The problem can be generalized to four doors as follows. Let one door conceal the car, with goats behind the other three. Pick a door d1 . Then the host will open one of the nonwinners and give you the option of switching. Call your new choice (which could be the same as all if you don't switch) d2. The host will then open a second nonwinner, and you must decide for choice d3 ifyou want to stick to d2 or switch to the remaining door. The probabilities of winning are shown below for the four possible strategies. d1 d2 d3 winning probability pick stick stick 2/8 pick switch stick 3/8 pick stick switch 6/8 pick switch switch 5/8