Much of the controversy around this problem revolves around whether this situation is isomorphic to the classic Monty Hall problem. As Kuroneko rightly says, even leaving psychology out of the problem, the problem is still ill-specified. The odds change even if the Emperor has a bias towards the left for releasing lions. (I'll get to that later.)
In the classic Monty Hall problem, the Emperor (host) always allows the switch and always reveals a lion (goat) behind one of the unchosen doors. Furthermore, if he has a choice of lions, he shows no preference in revealing either. In this case, changing always is the winning strategy as you only lose if you initially choose the winning door, whereas for staying, you only win if you initially choose the winning door.
If we change the behavior of the Emperor, such that he has a bias in revealing the leftmost lions, then which door he chooses to reveal is additional piece of information. If he has a 100% bias towards leftmost lions, then if the Emperor opens door #3, switching always wins (because the car is behind #2 — that's why he didn't open it!); if the Emperor opens #2, then either the lion is behind your door or its behind the other door. Your chances of winning is one half either way. The proportions change when the bias is less than absolute, of course.
If the Emperor chooses randomly regardless of his knowledge of the situation, then your probability of winning is one half if you switch, or so the current consensus concludes.
As above, the psychology of the Emperor matters, but only insofar as it effects the rules of the game. If the Emperor only allows a switch when you've guessed wrong, then switching guarantees a win; if the Emperor only allows switching when you've guessed right, then switching always loses. It depends on whether the Emperor is a fucking bastard.
Kuroneko is right in that, while the problem is ill-specified, for most of these choices of the exact game rules, switching is no worse than staying, thus a decision would lead you to switching. That said, however, I must remark that the prior probability of the bastard Emperor is quite high.
In the classic Monty Hall problem, the Emperor (host) always allows the switch and always reveals a lion (goat) behind one of the unchosen doors. Furthermore, if he has a choice of lions, he shows no preference in revealing either. In this case, changing always is the winning strategy as you only lose if you initially choose the winning door, whereas for staying, you only win if you initially choose the winning door.
If we change the behavior of the Emperor, such that he has a bias in revealing the leftmost lions, then which door he chooses to reveal is additional piece of information. If he has a 100% bias towards leftmost lions, then if the Emperor opens door #3, switching always wins (because the car is behind #2 — that's why he didn't open it!); if the Emperor opens #2, then either the lion is behind your door or its behind the other door. Your chances of winning is one half either way. The proportions change when the bias is less than absolute, of course.
If the Emperor chooses randomly regardless of his knowledge of the situation, then your probability of winning is one half if you switch, or so the current consensus concludes.
As above, the psychology of the Emperor matters, but only insofar as it effects the rules of the game. If the Emperor only allows a switch when you've guessed wrong, then switching guarantees a win; if the Emperor only allows switching when you've guessed right, then switching always loses. It depends on whether the Emperor is a fucking bastard.
Kuroneko is right in that, while the problem is ill-specified, for most of these choices of the exact game rules, switching is no worse than staying, thus a decision would lead you to switching. That said, however, I must remark that the prior probability of the bastard Emperor is quite high.
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