🔬 The Monty Hall Problem
One of the most famous puzzles in probability is undoubtedly the Monty Hall problem. It is named after the host of a popular TV game show from the 1970’s called “Let’s Make a Deal.” The puzzle goes like so:
- The host offers you three doors to pick from. Behind one of them is a new car which you get to keep if you pick that door, behind the other two are goats, which, presumably you are not really interested in winning.
- You pick a door.
- The host opens one of the two doors that you did not pick and shows you a goat behind it.
- He then offers you the chance to switch the door that you picked to the remaining door or stick with your initial choice.
What would you do in this case? If you are like many people you would leap to the intuitive conclusion that you should stick to your original choice because the odds of winning the car are now 1 in 2 while they started out at only 1 in 3 chances of winning. But this is wrong! In fact your odds of winning the car improve to 2 in 3 chances of winning. How this can be so is relatively easy to explain, but very difficult to convince many people of.
Here is an article from Open Culture with some great videos and other explanations of the problem and its solution published on the occasion of Monty Hall’s death in 2017.
The Famously Controversial “Monty Hall Problem” Explained: A Classic Brain Teaser
When the news broke last week of the death of game-show host Monty Hall, even those of us who couldn’t quite put a face to the name felt the ring of recognition from the name itself.
And here is a simulation of the problem which compares the percentage of times you’d win if you didn’t switch with the percentage of times you would win if you did switch. Note that after running the simulation for a little while the probability f winning gets close to 2/3 if you switch and 1/3 if you don’t.
See the Pen #1 – Monty Hall Simulation by Mladen IliΔ (@mladenilic) on CodePen.
I thought this simulator was interesting. When I first read the problem, I immediately thought that I would stick with my original choice because I was always told to go with my first instinct. But apparently, I wouldn’t have won the car. Good information to know if I ever find myself on a game show in the future.
I had heard of the monty hall problem before. I had never understoood how that one door has a 2/3 probbability until I watched the video explaining it with the 100 doors. In that case I would absolutely switch to door 37, so why wouldn’t I switch to door 3 as well?
I found this interesting because I feel this brain teaser really gave an informational output on how we perceive the certainty of situations. After interacting with the simulation, I was fascinated how I was more likely to stick with choices that gave me greater percentage to win.
This is very interesting. At first I was slightly confused by this but after thoroughly reading this article and using the simulation, it makes a little more sense. I’m not sure what I would do in this situation, I may have picked a different door but I may have also kept the same.
After going through the articles, playing with the simulator and reading the other comments, i have to say I probably wouldn’t have won the car either. this is an interesting topic id never really grasped but i understand it now.