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Our intuitions often leads us astray. A good reminder: study counterintuitive math and economic results.

Here are 9 of them 🧵

 The Birthday Paradox

In a room of 23 people, there's a >50% chance that 2 people share the same birthday.

This type of probabilistic thinking does *not* come naturally to many people.
The Coastline Paradox

Fractal geometry is also confounding:

The coastline of a landmass does not have a well-defined measurement. As the unit of measurement gets smaller (eg. from KMs to cm), the length increases without limit.
Winner's Curse

In an auction, the winning bid will usually exceed the intrinsic worth of an item leading to a significant overpay (and negative net profit for the winner).
Braess's Paradox

Removing an extra road can make everyone's commute time faster.

Why? The existence of a "fast" road leads to congestion because everyone uses it. If you remove the shortcut, traffic flows better.
Market for Lemons

If a seller has slightly more info than a buyer (eg used cars), it can lead to market failure:

◻️Buyer will pay price below market (b/c they can't confirm quality)
◻️High-quality sellers leave market b/c can't get good price
◻️Only low-quality sellers remain
The Potato Paradox

If you take 100lbs of potatoes which are 99% water by weight and you let it dry so that they are 98% water, their new weight is 50lbs.
The Pizza Paradox

One 18-inch pizza has more "pizza" than two 12-inch pizzas (still trying to process this fact).
Littlewood's Law of Miracles

An example of the law of large numbers: A person can expect to experience events with odds of one in a million at the rate of about once per month.

(Similarly: in a world with ~8B people, a one-in-billion event will happen 8x a month)
Queuing Paradox

If bank customers take on average 10 minutes to serve and they arrive randomly at a rate of 5.8 per hour...then the waiting time for

◻️one teller is *5 hours*
◻️two tellers is *3 minutes*

Waiting time is reduced by 93x by adding a second teller.
PS. I write interesting threads like this 1-2x a week. Follow @TrungTPhan to catch them in your feed.

Also check out my weekly Saturday newsletter:https://t.co/jGZs8brnVR
Sources

Here's the breakdown of the queueing theory: https://t.co/2vunn5mMTz

Check this awesome article for dozens more counterintuitive math, science + physics facts: https://t.co/8sejjm6AkH
VERY counterintuitive fact: Gabriel's Horn is a geometric figure with:

◻️ *infinite* surface area
◻️ *finite* volume
Deep dive on the Birthday Paradox https://t.co/3AAXUUVGP9

More from Trung Phan 🇨🇦

Trung Phan
Trung Phan
@TrungTPhan
Steve Jobs famously said innovation is "saying no to 1000 things" before you say yes.

For more than a decade, Apple has used Pablo Picasso's Bull to drive home the lesson.

Here's a breakdown 🧵


In Dec. 1945, Picasso created "The Bull", a series of 11 lithographs (stone prints).

With each successive print, a bull is simplified and abstracted. Picasso's goal was to find "spirit of the beast".

At Apple, employees are taught this philosophy.


Below are the 1st, 4th and last stone print.

The bull progresses from:
◻️a realistic drawing
◻️to a deconstructed image w/ the famous "abstract" style
◻️to lines outlining a shape

Through 11 iterations, Picasso simplified the image until it captured the "essence" of the bull.


Picasso said of the abstraction process:

"Two holes. That’s the symbol for the face, enough to evoke it without representing it. But isn’t it strange that it can be done through such simple means? Whatever is most abstract may perhaps be the summit of reality.”


Enter Apple University.

In 2008, Steve Jobs tapped the dean of Yale School of Management to create an internal training curriculum for Apple.

The program was meant to teach new employees Apple's culture and design philosophy (the teachings are rarely shared with the public).
ALL
Trung Phan \U0001f1e8\U0001f1e6
Trung Phan 🇨🇦...
@TrungTPhan
For decades, Jeff Bezos shunned ads.

But now, Amazon’s ad business is huge: it’s on a $30B+ annual run rate (more than 2x the combined sales of Twitter, Snap and Pinterest).

Here’s how it happened 🧵


1/ Amazon doesn’t break out its ad business separately in financial filings. However, most analyst believe ads make up the majority of its “Other” revenue segment.

This figure has exploded from $1B in 2015 to a current annual run rate of ~$32B.


2/ In 2009, Bezos said “ads are the price you pay for a crappy product”.

