Monty Hall Problem Calculator
Monty Hall Problem calculator. Should you switch? Interactive simulator and Monte Carlo proof. Switc
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Should You Switch? Interactive Simulation Proves Switching Wins 2/3
3 doors: 1 car, 2 goats. You pick. Host reveals a goat. Switch or stay? Switching wins 2/3 of the time. Try the interactive game and simulation.
Real-World Scenarios — Click to Load
Interactive Game
Simulation
Switch Win Rate by Number of Doors
Calculation Breakdown
For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- • Switch wins 2/3, stay wins 1/3 — switching doubles your chances
- • Marilyn vos Savant was correct in 1990; thousands of PhDs wrote in to say she was wrong
- • When you pick wrong (2/3 of the time), the host reveals the other goat — switching wins. When you pick right (1/3), switching loses.
- • Generalizes to N doors: Switch wins (N-1)/N, Stay wins 1/N
- • Connected to Bertrand's box paradox — same conditional probability structure
Did You Know?
Expert Tips
Always switch
Unless you enjoy 1/3 odds
Run the simulation
10,000 trials — watch it converge to 2/3
Connect to Bertrand
Same conditional probability structure
N doors
With 10 doors, switch wins 90%
Generalized N-Door Results
| Doors | Switch wins | Stay wins |
|---|---|---|
| 3 | 66.7% | 33.3% |
| 4 | 75.0% | 25.0% |
| 5 | 80.0% | 20.0% |
| 6 | 83.3% | 16.7% |
| 7 | 85.7% | 14.3% |
| 8 | 87.5% | 12.5% |
| 9 | 88.9% | 11.1% |
| 10 | 90.0% | 10.0% |
Frequently Asked Questions
Why does switching win 2/3?
When you pick a goat (2/3 of the time), the host must reveal the other goat. The remaining door has the car. Switching wins. When you pick the car (1/3), switching loses.
What did Marilyn vos Savant say?
In 1990 Parade, she correctly said switch. Thousands of readers (including PhDs) insisted she was wrong. She was right.
Does it matter which door the host opens?
No. The host always opens a goat. The key is that your initial pick is wrong 2/3 of the time.
What about N doors?
With N doors, switch wins (N-1)/N. With 10 doors, that's 90%. The effect strengthens.
How is this like Bertrand's box?
Both use conditional probability. Drawing gold from GG or GS — 2/3 chance it's GG. Same structure.
What if the host picks randomly?
If the host might accidentally reveal the car, the problem changes. Classic problem assumes host always reveals a goat.
By the Numbers
Official Data Sources
Disclaimer: This calculator demonstrates the Monty Hall problem for educational purposes. The theoretical result (switch 2/3, stay 1/3) is mathematically rigorous. Simulations converge with more trials.
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