If a search brought you here then you probably already know what the Monty Hall problem is. If not, and in case you are interested, the Wikipedia page explains it in detail.
In a nutshell: the game comes from a gameshow called Let’s Make a Deal, in which the contestant is presented with three doors, behind one of which is a car which will be won if the contestant chooses that door. Once the contestant has made their initial choice from the three doors, the gameshow host Monty Hall will open one of the other doors to show that the car is not behind that door. The contestant is then given a choice of staying with their original choice of door, or switching to the other remaining door which has not yet been opened.
I recently encountered the Monty Hall problem for the first time and succumbed to the logic failure that most people succumb to, i.e. feeling certain that staying on my original choice had exactly the same probability of winning as switching to the other available door.
Due to my initial difficulty in comprehending that switching doors actually gives approximately double the chance of winning, I decided to take the scientific approach of writing a Python program to test this out. The results of running this clearly demonstrated that my 50/50 belief was wrong, and that in fact one should always switch because doing so approximately doubles the chance of winning.
Continue reading “Testing the Monty Hall problem using a Python program to run game simulations”