A fair game that ends with a few people owning everything
The yard-sale model: fair coin flips, and wealth still piles up at the top.
100 households start with $100 each. Two at a time, they trade. The stake is a share of the poorer trader's wealth, and a fair coin picks the winner. There's no skill or cheating, and every trade has an expected value of zero for both sides.
Set the stake and a flat tax, then press Run.
household wealth · current richest · bars scale to the leader
The median goes broke
At a 20% stake, the median household is under $1 after about 20,000 trades. By 100,000, the richest ten own 99% and the Gini is around 0.97, more unequal than any country ever measured.
Gains and losses multiply. Lose 20% then win 20% and you're at 1.2 × 0.8 = 0.96. The poorer trader risks a fifth of everything on each flip. The richer one risks pocket change.
Follow any one household over time and it usually shrinks, while a few lucky ones hold up the average.
A 2% tax
Set the tax to 2%. Each round, everyone pays a small share of how far they are above average, and those below get topped up. The collapse stops. The Gini settles near 0.56 and the median household holds around $48. Set it back to zero and the middle class disappears.
In an economy of fair trades where wealth compounds, a few people owning everything is the default. A middle class has to be maintained.
What the model proves
The yard-sale economy is zero-sum. Trades in the world create value for both sides, economies grow, and skill exists. The model drops all that, so it can't say how much inequality is earned.
It does show that extreme inequality needs no explanation in talent or effort. Luck plus compounding is enough. The shape of a wealth distribution tells you almost nothing about the people in it. Same lesson as the segregation model: a pattern that looks intended can come from something else.