Six questions

All of these have the same answer.

To understand why, play a simple game.

A coin flip

Would you take this bet?

You have ₹100. I flip a fair coin, twenty times.

Heads+50%
Tails−40%
Rounds20 flips

No tricks, no fees, no small print. Work it out if you like — the arithmetic isn't hidden.

No real money. Nothing to win, nothing to lose. This is a teaching demonstration about averages. The rupees are imaginary. Nothing is staked, paid, collected or won, there is no wager and no prize, and there is nothing to sign up for or pay.

Two questions before you play. They matter at the end.

 
Question 1 of 2

Why are you playing?

There's no name to attach this to.

Question 2 of 2

Where will you finish?

After 20 flips, from ₹100.

Round 0 of 20—
 
₹100.00
imaginary money · nothing is staked or won
You
₹100
Everyone's average
—
Best anyone's done
—
Your twenty flips

You lost money.

You finished with
—
—
Best anyone has managed
—
same coin · same twenty flips · a different order
—

Everyone's twenty flips

Every game sharpens this picture. At a hundred players it is suggestive. At ten thousand it is undeniable.

The reason

Forget twenty rounds. Do two.

Win, then lose100 → 150 → 90
Lose, then win100 → 60 → 90

You won exactly half the time and you're down 10%. Not up 5%.

A 40% fall beats a 50% rise

Lose 40%₹100 → ₹60
To get back you need+67%
But a win only pays+50%

Every loss digs a hole the next win can't fill. Percentages come off whatever is left, and what's left keeps shrinking.

So where did the 5% go?

It's real. It just isn't yours. Line up ten thousand people and the average in that room genuinely rises 5%, because a few get extraordinarily lucky and drag the average up. That number belongs to the room.

You are not a room. You're one person moving through time, and each round multiplies whatever survived the last one.

And it gets worse the longer you play

At a hundred flips instead of twenty, the person who holds up the average turns up about once in 250,000 games. You would never meet them — and the average would still belong to them.

An average across people is not an experience. Nobody lives it. That's how an economy can grow while most people get poorer — and why neither of those is a lie.
Nobody cheated in this game. Same coin, same rules, the same ₹100 for everyone — and it still ends up looking like a rigged world. Some of what we call unfairness is not a fault in the system. It is multiplication doing what multiplication does.

The six questions

Every one of them is the arithmetic you just played.

This was never meant to be a lesson, and it does not answer these. If you are curious why any of them are true, here is where to go digging.

Where to go next →

Built on the work of Ole Peters, Nassim Nicholas Taleb and Mark Spitznagel.

Whose idea this is

The coin flip in this game is Ole Peters', from his work on ergodicity economics — the distinction between what happens on average across many people and what happens to one person over time. The wider argument, that this gap is where ruin and inequality come from, is developed by Nassim Nicholas Taleb and Mark Spitznagel. The maths itself is older still — Jensen's inequality dates to 1906, and the Kelly criterion to 1956. Nothing here is original; this page is only a way of showing it to you.

This is not gambling.

No real money is involved at any point. Nothing is staked, paid, collected or won; there is no wager, no prize, no payment and no account. It is a demonstration of what happens to an average, built for teaching.

No name, no sign-in, no email, no analytics, no cookies. Nothing here identifies anyone.

What is kept is a shared tally: how many games have been played, their combined result, and a count of how many games ended on each of the twenty-one possible outcomes. Those counts cover every game ever played. Separately, every coin sequence is kept, and a random sample of 500 of them is sent to your browser so their lines can be drawn on the chart. A coin sequence is twenty heads-or-tails results and nothing else: no name, no time, no location, no device.