Monty Hall Problem

Monty Hall - ongelma (Montyt Hall problem)

The Monty Hall problem is a classic problem in probability that originated with American game show host Monty Hall. The problem is also called the "three doors problem" or in English "three doors problem".

Let's imagine that you are a competitor in a game show with three doors: door number 1, door number 2 and door number 3. Behind one door is the main prize, a car. Behind the other two doors is a goat. First you have to choose one door. Let's say you choose door number 1. The game host knows which door the car is behind. He opens one of the doors, let's say door number 3, knowing in advance that he will reveal the goat to you. Then the host will give you the option to change your choice: you can stay with your original choice (door number 1) or change your choice to the other remaining door (door number 2).

The solution to the Monty Hall problem is based on probability. Although intuition may say that it is irrelevant whether to replace the door or not, statistically it is cheaper to replace. The probability of winning a car increases if you change the choice to another door. In fact, the odds of winning a car increase to ⅔ when you switch, while the odds of staying in the same door and winning a car are only ⅓.

Ending options, if the player initially chooses door number 1:

Selected doorDoor 2Door 3Result by switchingResult by not switching
WinGoatGoatGoatWin
GoatWinGoatWinGoat
GoatGoatWinWinGoat

The solution can also be illustrated by imagining that instead of three doors, there were 100 doors. When you initially choose one door, your chance of hitting the right door is one in a hundred, or 1%. After your choice, Monty opens 98 doors with a goat behind them. There are two doors left, the door you choose still has a 1% chance of winning and the door Monty left has a 99% chance. Which one do you choose?

Try the Monty Hall problem yourself!

You can try for yourself how good the theory behind the Monty Hall problem is. First choose a door and then decide if you want to change or stay with the same choice. The program collects statistics and you can see as the game progresses how many times you have changed the door and the winning percentage for your choices. From the settings, you can also change the number of doors or set the program to open doors automatically. By adjusting the speed, you get more door openings in a short time.

Pick a Door!

Total switches: 0

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Total stays: 0

Win rate %
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