened a door with a goat, you have no idea if the host always does this since the problem statement doesn't actually say it outright. It might be a good assumption to make, but it isn't in the description so it isn't a mathematically rigorous answer.
- ModernMech 8y ago
  But once you do have a proper explanation of the possible event chains, free will still doesn't play a part of it. It's a game with rules. You seem to be keyed in on some aspect of the rules being unclear, but even with the rules perfectly clear or not clear at all, the probabilities are the same regardless of the psychological state of the contestant.

indigodaddy 8y ago

But the odds of you guessing wrong are 2/3, so you should switch.