A thousand people inside, ₹100 each. Every round, everyone tosses a fair coin.
On average that’s +5% every toss: ₹100 becomes ₹105 after one toss. A bank FD pays about 7% in a whole year.
There isn’t one. The coin is fair, nobody cheats, and nobody knows anything you don’t. No real money is involved.
After 100 tosses, how many of the 1,000 people will have more than the ₹100 they walked in with?
We’ll come back to your answer.
Everyone starts equal. The crowd is sorted richest first.
Both headlines are true. Same coin, same room, same morning. How?
Of 1,000 people, about 500 get heads and have ₹150; about 500 get tails and have ₹60.
500 × ₹150 + 500 × ₹60 = ₹1,05,000
₹1,05,000 ÷ 1,000 = ₹105
That’s the “+5% on average”. It is true, for one toss.
Each toss multiplies the average by 1.05 again:
1 toss: ₹105 · 2: ₹110.25 · 10: ₹163
100 tosses: ₹100 × 1.05100 = ₹13,150
This is the expected value: what the average would be in a room with infinitely many people.
50 heads, 50 tails:
₹100 × 1.550 × 0.650
= ₹100 × 0.950 = 52 paise
The biggest share of that ₹13,150 comes from people with about 72 heads out of 100. Each of them would have about ₹29 crore. But only about 1 person in 1,59,000 is that lucky, so a room of 1,000 almost never has one, and its average usually comes out lower. Once in a while a room gets one extraordinarily lucky person and shoots past it.
What a room gets depends on how many moderately lucky people it happens to have, so the average swings a lot. In simulated rooms of 1,000, the middle 80% ended between ₹900 and ₹12,500.
| People in the room | Typical room average after 100 tosses |
|---|---|
| 1,000 | ₹2,450 |
| 1 lakh | ₹8,230 |
| 1 crore | ₹11,800 |
| 10 crore | ₹12,650 |
| infinitely many | ₹13,150 |
And more tosses push the other way: a room of 1,000 keeps up with the formula for about 20 tosses, then falls further behind with every toss. You are not a room of infinitely many people. You are one.
Your room after 100 tosses, sorted by how much each person has.
A few people at the top carry the whole average. The average describes them, not the room.
A kurta costs ₹100. Before Diwali, the shop raises the price by 50%.
Then comes the Mega Sale: 40% off. What does the kurta cost now?
It costs ₹90. The 40% came off ₹150, so it took away ₹60. The 50% had only added ₹50.
That was one heads and one tails. A win and a loss, and you’re 10% poorer. That’s the coin, every time.
Most people in the room get about as many heads as tails: 50 and 50 in 100 tosses. That’s this sale, fifty times over: ₹100 becomes 52 paise.
Everyone at the stall has ₹100. The average is ₹100. Fair enough.
The average is now . Did anyone at the stall get a single rupee richer?
Nobody did. The average just followed the one very rich person.
The room’s average is what the whole crowd adds up to. Your money is one person, one toss after another, and each win-then-loss is another kurta sale.
People found two ways to beat this coin long before anyone wrote down the maths: bet less, or share. Pick a rule and replay your room.
“Sharing isn’t charity.
It’s arithmetic.”
Joint families, village grain stores, chit funds, insurance: people built these long before anyone could explain why they work. On your own, a fair coin can quietly ruin you. Together, the same coin makes nearly everyone richer.
And the next time you read that “the economy grew”, remember the chai stall. An average can rise while most of the people inside it fall.
The coin and the case for pooling come from Ole Peters and Alexander Adamou’s work on ergodicity economics. “Bet a quarter” is the Kelly rule (1956). Nothing here is original; this page only shows it.
What it leaves out: real life isn’t a fair coin, and real pooling needs trust and rules. No money is involved, and nothing you do here is stored or sent anywhere.