But the business is so lucrative that Amazon’s interface has been swamped with ads:

◻️ First 3-7 search results (left in red)
◻️ Most of the product page (right in blue)


3/ Prior to the rise of ads, Amazon set out to build the ultimate organic customer recommendations engine.

The approach was codified in a famed 2003 research paper: “Amazon Recommendations: Item-to-Item Collaborative Filtering.”


4/ In recent years, Amazon organic recommendations:

◻️"Customers who bought this also bought this"
◻️"Customers who viewed also viewed"

Have been replaced w/ ads:

◻️ "Sponsored products related to"
◻️ "Brands related to this category"
TECH
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Trung Phan \U0001f1e8\U0001f1e6
Trung Phan 🇨🇦...
@TrungTPhan
A Netflix user will browse the app for 90 seconds and leave if they find nothing.

Thumbnail artwork is actually NFLX's most effective lever to influence a viewer's choice. A user will look at one for only 1.8 seconds, so NFLX spends huge to optimize them.

Here's a breakdown🧵


1/ Spoiler alert: humans are visual animals.

Our eyes move 3-4x per second to process information and we can analyze an image in as little as 13 milliseconds.


2/ In 2014, Netflix consumer research showed that thumbnail artwork:

◻️ is "the biggest influencer...to watch content"
◻️ is the focus of 82% of browsing time

A user looks at one for only 1.8 seconds. If they can't find Netflix content in 90 seconds, they'll leave the app.


3/ Consequently, Netflix uses an elaborate thumbnail selection process for each of its 200m+ users.

The process is called aestethic visual analysis (AVA), which starts by pulling all the frames from a video.

For reference: a 1hr episode of "Stranger Things" has 86k frames.


4/ In a process known as "Frame Annotation", each frame is tagged with metadata identifying key variables:

◻️ Saliency
◻️ Frame #
◻️ Brightness / Contrast
◻️ Nudity probability
◻️ Face / skin tone
ALL , MARKETING INSIGHTS
Trung Phan \U0001f1e8\U0001f1e6
Trung Phan 🇨🇦...
@TrungTPhan
“I spend too much at Starbucks” is a legendary meme.

It's also not an accident: the coffee retailer -- worth $120B -- uses many psychological hacks in its store and menu designs to get you to drop more cash.

Here are 11 of them 🧵


1/ Starbucks is all about positioning

The chain has higher prices vs competitors. But that's the point.

People typically assign higher value/quality to higher prices. Known as "irrational value assessment", this makes Starbucks an everyday luxury that people will pay for.


2/ Premium brand = premium customer base

By setting its prices higher, Starbucks attracts clientele that are relatively price insensitive.

Starbucks frequently raises its prices with little negative effect to its bottom line.


3/ "More than coffee"

Former Starbucks CEO Howard Schultz created the premium feel by emphasizing experience:

◻️Positioned SBUX as a "third place" (b/t home, work)
◻️Brought bean grinding in-store (for aroma)
◻️Banned auto espresso machines (it took away from the barista craft)


4/ Lighting and visual cues

The Starbucks operations is about "flow", efficiently moving people around the store+ getting them to spend.

To form lines, it directs people to well-lit areas (usually the merchandise, which provides the added benefit of nudging products for sale).
BUSINESS MENTAL MODELS
\U0001d683\U0001d69b\U0001d69e\U0001d697\U0001d690 \U0001d67f\U0001d691\U0001d68a\U0001d697 \U0001f1e8\U0001f1e6
𝚃𝚛𝚞𝚗𝚐 𝙿𝚑𝚊𝚗 🇨🇦...
@TrungTPhan
1/ Marcus Bullock went to prison in the mid-90s at the age of 15.

Today, he's the CEO of Flikshop -- the "Instagram for the Incarcerated", an alternative to the outrageously expensive phone call system.

This is a truly inspirational founder story 👇👇


2/ In 1996, Bullock was living in Maryland. One night, he and a friend carried out an armed carjacking on a man sitting idle in a shopping mall parking lot.

It was the biggest mistake of this life.

3/ Several years prior to hit actions, there was the famed 1989 Central Park "Jogger Case", in which 5 minority youths were (falsely) accused of raping a jogger.

In the aftermath, nearly every state passed new laws that made it easier for courts to try youth as adults.


4/ For the carjacking, Bullock was charged as an adult and served 8 years in prison.

With onerous prison phone charges ($18 / 15 mins), Bullock's mother kept in touch with him by sending a photo or letter every day.

"She saved me," he says of his mom's efforts.


