He added two more doors, for a total of 5 instead of 3, behind which 4 held a goat, and 1 held a brand spanking new electric car (hey, gotta keep up with the times, eh?).

In the first round, the player chooses

*two*doors instead of one. Then Monty opens up one of the other three doors and reveals a goat. Then the player may choose one of his two original doors or switch to one of the unchosen doors. Monty then releases one more goat (gotta give the first goat some company or else it'll eat Monty's brand new trousers), and the player is then given a final choice of the remaining three doors.

What is your play, if:

1) The second door Monty opens is random?

2) He is purposely playing against you, trying to keep that new car for himself?

And 3) If you weren't sure, how much would you have to suspect dear old Monty's honorable intentions to make either play?