A simple game. There is a game master and a player, you!

- There are
*n*doors. Let’s take*n*= 3. - Behind one door there is a price, only the game master knows where it is.
- You must pick a door.
- The game master will open one door. He has two rules:
- do not open the winning door
- do not open the door picked by the player

- When
*n*> 3 the game master will continue opening doors, given the rules, untill there are 2 doors left. - Now you have a choice again and this is the main question of the game: do you want to switch? Or: will switching give you a better change of winning?

## Analysis

- Let’s take 3 doors.
- ‘P’ means the door with price and ‘Y’ means that you picked that door.

This are all the possible scenarios.

1 | 2 | 3 |
---|---|---|

P,Y | ||

Y | P | |

Y | P | |

P | Y | |

P,Y | ||

Y | P | |

P | Y | |

P | Y | |

P,Y |

Now the game master must open a door. When we merge the possible scenarios we get to following list.

# | ||
---|---|---|

P,Y | 3x | |

Y | P | 6x |

So now it is trivial to see that switching gives you a 2/3 change of winning.

## What!?

For me this is really counterintuitive. When you take a large number for *n*, switching gives you a near 100% change of winning the price! Because I couldn’t believe my own analysis I decided to make a small C# console program to validate this result and to play a little with different game master strategies.

See the code on Github.