5/ The $1.2B+ prison phone system is dominated by 2 PE-backed firms (Global Tel Link, Securus Tech).

For the right to operate these phones lines, prisons effectively pay kickbacks to state and local government. The highest kickbacks win bids, which drive up costs.
CULTURE

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Brian Feroldi
Brian Feroldi
@BrianFeroldi
My investing style: Buy and hold high-quality businesses

Here are 15 traits that tell me I've found a great business ⬇️

1/ Recurring Revenue

Types:

Business Services $MCO
Contracts $AMT
Consumables $MNST
Exchange $MKTX
Franchise $WINA
Membership $TDOC
Platform $ETSY
Razor/blade $DXCM
Real Estate $STOR
SaaS, PaaS, IaaS $TWLO, $NOW, $FSLY
Subscription $NFLX
Tollbooth $BIP


2/ Recession-Proof Demand

Great companies sell products/services that are in-demand in good times and bad

That allows them to grow regardless of what is happening in the broader economy


3/ Organic Growth

"Organic" growth: Growing by increasing sales of internally developed products/services

"Inorganic" growth: Growing from mergers & acquisitions

Organic Growth > Inorganic Growth


4/ High & Expanding Gross Margin

Indicates that the company’s products/services create a huge amount of value for the customer

Rising gross margin also indicates pricing power
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Kostas \U0001f468\u200d\U0001f4bc \U0001f4c8 \U0001f4b8
Kostas 👨‍💼 📈 💸...
@itsKostasWithK
If you want to become financially independent and don't know where to start, here is a thread that will help you get started

/THREAD/

1. Review your expenses and make a budget

It will help you see where you overspend, make a plan to save, pay down debt and start


2. Set your investing and retirement goals

How much do you need to support yourself in retirement and when do you want to


3. The earlier you start investing, the better.

Here's why and how time and compounding can become your


4. Invest in an index fund

It's easy, safe, cheap, and the best choice for a beginner in investing, with not much time for
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10-K Diver
10-K Diver
@10kdiver
Get a cup of coffee.

Let's kickstart 2022!

To that end, here are 22 key concepts to help you appreciate and achieve Financial Independence.

Concept #1.

What is Financial Independence?

It's a state of *self-sufficiency*. It's when you have enough money, and enough income-producing assets, that you and your family can live comfortably for the rest of your lives -- WITHOUT needing a job.

Concept #2.

Financial Independence is not really about spending MONEY how we like -- although, to an extent, that becomes possible.

It's about being FREE to spend our TIME how we like.


Concept #3.

Financial Independence is not really about quitting our jobs and retiring from work -- although that's possible.

It's about being FREE to pursue *whatever* kind of work we find most fulfilling. Things we love to do. Things the world benefits from. Etc.


Concept #4.

For most of us, the path to Financial Independence consists of:

- Starting Early,
- Saving Diligently, and
- Investing Responsibly.

Here's an inspiring story of a janitor who amassed an $8M fortune by following this very playbook:
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Shuchi Nahar
Shuchi Nahar
@shuchi_nahar
To understand Financial Shenanigans & detect accounting manipulations from Annual Reports with checklist
In detail and lucid terms

Financial Shenanigans
(Part-1)
https://t.co/wa6HSElug0

(Part-2)
https://t.co/Vrva17GvgP

(Part-3)
https://t.co/XuziOCDHL2

@dmuthuk @ms89_meet
FINANCE , ACCOUNTING AMP FINANCIAL STATEMENTS
Investment Books (Dhaval)
Investment Books (Dhav...
@InvestmentBook1
10 Key Takeaways from the book: The Emotionally Intelligent Investor


1. Investing success does NOT come from ignoring or suppressing emotion. Assuming that you have relevant expertise, disregarding intuition and empathetic feelings because they cannot be explained, is a mistake!

2. Self-awareness is the first and most important step in improving as an investor. An investment approach needs to fit with your unique set of motivations, personality traits, weaknesses, and strengths. Don’t try to be exactly like Warren Buffett if you are not like him!

3. Humans have certain common investing vulnerabilities, but everybody is unique in their susceptibility to them. Consider your weaknesses to be the investing biases and traps to which you are most prone.

4. Because we are constantly changing, introspection should be incorporated into the daily and weekly routines of any investor. Try writing in a trading/Investing journal.
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Seek wealth, not money or status. Wealth is having assets that earn while you sleep. Money is how we transfer time and wealth. Status is your place in the social hierarchy.

