[yen223]

https://github.com/yen223/monty_fall/blob/master/Monty%20Hal...

The math is contingent on whether you know the host knows or doesn't know where the door with the car is. This is the counterintuitive bit.

[auggierose]

Your program shows exactly what I mean: "Impossible" cannot be non-zero, your modified question is not well-defined.

Yes, of course it depends on the host knowing where the goat is, because if he doesn't, the scenario is not well-defined anymore. This is not annoying, this is to be expected (pun intended).

[yen223]

The scenario is well-defined. There's nothing logically impossible about the host not knowing which door has the car, and still opening the goat door.

"Impossible" in the program just refers to cases where the host picks the car door, i.e. the path that we are not on, by the nature of the statement. Feel free to replace the word "impossible" with "ignored" or "conditioned out". The math remains the same.