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📊StatisticsConditional Odds18 sec read

Switching Doors in the Monty Hall Problem Doubles Your Odds From 33% to 67%

After you pick 1 of 3 closed doors and the host reveals an empty door, switching to the remaining door jumps your win probability to 2/3.

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Switching Doors in the Monty Hall Problem Doubles Your Odds From 33% to 67%
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Statistics

🚪 Conditional Odds

Conditional Probability & Bayes

Key Metric+20 XP

After switching doors, what percentage of games do you expect to win?

Your guess:0%
Key Insight

Unlike a blind coin flip, the host never opens the winning door, preserving the 2/3 chance for switching.

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📊 Statistics

Conditional Odds

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Why / How?

01

Scientific Mechanism

Your first pick only has a 1/3 chance of hiding the prize, leaving a 2/3 probability in the other two doors combined. Because the host deliberately opens an empty door, that entire 2/3 probability collapses onto the single remaining door.

02

Why It Matters

Unlike a blind coin flip, the host never opens the winning door, preserving the 2/3 chance for switching.

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Britannica — Monty Hall Problem
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Why doesn't the probability split 50/50 after the host opens a losing door?

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Quick Q&A Knowledge Cards

Quick Guess

After switching doors, what percentage of games do you expect to win?

67%

Fact Check

Why doesn't the probability split 50/50 after the host opens a losing door?

The host's knowledgeable choice concentrates the 2/3 odds onto the unpicked door

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