Understand that ethical wealth creation is possible. If you secretly despise wealth, it will elude you.

Ignore people playing status games. They gain status by attacking people playing wealth creation games.

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PAKISTAN-INDIA WATER ISSUES – HOW INDIA STOPPED WATER IN PAKISTAN's CANALS IN 1948

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After partition in 1947, the water system was also bifurcated between Pakistan n India.

India cheated Pakistan when on April 1, 1948, India suddenly n without warning stopped...
1/n


...the supply of waters flowing into Pakistan's Central Bari Doab and Dipalpur Canals.

The boundary award on the partition of the sub-continent had left the headworks of these canals in Indian territory, and in accepting it India had implied her willingness to leave...

2/n


...the historic distribution of common waters undisturbed.

India's action was therefore in flagrant disregard not only of international law n morality, but of her solemn commitments with Pakistan and a gross violation of this country's historical rights over common waters.

3/n

Faced with a threat of utter desolation of millions of acres of fertile land, Pakistan had perforce to sign a document with India in which she agreed to "India's progressively diminishing water supplies to these canals and to the West Punjab government's tapping...

4/n

...alternative resources".

A specific reservation was made in the document with regard to India's claim that she had full property rights over waters flowing into her territory, and could therefore use them as she liked.

The issue was, however, to be examined...

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Remember: Just because an idea is old doesn't mean it's good.

Knowing whether old ideas are more likely to be good requires understanding whether conditions have changed in important ways.

Horse archery was an amazing method of warfare for over a thousand years...then people invented guns, and suddenly this great idea that had stood the test of time became obsolete.

Then again, when underlying conditions don't change much, tried-and-true approaches are probably better.

"Learning the lessons of history" usually just means assuming ergodicity and stationarity in an informal time-series model...

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LESSER KNOWN DETAILS ABOUT THE BATTLE OF PRATAPGAD - THIS YOU ALL SHOULD READ

In the 1659 Adilshah sent Afzalkhan with the army of 75000 soldiers to destroy Chhatrapati Shivaji Maharaj with his empire. He was the main soldier, warrior and minister in Adilshahi Sultanate.


He was the Subhedar of Wai province.

He was very powerful physically. His height was 7.3 ft. due to same he was very popular as a strong man from Adilshahi Sultanate.

Whole India was not daring to fight with Adilshahi due to Afzal Khan.

Badi Begum Sahiba sent him to kill Chhatrapati Shivaji on any cost.

Voluntary he decided to destroy Chhatrapati Shivaji’s empire with him. He started his operation against Chhatrapati Shivaji from "wai". He destroyed many temples like as Tulja Bhavani Temple.

He destroyed so many villages, killed villagers to torture Chhatrapati Shivaji.

DETAILED VIEW- Running commentary

1. Chhatrapati Shivaji chose Pantaji as a lawyer to communicate with Afzal Khan. Pantaji was very sharp minded, who did his job very nicely.

2. He presented Chhatrapati Shivaji is fearing Afzal Khan and he wanted to invite him in his kingdom near Pratapgad.

3. Pantaji succeed in the communication with Afzal Khan and he brought him as per the planning of Chhatrapati Shivaji.
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THE LAST PRINCESS OF LAHORE - BAMBA DULEEP SINGH (1869 - 1957)

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Post partition, every morning a weak old woman would board the Model Town bus service headed to the city. The conductor never asked her for money or he would invite anger of the last Queen of Punjab.

1/n


Princess Bamba Sutherland, the eldest daughter of Maharaja Duleep Singh and grand-daughter of Maharaja Ranjit Singh, was born on Sep 29, 1869, in London.

Duleep Singh, the last Maharaja of Punjab was taken away to England by British after annexing Punjab.

2/n


Since he was still a child he was forcibly converted to Christianity and made to adopt British values in order to prevent him from ever thinking about regaining Punjab.

He was also kept away from his mother Maharani Jindan.
When he finally met his mother years later...

3/n

...he was told about his lost kingdom and religion after which he decided to reclaim it from British treachery.
During his struggle he married and had six children, 3 sons & 3 daughters from the 1st marriage.

Bamba was the most colorful character among 6 and was a rebel...
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...like her father and daring like her Grandfather Ranjit Singh. She married Col Sutherland who later became principal of King Edward Medical College.

When she got permission to bring her grandmother Maharani Jindan's ashes to Lahore in 1924, she saw a huge crowd gathered...
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