Interesting variant of Monty Hall I was wondering how we could think about the following variant of the classic Monty hall theorem,

Suppose now that the host actually does not remember what is behind any of the doors, once you choose one of the three doors, he will open at random one of the other two doors. If he reveals the prize the show ends, if he does not reveal the prize, should you still switch doors?

I was trying to formulate it but I am just not sure if I am making correct assumptions.

For example,

say we choose door $A$, then the probability that he opens door $B$ is equal to the probability he chooses door $C$ is equal to $0.5$.

The probability that the prize is behind door A, B and C is 1/3

the probability that Monty ends up opening any given door is also $1/3$

So should one just condition on something else now?

Looking forward to hearing any opinions on this,

Thanks
Suppose you choose door 1. And Monty reveals door 2, but Monty has no prior information.

Then the conditional probability that the prize is in fact behind door one, given that it is not behind door 2 is $50\%$ 

If Money has no information, then not enough information gained by the reveal, to justify switching.
There is a long discussion of this on The Straight Dope by Cecil Adams. I will add the link here:

http://www.straightdope.com/columns/read/916/on-lets-make-a-deal-you-pick-door-1-monty-opens-door-2-no-prize-do-you-stay-with-door-1-or-switch-to-3