At least for me, Monty Hall makes more intuitive sense to me when there are 10 doors than when there are 3, even though the benefit of the optimal strategy is quite small: there's a 1/10 chance you picked the car and shouldn't have switched, but a 9/10 chance that you can play the game again with 1:9 odds. Without doing the math, it makes sense to me that the optimal strategy actually does improve your odds.

Yet for some reason a 2/3 chance you can play the game with 50-50 odds is harder to accept - in particular I have to consider the 10 door case to understand why the 3 door case makes sense. I suspect it has to do with the psychology of loss aversion: a 1/3rd chance that you incorrectly switched "feels like" a reckless risk.