If you are like me, when you see a problem you don’t try to fix it first. You try to understand what caused the problem and fix the root causes. And if you often do that, you probably consider yourself to be more rational than your peers.
In my attempt to find the right answers I have read and discovered a bunch of mental frameworks that allow me analyse a problem faster. With my solid understanding of these frameworks, I apply the context of the problem across each of the frameworks and find the framework that helps me understand the problem on a deeper level. Once I get the best framework to analyse the problem I can solve the problem within the boundaries of the framework.
Now, I want to teach you how to be right 96% of the time by teaching you how to think in the right way. Unfortunately, I cannot exhaust every mental framework, but I will show you how to think using probability and elimination as a mental framework as you are most likely to have applied it unconsciously. Once you understand how frameworks can help you think better, make it your mission to unravel as many mental frameworks as possible.
TL;DR: Using probability and elimination as a thought framework you can quickly go from a 1 in 100 chance of being correct to a 96 in 100 chance of being correct by reducing the possible set of answers from 100 to 4 which means that you will be correct 96% of the time if you can always reduce possible solutions to every problem to a smaller set.
So on a Friday evening in February, I got a few of my colleagues in a room and asked them if they thought they could have the right solution most of the time. They were not sure, so I volunteered to show them.
First demonstration: Using probability
The fastest way to be right is to increase your probability of being right all the time.
There’s a popular game show called the Monty Hall show where the game master presents 3 doors to the contestant. Behind 1 of the doors is a million dollars and the other 2 have a goat behind them. If the contestant chooses right, they could go home with a million dollars.
The game master asks the contestant to choose a door that he believes has the million dollars. The contestant picks door 2.
The game master then opens door 1 which does not have the million dollars behind it. Leaving door 2 and door 3 unopened. The game master then asks the contestant if he would like to change his door.
I asked my colleagues if the contestant should change his option. Try and answer this question too before you continue reading.
The room was almost unanimous in their decision that the contestant should not change his door. And the ones that said he should were only being contrarian. The varying reasons for their choices were:
- The game master is trying to trick me by making me change my choice.
- Those that believed Door 2 had a 50% chance of being correct.
- Those that believed that if the majority of the audience think I should not change doors, then I should change doors.
I disagreed with all 3 reasons because the contestant had gone from a 1 in 3 chance of being correct to a 2 in 3 chance of being correct. I will simplify further.
If there were 100 doors, the contestant would have had a 1 in 100 chance of winning. Imagine the game master then opened 98 other doors with nothing behind them and left your door and 1 other random doors. Changing your door would mean that you just went from a 1 in 100 chance of winning to a 98 out of 100 times of you winning.
If you do not change your door, then you maintain your 1 in 100 chance of winning because when you picked you had no idea what door would be correct. Now that you have removed 98 incorrect doors, your odds of winning will dramatically improve by changing your door.
Now you have a 98% chance of winning a million dollars by changing your door.
Second demonstration: Using elimination
If you look for the right answer first, you will most likely be wrong. You have to look for the wrong answer first.
I have 2 examples in this demonstration. The first is common to everyone and you will be able to relate easily with it — multiple choice questions.
We’ve all had that exam paper were the lecturer tried to play on our intuition and the choices were misspelled or similar to the right answer. Do like this if you can relate 🙋
If you breezed through the paper and picked the first answer that looked familiar, you would fail the paper. But if you spent time eliminating all the wrong answers, then you would be correct a lot of the times.
This shows that some problems might have very similar answers, and your ability to eliminate the wrong answers will bring you excellence.
Second example of how to be right 96% of the time using elimination by categorization.
This method works well when you have big data sets. That is, when your problem could have more than 10 options as a solution.
My colleagues and I tried to figure out in which country the city of Marrakech is located in. All we knew about Marrakech was that it was a popular tourist attraction, and we had seen it on CNN weather report. We had no other information about the place.
We knew there were over 190 countries in the world and we all had varying answers on our lips. So we zoomed out to the bigger picture and decided to categorize all countries of the world using continents. And we tried eliminating continents we were certain Marrakech was not in. We eliminated North America, South America, Australia, and Antarctica.
