Monty's Dilemma (Standard 3 Doors)
Wins: 0 / 0 Played (0%)
Pick a door to begin the standard game.
Monty's Dilemma (Custom Doors)
Set the number of doors (3-25) and start the custom game!
Setup the number of doors and start the custom game to explore the problem further.
Run Simulations (Standard 3 Doors)
Simulate the standard 3-door game many times to see the probability of winning if you always switch versus always stay. This helps understand the core concept.
Run the simulation for the 3-door game to visualize the probabilities.
Simulations clearly demonstrate the counter-intuitive advantage of switching in the Monty Hall problem.
Why Switching Works: The Probability Explained
The game seems like a 50/50 chance after Monty opens a door, but it's not! Let's look at all three possibilities based on your *initial* choice. Remember, each scenario has an equal (1/3) chance of happening.
Scenario 1: Picked Prize (1/3 Chance)
You got lucky on your first try!
Your Pick
Opened
Switch Here?
If you SWITCH: You get a Goat.
If you STAY: You WIN the Prize!
Scenario 2: Picked Goat A (1/3 Chance)
Your first pick was a goat.
Your Pick
Switch Here?
Opened
If you SWITCH: You WIN the Prize!
If you STAY: You get a Goat.
Scenario 3: Picked Goat B (1/3 Chance)
Your first pick was also a goat.
Your Pick
Opened
Switch Here?
If you SWITCH: You WIN the Prize!
If you STAY: You get a Goat.
Conclusion: In 2 out of the 3 equally likely scenarios, switching your choice leads to winning the prize. Sticking with your initial choice only wins 1/3 of the time. That's why the best strategy is to always switch!