esimms999/monty_hall

Monty Hall Problem and Collaboration Summary

The Monty Hall Problem

The Monty Hall Problem is a probability puzzle named after the host of the TV game show Let’s Make a Deal. In its classic form:

• There are 3 doors: one hides a car (the prize), and two hide goats.
• The player picks a door (e.g., Door 1).
• Monty, who knows what’s behind all doors, opens one of the other two doors to reveal a goat (e.g., Door 3).
• The player can then stick with their original choice (Door 1) or switch to the remaining unopened door (Door 2).
• Solution: Sticking wins 1/3 of the time (probability of picking the car initially), while switching wins 2/3 of the time (Monty’s reveal shifts the odds). This counterintuitive result, popularized by Marilyn vos Savant in 1990, demonstrates how conditional probability changes with Monty’s action.

Collaboration between esimms999 and GrokAI

We collaborated to create two R simulation programs to explore this problem, now hosted in esimms999's GitHub repository at https://github.com/esimms999/monty_hall:

1. Initial Setup (three_doors.R)

   • esimms999 requested an R simulation of the classic 3-door Monty Hall Problem.
   • GrokAI provided code simulating 10,000 trials, showing sticking wins ~1/3 (~0.333) and switching ~2/3 (~0.667), with a bar plot.

2. Generalization (n_doors.R)

   • esimms999 asked for a version supporting n doors (e.g., 5 doors: 1 car, 4 goats).
   • GrokAI adapted the code to handle variable doors, targeting sticking at 1/n (0.2 for 5) and switching at (n-1)/n (0.8 for 5).
   • This can be run with multiple repeats of simulations.

3. GitHub Repository

   • esimms999 requested GrokAI provide assistance in creating a GitHub repository.
   • GrokAI provided guidance in creating a local git repo and linking it to GitHub.
   • GrokAI contributed the content for the README.

Outcome

• three_doors.R: Simulates the classic problem, confirming the 1/3 vs. 2/3 probabilities.
• n_doors.R: Extends it to n doors, validated with 5 doors (e.g., ~0.2 stick, ~0.8 switch), summing to 1.0.

Our collaboration turned esimms999's request into a robust, generalized simulation, now shared with the world!