Monty Hall Calculator

Monty Hall Problem Calculator

Simulate the Monty Hall problem and compare the switching strategy against staying with your first choice.

Last updated: March 2026 | By ForgeCalc Engineering

Monty Hall Simulator

Theoretical Probability

Switch66.67%
Stay33.33%
Simulation Result
Ready to Simulate

Enter values and run the simulation to see the win rates.

What Is the Monty Hall Problem?

The Monty Hall problem is a probability puzzle in which a contestant chooses one door out of several, then is given information that changes the odds if they decide to switch.

How to Analyze Monty Hall Probabilities

  1. Select the number of doors.
  2. Run many simulated games.
  3. Count how often switching wins.
  4. Compare the result with the theoretical probabilities.
P(switch) = (doors - 1) / doors

Worked Example

With 3 doors, switching wins about 66.67% of the time.

P(switch) = 2/3

Frequently Asked Questions

Should you always switch?

In the classic setup, switching gives the better odds.

Why simulate the problem?

Simulation helps visualize the probability result over many trials.

Why is three the minimum number of doors?

The classic Monty Hall problem requires at least three doors.

Does this calculator accept decimals?

No. The problem is defined on whole door counts and whole simulation counts.

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