The Monty Hall Problem Visually Explained

If you are given three doors—one hiding a car and two hiding goats—and you pick Door 1, you have a 33.3% chance of winning. But what happens to the math when a losing door is revealed?

Most people think the odds magically reset to a 50/50 coin toss. They are wrong.

This visualization breaks down the famous Monty Hall Problem by mapping the flow of probability. The simulation reveals the secret to the paradox: probability must be conserved. When the host acts as a "Goat Filter" and eliminates a losing door, that empty 33.3% probability doesn't vanish—it transfers entirely to the remaining unpicked door.

You aren't choosing between two equal doors. You are choosing between your initial blind guess, and the combined power of the entire filtered group.

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