Astonishing how the effort is different given your knowledge base. The author of this post took as long coding the problem as it took me going through the math.
There is a puzzle used in game shows known as The Monty Hall Problem.
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats.
You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat.
He then says to you, “Do you want to pick door No. 2?”
Is it to your advantage to switch your choice?