whatFour hundred commuters cross a diamond of roads from west to east, over and over, each picking whichever route currently reads fastest. Two mirror routes: a congestible leg whose travel time grows with the fraction of drivers on it, then a wide fixed-time leg, or the reverse. The dashed line down the middle is a shortcut the city can open. The ticker bottom right is the average trip, with the honest optimum dotted.

whyBraess's paradox, measured: left alone the drivers split half and half and settle at six and a half seconds. Open the nearly free shortcut and each driver reasons that two congestible legs and a free hop beat queueing on a wide road; nine in ten defect, packing both congestible legs with everyone, and the average climbs to eight. Nobody can do better by switching, yet all are worse off than before the road existed. Close it and the traffic heals. An extra road here is a tax.

howFlow-priced congestion, the classic ledger: a congestible leg costs in proportion to the fraction of current travellers whose chosen route uses it; wide legs are constant; the shortcut is nearly free. Drivers re-choose at each departure with a whisper of exploration, which is enough to find the Nash equilibrium either way. Click to open or close the shortcut; left alone the city cycles it. One integer seeds every driver's temperament.