You only remove games as moot when Monty reveals a car, which can only happen when you haven't initially selected the car. Therefore, no games are removed as m

You only remove games as moot when Monty reveals a car, which can only happen when you haven't initially selected the car. Therefore, no games are removed as moot when you have initially selected a car, and 50% of games are removed as moot when you have initially selected a goat. So it ends in a coin toss whether you switch or not. The 2/3 to 1/3 split only happens when Monty removes a goat using privileged information.