The Monty Hall
Paradox Explained.
MONTYLAB is a digital observatory for probability. Test your intuition against the math, simulate N-door scenarios, and master the logic behind the switch.
Monty Hall Logic Engine
Probability & Heuristics
Join thousands of students using our simulator to visualize the counter-intuitive nature of conditional probability.
Mastering the Paradox
Unifying mathematical rigor with interactive simulations to dismantle cognitive probability illusions.
Stay vs Switch
In a 100-door scenario, the choice to switch is mathematically superior. Compare the win rates and see why switching leverages host data to maximize your prize probability.
Initial choice accuracy
Host reveals 98 goats
Sticking to 1/100 odds
Ignoring host data
Optimal strategy gain
Host reveals 98 goats
Leveraging host info
Using host data set
Probability Matrix
Detailed comparison of outcomes based on strategy.
| Metric | Stay | Switch | Advantage |
|---|---|---|---|
Win Rate (100 Doors) Probability | 1.0% | 99.0% | 99x higher |
Loss Rate (100 Doors) Probability | 99.0% | 1.0% | 99% reduction |
Host Information Logic | Ignored (Stay) | Utilized (Switch) | Data-driven |
Pólya Heuristic Strategy | Guessing | Systematic | Proven path |
Prize Certainty Outcome | Low confidence | High confidence | Near-certain |
Decision Model Strategy | Static choice | Adaptive choice | Optimal gain |
Test the theory yourself.
Run thousands of trials in our simulator to see the law of large numbers in action.
Solving the Paradox in Four Steps
George Pólya’s framework provides the logical rigor needed to dismantle the Monty Hall illusion through systematic analysis and empirical verification.
Define the Paradox
Model the Sample Space
Execute the Simulation
Verify the Solution
Test the Theory Yourself
Apply the four-step method in our interactive simulator to see how probability shifts when you switch doors.
The 1990 Controversy
A look back at the famous column that challenged thousands of experts and redefined our understanding of probability.
Monty Hall hosts the iconic game show where contestants choose between three doors, unknowingly setting the stage for a future mathematical firestorm.
Game Show Debut
Marilyn vos Savant publishes the correct solution in Parade, asserting that switching doors doubles your probability of winning the prize.
Parade Column
Over 1,000 PhDs wrote to Parade claiming Marilyn was incorrect, highlighting the deep-seated human cognitive bias against conditional probability.
Academic Backlash
Applying George Pólya's method: Understand the problem, devise a plan, carry out the plan, and look back to verify the probability logic.
Pólya Heuristic
With 100 doors, the host opens 98, leaving 2. Switching yields a 99% win rate, proving the logic holds regardless of the number of doors.
N-Door Simulation
We continue to explore probability through interactive simulations, archival exposition, and rigorous mathematical heuristic frameworks.
Digital Lab
Master the probability logic
Explore our interactive simulator to test the Monty Hall problem yourself and see the math in action.
Test your intuition against reality
Dismantle cognitive illusions with our interactive simulator. Experience the Monty Hall paradox through rigorous computation and historical analysis.
N-Door Logic
Configure your simulation with any number of doors to test probability.
Pólya's Method
Understand the paradox through the four-stage heuristic framework.
Historical Roots
Explore the origins of the problem and its impact on statistics.
Live Simulator
Run thousands of trials to see the Law of Large Numbers in action.
Ready to run a trial?
Launch the simulator to see if switching doors truly increases your odds of winning.