Statistics & Probability

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Monty Hall Problem Calculator.

Compare staying and switching in the generalized Monty Hall setup.

On-device calculationNo signup
01

Set your values

Results update as you type.

stayProbability: 0.333333

stayProbability

0.333333
switchProbability: 0.666667

switchProbability

0.666667
stayPercent: 33.333333

stayPercent

33.333333
switchPercent: 66.666667

switchPercent

66.666667

Results update automatically as you type.

Use Cases

Teaching Probability Concepts

Demonstrate the counterintuitive nature of conditional probability in classrooms or self-study. Adjust the number of doors to see how the advantage changes.

Example: Set doors to 3 to show the classic 1/3 vs 2/3 result.

Game Show Strategy Analysis

Analyze optimal strategies for game shows or simulations that follow the Monty Hall format. Understand the impact of the number of doors on your best choice.

Example: With 5 doors, switching gives an 80% win rate.

Frequently Asked Questions

What does the Monty Hall Problem Calculator do?
It calculates the probability of winning if you stay with your original choice versus if you switch after a door is revealed. You input the number of doors, and it shows the win chances for both strategies.
How does the number of doors affect the probabilities?
With more doors, the advantage of switching increases. For 3 doors, staying wins 1/3 of the time and switching wins 2/3. For 10 doors, staying wins 1/10 and switching wins 9/10.
Is this calculator useful for real-life decisions?
It's mainly for educational and entertainment purposes. It illustrates a classic probability puzzle, but it's not meant for high-stakes decisions. Use it to understand how probability works in games of chance.

Tips & Common Mistakes

Tips

  • Always consider switching if the host always reveals a losing door and offers a switch.
  • The more doors there are, the more beneficial switching becomes.
  • Use this calculator to verify your intuition: try different door counts and see the pattern.
  • Remember that the calculator assumes the host knows where the prize is and always reveals a goat.

Common Mistakes to Avoid

  • Assuming that after a door is revealed, the remaining two doors each have a 50% chance.
  • Forgetting that the host's action is not random; it always reveals a losing door.
  • Thinking that the number of doors doesn't matter; it significantly changes the probabilities.

Last updated: August 13, 2026