If you switch "you" get to "open" two doors in fact, not one. It's just that Monty picks which one for you. And since your choice is random, you might as well l

If you switch "you" get to "open" two doors in fact, not one. It's just that Monty picks which one for you. And since your choice is random, you might as well let an RNG do it for you. If you consider it two independent rounds instead of stay/switch, Stay: you get to roll 1d3, "1" wins Switch: you get to roll 1d3, "1" loses, "2" or "3" wins