Refuting False Logic: Proving the Monty Hall Problem Correct

The Monty Hall problem is counterintuitive, which makes it hard to grasp, and even harder to explain to a logical listener. Therefore, the Monty Hall Problem needs to be broken down as much as possible in order to make it understandable for those who believe that they are right.

It is important to understand the problem in its entirety. There are three doors, one of which has a car behind it, and the other two have goats. Naturally, the goal of the game is to pick the door with the car behind it, a 1/3 chance. A contestant picks a door at random, without knowing what is behind any of them. After the contestant picks, Monty Hall reveals one goat behind a door that was not chosen by the contestant, eliminating that possible choice. Now, Monty gives the contestant a chance to either swap the door picked at first for the only remaining door or keep with the door originally picked. Once a choice is made, the game is over and the contestant opens the door that he ended up with.

Now, the argument of this game is that by switching doors, the contestants chance actually jumps from 1/3 to 2/3 of picking the car. Switching feels counterintuitive to players and observers, but the mathematics that makes it the more effective strategy is irrefutable.

In Marilyn Vos Savant’s article on The Game Show Problem, mathematicians all over refuted her analysis of the problem, which was correct the entire time. We tend to think that after a door is removed, there is a 50/50 chance of picking the car. Once that common answer was proved to be wrong by breaking down the problem to its core, people finally realized their error and that Marilyn was correct all along.

Now, switching is understood to yield a higher chance of winning, but it is important to realize that it only works if the game is played the way we believe it is. For instance, Monty could have just opened any door, and happened to never open a door with the car. What if every few games, there was no car behind any of the doors and just three goats? It goes back to the two-headed coin mentioned in my Definition Essay. While we know how a coin flip works, it only proves to be correct if the coin was an honest coin.

What Monty knows is always important, no matter what the situation. Weather Monty attempted to trick a contestant or not, he knows what is behind all three doors. He always knows which doors to open when and that has a major impact in the game. He could have helped or hindered contestants depending on his actions.

The game show problem only works if the way the game is believed to be played is true and Monty is not a liar. Otherwise, the entire problem is false. If the problem and Monty both proved to be truthful, then logic can take over and explain the problem thoroughly. Any refutation that comes towards this problem can be refuted by logic, but only if we are knowledgeable of exactly how all of the variables work.