A BUSINESS APPLICATION OF THE MONTY HALL PROBLEM
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A BUSINESS APPLICATION OF THE MONTY HALL PROBLEM
Let’s Play a Game
Remember “Let’s Make a Deal”?
It was a popular game show in the 60’s
A Popular Segment
One of the most popular segments was the three door game.
Pick a Door!
A contestant is asked to pick a door.
Pig? Car?
Behind one of the doors is a cool prize, usually a car.
Pig? Car?
Behind one of the doors is a cool prize, usually a car.
Pig? Car?
But behind 2 doors is a gag, often a farm animal.
Pig? Car?
But behind 2 doors is a gag, often a farm animal.
Which door?
So the contestant chooses a door.
? ? ?
The choice is made
Our contestant picks door #3
? ?
The Tease!
Now Monty shows us what is behind one of the remaining doors. Let’s say he shows us door #1.
? ?
The Tease!
Now Monty shows us what is behind one of the remaining doors. Let’s say he shows us door #1.
? ?
The Dilemma.
Monty now asks if we would like to stick with our original choice or switch to door #2.
?
The Dilemma.
What should our contestant do?
?
The Solution!
Or contestant should change doors.
?
The Solution!
Our contestant should change doors!
The Solution!
As we see, our original door wasn’t the winner. (Unless you prefer to win a pig)
But The Question Is…
Why was changing doors the better choice? Let’s start over and see why…
But The Question Is…
Our contestant chose a door.
But The Question Is…
1 door was eliminated. That leaves 2 doors. Isn’t that a 50/50 chance?
?
But The Question Is… Why is changing doors the better choice? After choosing, there is a 2/3 chance of being wrong.
2/3 Chance of the car being in this group 1/3 Chance of the car
being here
But The Question Is…
One door is eliminated leaving 2/3 chance on the other door in the NOT chosen set.
2/3 Chance of the car in this group
1/3 Chance of the car
But The Question Is…
Why was changing doors the better choice?
Do You Believe It?
Most people struggle with this even after seeing the explanation.
Do You Believe It? That’s why I want to discuss it further and help you apply this to business. You will make better choices.
What If There Were 100 Doors?
We Can ALWAYS Get Down To 2 Doors
? ? ? ? ? ?
No Matter Which Door We Choose, Monty Can ALWAYS Show All Other Doors But 2: Ours and 1 Other Door
? ? ? ? ? ?
If we choose a door, and then are shown every other door but 1 other, do we have a 50/50 chance if we stay with our first choice?
? ? ? ? ? ?
Remember! The car must now be behind the door we chose or the last door Monty has to reveal.
?
Do you think there is a 50/50 chance that our original choice is correct?
?
That would mean if we never changed doors, we would choose correctly, from 100 doors, 50% of the time!
? ? ? ? ? ?
So What? It’s Just a Game.
Is it? We often stick with business decisions that were made when we had less information. Governments will “stay the course” despite ever growing evidence that the course is wrong. We can see examples of this every day.
But The Question Is…
Why? 1. We don’t like to admit mistakes 2. We cling to sunk costs 3. Sometimes our judgment is clouded by our
being goal focused. *
* 1996 Everest disaster: Blinded by the goal, 8 people died on a single day in spite of knowing it was too late to reach the summit and safely return to base.
Can Be Costly and Deadly
“In many cases, business failures, such as the Millennium Dome in London and cost overruns at Denver International Airport, can be blamed on basic foibles of human decision makers, such as the tendency to overestimate one’s capabilities, and the strong desire to recoup sunk costs(Nutt, 2002).”
LEADERSHIP IN EXTREME CONTEXTS: A GROUPTHINK ANALYSIS OF THE MAY 1996 MOUNT EVEREST DISASTER JENI L. BURNETTE, JEFFREY M. POLLACK, AND DONELSON R. FORSYTH
Which Is Why…
We so often end up with
Instead of…
Okay, Let’s Summarize
1. We generally are not very good at predicting success (odds)
2. Our information is always imperfect 3. We tend to “stay the course” longer than we
should in spite of improved data 4. We don’t like to admit mistakes 5. We sometimes fall into a bravado of a given
goal
What Should We Do? 1. Education: Just watching this made you
smarter! 2. Encourage independent thinking 3. Admit mistakes, learn, adapt 4. Host a presentation by Chris Reich of BizPhyZ
(530) 467-5690
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