> Do you just mean the subset of "he chose randomly and happened to draw a goat out of one of the two you did not choose"? In which case switching isn't benefic

> Do you just mean the subset of "he chose randomly and happened to draw a goat out of one of the two you did not choose"? In which case switching isn't beneficial because you no longer are also capturing the cases that would otherwise be the "he chose randomly and opened the one with the car that you did not choose" that are included in the original "switch or not" decision because he always goes to a goat? He chooses randomly from the doors you did not choose, and draws a goat. When offered the choice to switch to the third door, it offers you no benefit. Both are equally likely to contain the car.