Talk:Monty Hall problem/NotMorgan

=Which problems does Morgan's solution apply to?=

The following rules apply throughout

The host always offers the swap. The host always opens an unchosen door to reveal a goat.

The situation described by Morgan is: The player has chosen door 1, the host has then revealed a goat behind door 3.

Morgan's solution is that the player wins on switching with a probability of 1/(1+q) where q is the probability that the host will open door 3 if the car is behind door 1.

For the moment at least we will take it that Morgan do not claim that their solution applies to any other case.

In all cases below we take the probability of winning by switching to be the fraction of times that the player wins the car if they switch if the game is repeated with the stated conditions.

=The player chooses door 1==

The host has not yet opened a door
This is the unconditional problem.

'''Morgan's solution does not apply. The probability of winning by switching is always 2/3'''

2.2.1 The host always has the same preference for door 3 when the car is behind door 1
In this case we repeat the experiment with the car being randomly placed but the host always having exactly the same preference for opening door 3 when the car is behind door 1.

'''Morgan's solution does apply. The probability of winning by switching is 1/(1+q)'''

2.2.2 The host has a random preference for door 3
In this case we repeat the experiment with the car being randomly placed but the host having a random preference for opening door 3 when the car is behind door 1.

Morgan's solution of 1/(1+q) does not apply.

2.3.1 The host always has the same preference for door 3 when the car is behind door 1
In this case we repeat the experiment with the car not being randomly placed but the host always having exactly the same preference for opening door 3 when the car is behind door 1.

'''Morgan's solution does not apply. The probability of winning by switching is dependent on the probability that the car was placed behind door 1'''

2.3.3 The host has a random preference for door 3
In this case we repeat the experiment with the car not being randomly placed but the host having a random preference for opening door 3 when the car is behind door 1.

'''Morgan's solution does not apply. The probability of winning by switching is dependent on the probability that the car was placed behind door 1'''