1. What is the Monty Hall Problem?

The Monty Hall problem is a probability puzzle based on the American TV show "Let's Make a Deal." It demonstrates that switching doors after a host reveals a goat increases your chances of winning the car from 1/3 to 2/3.

2. How Does the Simulation Work?

The simulation runs multiple trials of the Monty Hall scenario:

1. Randomly places a prize behind one of three doors
2. Simulates player's initial random choice
3. Host opens a remaining door that doesn't have the prize
4. Player either stays or switches based on selected strategy
5. Records whether the final choice was correct

3. Probability Explanation

Explanation: Switching doors gives you a 2/3 chance because your initial choice was likely wrong (probability 2/3), and the host's action of revealing a goat provides additional information.

4. Using the Calculator

Tips: Enter number of trials (more trials = more accurate results) and select strategy (switch or stay). The simulation will show actual win rate vs expected probability.

5. Frequently Asked Questions (FAQ)

Q1: Why does switching give better odds?
A: Because your initial choice has only 1/3 chance of being correct, so switching after one wrong door is revealed gives you the remaining 2/3 probability.

Q2: How many trials should I run?
A: More trials give more accurate results. 10,000+ trials will typically get very close to the theoretical probabilities.

Q3: Does the host's behavior affect the outcome?
A: Yes, this assumes the host always reveals a goat and never the prize, and always offers the chance to switch.

Q4: Is this counterintuitive?
A: Yes, many people (including mathematicians) initially believe the probability should be 50-50 after one door is revealed.

Q5: Are there real-world applications?
A: The principle applies to any decision-making scenario where additional information is revealed after an initial choice.