Nope! That’s you adding a constraint that does not exist in the original problem.

> Was Mr. Hall cheating? Not according to the rules of the show, because he did have the option of not offering the switch, and he usually did not offer it.

From [1].

Constraints matter. Don’t play fast and loose with them.

[1] https://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-do...