> Removing the host's freedom to choose a non-winning door (and effectively help the player) changes the math. As it does removing the host's ability to choose

> Removing the host's freedom to choose a non-winning door (and effectively help the player) changes the math. As it does removing the host's ability to choose a non-winning door in the variant where "the host had just picked at random from the two doors, and it happened to show a goat". That doesn't work the same either because it's not the same game.