Sample space of the Monty Hall problem I have read two sources where the outcomes of the Monty Hall problem are triples of the form: ( _initial guess_ , _the curtain Monty opens_ , _the curtain where the car is_ ) However, I think it should be: ( _initial guess_ , _the curtain Monty opens_ , _switched curtain_ , _the curtain where the car is_ ) Is the sample space consisting of these outcomes wrong? It seems that it is because I am getting that it doesn't matter if one switches curtains.

Your two statements are equivalent as the initial guess and the curtain (or door) Monty opens determine the remaining curtain (or door) in the standard version of the problem.

But the real issue is that not all the possible events you would list are of equal probability: if your initial guess is the same as the car's location then Monty has a choice of two; if your initial guess is _not_ the same as the car's location then Monty does not have a choice, at least in the standard version of the problem.

The events where Monty has had to make a choice have half the probability of those where he does not, assuming he has made a random choice.