# The Monty Hall hospital business strategy

The Monty Hall problem is named for its similarity to the Let’s Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let’s say you pick door 1. Before the door is opened, however, someone who knows what’s behind the doors (Monty Hall) opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened). The Monty Hall problem is deciding whether you do.

The correct answer is that you do want to switch. If you do not switch, you have the expected 1/3 chance of winning the car, since no matter whether you initially picked the correct door, Monty will show you a door with a goat. But after Monty has eliminated one of the doors for you, you obviously do not improve your chances of winning to better than 1/3 by sticking with your original choice. If you now switch doors, however, there is a 2/3 chance you will win the car.

I think selecting a business strategy along those same lines is at least as productive as whatever business strategy your organization has chosen.  Let us assert that behind two of the doors are bad strategies, and behind a 3rd door is a winning strategy.  Your current strategy is behind whichever door you select.  On your behalf, I reveal to you what is behind one of the two remaining doors—a strategy destined to fail.

The question becomes, do you stick with the strategy you’ve selected knowing that you have a 1/3 chance of it being a winning strategy, or do you switch your choice to the strategy behind the door not chosen, knowing with certainty that doing so improves your chances of being correct to one in two?

Most people, like most businesses, stick with their original choice.  Change is difficult.

Paul M. Roemer
Chief Imaginist, Healthcare IT Strategy

1475 Luna Drive, Downingtown, PA 19335
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## 2 thoughts on “The Monty Hall hospital business strategy”

1. That’s an interesting application of that lesson in probability, although I would hope that anyone challenged with selecting a business strategy wouldn’t be so confused that they leave it up to random chance 🙂
For anyone reading Paul’s example above and wishing to better understand why it’s good to switch in that situation (this seems counterintuitive to even some who are good at probability and statistics), I suggest reading “The Drunkard’s Walk: How Randomness Rules Our Lives” by Leonard Mlodinow. I have no stake in that recommendation other than passing on something very educational. That book does a great job of taking what may seem like a boring (or hard to understand) math domain such as probability and explaining it very well with some fascinating examples, including the Monty Hall scenario. It also explains how we often mistake random chance as a pattern that can lead one to incorrect conclusions. Understanding that last point is important to scientists (i.e. doctors, software engineers, researchers, etc.).

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