Monty Hall Problem

A colleague of mine gave me the following puzzle to solve, which is the famous 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 number 1, and the host, who knows what’s behind the doors, opens another door, say number 3, which has a goat. He says to you, “Do you want to pick door number 2?” Is it to your advantage to switch your choice of doors?

In the evening I wrote a simple console application that proves the solution practically running the game 10000 times.

The application shows you validation of the .NET random engine first. There are percentages of 0, 1, 2 numbers received from the Random class executed for 10000 times. Then it shows percentage of success when you “pick door number 2” (switching your choice) and percentage of success when you stay with your first selected door.

The success rate is 2/3 when the door is switched and 1/3 for the runs that stick. There is only one cs file on GitHub. You can compile it in Visual Studio command line “csc.exe GoatSelector.cs” and execute GoatSelector.exe.