Monty Hall Problem
Overview
The Monty Hall Problem is one of the most famous probability puzzles, demonstrating how our intuition about probability can be spectacularly wrong. After you pick one of three doors and the host reveals a goat behind another door, you should always switch to the remaining door to maximize your chances of winning (66.7% vs 33.3%).
Tips
Play the game yourself first: Make your own choices for 20-30 rounds to experience the puzzle before running automated simulations.
Run large-scale simulations: Execute 1,000+ games comparing “Always Switch” vs “Always Stay” strategies to see the 2:1 win ratio emerge clearly.
Think about the 100-door version: Imagine 100 doors where the host opens 98 goat doors - would you switch? This extreme case makes the logic much more intuitive.
Focus on your initial choice: Remember that your first pick has only a 1/3 chance of being correct, so switching means betting you were initially wrong (which happens 2/3 of the time).
Track the statistics in real-time: Watch the win percentages converge to the theoretical values as you accumulate more trials.