Monty Hall's 3 Door Problem

Setup

The 3 door problem is based on Monty Hall's TV show Let's Make a Deal.

• Behind 1 door there is a new BMW, behind the other 2 doors are goats.
• Contestant picks a door.
• Monty always opens an unpicked door to show contestant a goat.
• Monty alwasys offers contestant a chance to switch doors.
• What should contestant do? Stay with original door? or Switch?

Results

It is better to switch. Contestants that always stay with their original door win 1/3 of the time. Contestants that always switch win 2/3 of the time. Contestants that randomly switch or stay win 1/2 the time.

Ramification for DIY Portfolio Managers

Strategy counts. Contestants with a winning strategy, switching, win 2/3 of the time. Contestants with a losing strategy, staying, win 1/3 of the time. Contestants with no strategy, random stay switch, win 1/2 the time. It is better to have no strategy than a bad strategy.

Some investors prove there are winning strategies in the stock market. Some investors prove there are losing strategies in the stock market. Is it better to have no strategy than a bad strategy?

Winning stock market strategies are harder to find and more perishable than winning 3 door strategies.

Search 3 doors

Curious about the 3 door results? Have some fun searching the internet with keywords: 3 door Monty Hall. There are many websites that have something to say about the problem. Some even have simulations where you can click on doors.

STRATEGY COUNTS