The Monty Hall problem is a probability puzzle named after the host of the American television game show "Let's Make a Deal," Monty Hall. The problem goes as follows:
You are a contestant on a game show and are presented with three doors. Behind one door, there is a valuable prize, such as a car, and behind the other two doors, there are goats. You are asked to choose one of the three doors.
Once you've made your choice, the host, Monty Hall, who knows what is behind each door, opens one of the other two doors to reveal a goat. Now, there are two doors left: the one you initially chose and the other unopened door.
At this point, Monty gives you a choice. You can either stick with your original choice or switch to the other unopened door. The question is: What should you do to maximize your chances of winning the car? Should you stick with your initial choice or switch doors?
The counterintuitive answer is that you should switch doors. The probability of winning the car if you switch is 2/3, while the probability of winning if you stick with your original choice is 1/3. This result can be proven mathematically and has been the subject of much debate and confusion among people.
Intuitively, switching doors increases your chances of winning because Monty's decision to reveal a goat provides you with additional information. When you initially chose a door, there was a 1/3 chance of it hiding the car. However, when Monty reveals a goat, the probability shifts to the unopened door, making it more likely to contain the car.
This problem demonstrates the concept of conditional probability and challenges our intuition about probability and decision-making.
Welcome to my Monty Hall Game!
This project holds a special place in my coding journey as it was my very first CS project when I started learning coding back in 2018. The Monty Hall problem fascinated me with its intriguing and counterintuitive nature, sparking a deep dive into the realms of math, statistics, and probability. This exploration eventually inspired me to pursue a career as a machine learning practitioner.
Although the code may be simplistic by today's standards, it represents a beautiful memory, reminding me of the exciting steps I took into the coding world. I invite you to enjoy the game and experience the magic of the Monty Hall problem.
You can find the game at this link. Feel free to explore, have fun, and witness the astonishing probabilities at play. May it ignite your curiosity and enthusiasm, just as it did for me.
Happy gaming!