The Infamous Monty Hall

In my math class we were shown this video that introduces the Monty Hall problem. Monty Hall hosted a game show named Let's Make a Deal in 1963, and one of the big games in this show was having a contestant pick a door out of the three shown. The objective of the game was to get the car. Mathematically there is a higher chance to pick the non-car since the probability would be about 66 percent. Then Monty would show one of the doors that was a non-car. Therefore, there is a 50 percent chance of getting the car right? Wrong! So what should you do? Stay with the picked door? Or swap your door?

Try it out by clinking here and see what happens after doing this experiment nine times.

So what was your result? You should have noticed that when you switched the door you would most likely get the car and if you stayed with your door, you would end up with a goat. Why? Well no matter what, the door with the non-car will be shown. There is a less chance of picking the car first so if you swap doors you have a 66 percent of getting a car instead of staying, which if you do stay, it will make you have a 33 percent chance of getting a car. Therefore if you swap, the higher probability you will have to win the car. Now that you know, don't you want to participate in the current Let's Make a Deal?

What's the Probability I Will Win?

Have you ever been in a conflict with someone and you don't know how to solve it fairly? For example, my friend and I would always argue on who should pay for our food. Normally, people would just split the check, but not us! We were both stubborn, which meant I hated losing against her. How do we solve our problem? Easy, have three matches of rock, paper, scissors and see who two out of three!

The game is simple: Paper beats rock, rock beats scissors,and scissors beats paper. Mathematically we both have an equal chance of winning since we can pick one out of the three. However, is this game really fair?

Play this game with a friend or play Rock, Paper, Scissors against the computer 45 times. Keep track on how many times you win, lose, or tie. At the same time tally mark how many times you showed rock, paper, or scissors. Make sure your partner keeps track of theirs or if you are playing against the computer, keep track of the computer's data.
Now out of 45, make a fraction of how many times you won, lost, and tied. Who won? Was the results fair ( both of you won the same number of times)?

Well theoretically there should have been an equal amount of times of winning, losing, and tying. Since there is 1/3 of winning, 1/3 of losing, and 1/3 of tying, but why is it 1/3? Well there are a total of three choices to pick from and there are three possible outcomes.

However, we all know that we do not live in a perfect world. The activity you did earlier was the practice of experimental probability. There are multiple factors that could differ the results such as basing off what the opponent did previously or watching them closely to find patterns your partner makes when throwing a specific hand gesture. If you went against the computer you may have seen the patterns it was making.

Therefore, theoretically playing rock, paper, scissors is a fair game to play, but in reality it may or may not be depending on your luck. So make sure to know your opponent's moves since it can be crucial when paying for food.