We were all fairly confident that Marrakech was in one of these continents: Europe, Asia, and Africa.
We tried to come up with a new category that we could use to classify all the countries on this continent. We concluded on language. Based on the different dialects we had heard we tried to match “Marrakech” to words we had heard in other languages. We were able to eliminate Chinese, English, German, French, Spanish, Russian, Italian, and Portuguese speaking countries. Leaving us with less than 30 countries. Down from 190+ countries.
The room was split on the Hindi language commonly spoken in India, so we could not eliminate India and surrounding regions yet. And everyone agreed Marrakech sounded Arabic.
We had officially gone from 195 countries to a handful of countries. We knew that Arabic was extensively spoken in the Middle East and North Africa. Meaning we had annexed all of Europe, and a majority of Asia and Africa.
The remainder prominent countries that were obvious to us either as popular tourist destinations or countries that appeared frequently in the media were India, Saudi Arabia, U.A.E, Afghanistan, Pakistan, Iraq, Egypt, Syria, Libya, Algeria, Morocco.
India — It’s a popular country. We knew a majority of the city names and no one could recall ever hearing Marrakech in India.
Saudi Arabia — We knew that asides the holy city of Mecca, tourists did not often visit.
U.A.E — This seemed like a likely option because Marrakech is known for tourism, but everyone knew Abu-Dhabi and Dubai. If Marrakech was in U.A.E, we would have known.
Afghanistan, Pakistan, Syria, Libya & Iraq: We knew Baghdad was in one of these regions and Tripoli was in Libya. The only other thing we knew was that they were either war-torn or under authoritative regimes, so it couldn’t be a hot spot for tourists.
We were left with Egypt, Algeria, and Morocco. We didn’t know much about Algeria asides its capital, Algiers. And we knew Egypt and Morocco as hot spots for tourists. Morocco more than Egypt. It got really tricky at this point, but we made an assumption which was invalid, but even if we did not make the assumption we would have arrived at the right answer.
We assumed that for Marrakech to be so popular that it has to be a capital of a country. We knew that Egypt’s capital was Cairo, and we were also certain that the countries we eliminated earlier did not have their capitals in Marrakech. This left us with Morocco.
We were right. Marrakech was in Morocco. However, the capital of Morocco is Rabat.
We had gone from a 1 in 190 chance of being right, to a 189 in 190 chance of being right by eliminating 189 countries using a broad categorization framework which allowed us to zoom out and solve the problem from a higher level (outside the box, rather than inside the box).
The take-away is this: If you are able to zoom out of the picture, and not focus on the details, you’ll be able to create broad categorizations that allow you to articulate the problem using questions that satisfy the intent of the categorization. Those questions will invariably have a bunch of possible answers. Eliminating the wrong answers will help you solve the problem.
Bonus demonstration: Equality
We did not discuss using Equality as a mental framework in our session, but I thought to include a quick puzzle for you on using equality as a framework
This is a common puzzle. So if you know the answer, I would like you to think deeper about how you could apply this framework in other scenarios.
In mathematics, when there’s an equality sign, denoted by “=”, it means the LHS (left-hand side) of the equation has the same value as the RHS (right-hand side) of the equation. Given the puzzle below, what is the solution for X?
1 = 5
2 = 25
3 = 35
4 = 45
5 = X
Try and solve “X” before moving on.
This is an easy problem that is disguised as a puzzle. Sometimes a problem is shrouded in mystery, “X”, and you will spend time trying to decipher “X”. If you apply the equality framework you will quickly be able to see the solution.
The answer is 1. Equality exists in a natural phenomenon and demonstrates the relationship between naturally occurring things.
Final note, knowing how to think better is an ability you have to work on and be deliberate about improving. It also has a compounding effect, and this is why company executives and really smart people might be more astute than others. So build the ability. It’s important for your career.
There are many more thought experiments I have explored in the past like how to predict behavioral outcomes and Schrodinger’s cat. Some of them are more complex than this. If you had like to talk about this, shoot me an email at ayemijohnson[at]gmail[dot]com.