I don t want to make a meal of the door identity question I just want any arguments which are presented as logical arguments to be correct Devlin pretends to present a logical argument but gives no justification for his last step Some people thought it was obvious some people thought it wasn t obvious When Devlin was informed of this he suddenly began to doubt himself In order to justify Devlin s last step you need to explain why the question of which particular door he opens door 2 or 3 is irrelevant to the question of whether or not the car is behind door 1 You can say it is obvious or you can write out the argument if you think it is not obvious If you say something is obvious but you are challenged as Devlin was you are obliged to fill in the details This is not pedantry After all by opening door 2 or door 3 he does dramatically change the chance the car is behind door 2 or behind door 3 Some readers are uneasy here Devlin was uneasy Nijdam screams murder The more you put in the more you get out I don t think it s a big deal But let s at least be clear as far as the logic is concerned If you want to argue that switching gives the car with probability 2 3 then you have a very easy job The simple solution Switching gives the car if and only if your initial choice is a goat probability 2 3 Combined doors it s as if you are offered the option of exchanging door 1 for doors 2 3 1 3 versus 2 3 Very intuitive completely true If you want to argue that switching gives the car with probability 2 3 given you chose door 1 and the host opened door 3 you have a little more work to do You ll need somewhere to use your natural assumption that the host is equally likely to open either door if he has a choice For instance you could do the simple solution first and then say that by symmetry the conditional probabilities are the same I think the whole idea that some solutions are correct and others incorrect is a waste of time Every solution is correct in its own terms Let s just be clear about this Secondly like it or not everyone who is trained in elementary probability is going to figure out the conditional probability of finding a car behind door 2 given the player chose door 1 and the host opened door 3 Like it or not the article is going to contain a heap of material on conditional solutions On wikipedia we are not supposed to make original syntheses but my job as a mathematician outside of wikipedia is to do this I like to show people the synergy between simple and conditional the easy bridges the smart ways to avoid doing blind computations I would also like to counter the Morgan et al propaganda