Yard Sale

0Gini: 0 = everyone has the same, 1 = one person has it all

10%of all money held by the richest 10% of people

50%held by the poorer half of the town

–held by the richest single person

richest 1% next 9% middle 40% poorer half circle size = money · click people to follow them

Who holds the money

richest 1% richest 10% poorer half Gini a change you made

The people you follow

Click someone in the town to follow their money (up to 6).

Lorenz curve: now

People lined up from poorest to richest (across) against the share of all money they hold together (up). The straight line is a perfectly equal town; the further the curve sags below it, the more unequal.

How much tax is enough?

Each point: a town with your rules, run until it settles, at one wealth tax rate.

Why: the ±20% coin

Why the money piles up when nobody has an edge

Every trade is fair in euros: on average nobody gains or loses. But it is not fair in percent, and in this game percent decides who survives. Four steps:

1. Up 20% and down 20% do not cancel

You have €100. Win 20%: €120. Lose 20%: €96. The other way round: €80, then €96 again. One win and one loss, and 4% is gone. The bigger the swings, the bigger the leak: ±10% loses about 1% per pair, ±50% loses 25%. The ±20% coin chart above shows 1,000 players doing this 100 times.

2. The poor bet a big share, the rich a tiny one

The bet is a share of the poorer player's money. Rich has €1,000, Poor has €10, so they play for €1:

	Poor	Rich
Poor wins	€11 (+10%)	€999 (−0.1%)
Poor loses	€9 (−10%)	€1,001 (+0.1%)

Same euro, but Poor swings ±10% and Rich ±0.1%. By step 1, big swings leak money and tiny ones barely do. In every meeting, the poorer player pays the hidden cost.

3. Winning back does not make you equal again

Two friends with €100 each, playing for 10% of the poorer one's money. A wins: A €110, B €90. Then B wins back, but now the bet is 10% of B's €90 = €9: A €101, B €99. One win and one loss each, yet B is behind. Falling behind is easy and catching up is hard: there is no safe middle. Try it below.

4. Money cannot vanish, so it piles up somewhere

Steps 1 to 3 pull almost everyone down a little in every trade, the poorer the faster. But the total stays the same (€100 each on average). So the money flows to the few who happened to win early, and since they then risk only a sliver of their fortune per trade, they keep it. Nobody cheated and nobody was smarter: early luck, then the rules protect the winners.

Try it: two players, a fair coin

Both start with €100 and play for 10% of the poorer one's money. Press the buttons and watch: wins and losses even out in number, but not in euros.

€100.00

What happened

Why a small tax is enough

The leak from step 1 is small per trade: with 10% bets, about 0.5% of a player's money (half the bet share, squared). A wealth tax shared out equally hands everyone the same number of euros back. For a poor player that is a big percentage, enough to plug the leak; for a rich player the tax is a small percentage cut. So already 0.1% per round stops the slide to one owner, and about 1%, twice the leak, keeps the town fairly equal. Run the tax test above with your own rules.

And when the rich have an edge?

Then the coin itself is no longer fair: the richer player wins a bit more often. That is a push in the wrong direction on top of the leak, and the tax has to beat both. With a rich edge of 0.2, a 0.1% tax still leaves the town almost as unequal as no tax at all (Gini 0.86); it takes about 1% to bring it back to 0.5. Try "The rich get an edge".

Run

Speed

In one round everyone meets one random person and they trade.

Try this

The money game

Everyone gives €1 to a random person each round. It gets unequal, but it stops there: like a fair lottery, today's winner is tomorrow's loser.

Yard sale

Pairs flip a fair coin for 10% of the poorer one's money. Every single trade is fair, yet almost all the money ends up with a few people.

A tiny tax

The same, but every round everyone pays 0.1% of their money into a pot that is shared equally. Look how much that changes.

The rich get an edge

The coin leans a little toward the richer player (better lawyers, better deals). Now a tiny tax is not enough.

A safety net

No wealth tax, but nobody may fall below half the average: everyone above chips in. It also stops the collapse.

The rules

Game Bet size Rich edge People Start

Bet size: the share of the poorer player's money at stake in each trade. Rich edge: how much the coin leans toward the richer player (0 = fair; the lean grows with the gap between them). People and Start make a new town.

Taxes and help

Wealth tax Tax only above Tax on wins Safety net

Wealth tax: share of everyone's money (or only the part above the line) paid each round. Tax on wins: share of every win. All tax goes into one pot that is shared equally among everyone, so no money is lost. Safety net: nobody falls below this share of the average; the richer pay for it. All of these apply at once.

Why it happens

Two reasons. First, losing 20% then winning 20% leaves you with 96%: wins and losses of the same percentage do not cancel, so a run of fair bets slowly drains most players while a lucky few pile up the money. Second, the bet is a share of the poorer player's money, so the rich risk only a sliver of their fortune in each trade while the poor risk a real chunk of theirs. Nothing stops the slide, until something pulls the other way: a tax shared out equally gives the poor a steady push back up. Physicists and economists (Chakraborti 2002, Boghosian 2014-2017) found this simple model fits real wealth data surprisingly well, including how much the rich's edge and a country's taxes matter.