whatFour hundred agents start equal, each drawn as one vertical stroke scaled by its wealth. Two meet at random and wager a fifth of the poorer one's wealth on a fair coin, four thousand trades a second. Nobody cheats; every flip is fifty-fifty. That is the entire economy. The bow bottom right is the Lorenz curve against the diagonal of perfect equality; the trace above it is the Gini index.

whyThe claim: fairness condenses. Multiplicative luck compounds, and the poorer you get the smaller your bets and the slower any recovery, so the field of equal strokes wilts into stubble beneath a few towering fortunes with no villain anywhere in the rules. The Gini climbs from zero toward one and the Lorenz bow scrapes the corner. Then the other half: a redistribution tax, slow beside the churn of trading, holds a middle class that fair trading alone can never keep. Slide it and the stubble grows back.

howThe yard-sale model: stake is a fifth of the poorer side, winner takes it. The tax drifts every wealth toward the mean at the slider's rate per second, which is a flat wealth tax rebated equally. Click for a jubilee: wealth reset equal, and condensation begins taking it all again. Gini and Lorenz are recomputed from a full sort twice a second. One integer seeds every meeting and every coin, so the same seed grows the same fortunes.