Yes. If the host's algorithm is to pick a door randomly, then your odds change. In this other scenario, your odds do not improve by switching. If the problem d

Yes. If the host's algorithm is to pick a door randomly, then your odds change. In this other scenario, your odds do not improve by switching. If the problem does not state what the host's algorithm is, and you have no knowledge of the host's algorithm (example: you have never seen the TV show before), then the logical action is to assume the host chooses a door to reveal randomly.