If you say that the doors are intially equally likely to hide the car and that Monty is equally likely to open either door when he has a choice you are being strictly neutral with regard to probability interpretation but you are already biased to solutions which require full probability assumptions host side Many people solve MHP without these assumptions at all they only assume that their own initial choice was random Please note that chooses randomly is ambiguous I suppose Rosenhouse who is not a probabilist or a statistician means completely randomly However chooses randomly biases the reader to the frequentist interpretation For the subjectivist the uncertainty is in the mind of the player not in the brain of the host