Expected value
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
A room where nobody is alone
Twenty-three people probably include two who share a birthday. How many are needed before every single person shares a birthday with somebody else in the room? The answer is 3,064 — more than it takes for every day of the year to be somebody's birthday — and the reason is a count of loners, which rises as the room fills, peaks at 134 when the room is the size of the year, and then falls so slowly that the last loner lingers for thousands of arrivals.
Two losing games that win together
Game A is a coin that wins 49.5% of the time. Game B tosses a bad coin when the capital is a multiple of three and a good one otherwise, and it loses too, because the capital spends more than a third of its time on multiples of three. Choose between the two games at random and the walk drifts upwards by 0.0157 a round; play A, B, B over and over and it gains 0.0574. Nothing is wrong with the arithmetic. The losing coin A wins by knocking the capital off the bad remainder.
Named alongside it
The objects these essays reach for when they reach for this one.
Markov chainBirthday problemCoupon collectorDriftParadoxPeriodicityPoisson approximationRandom walkSimulationStationary distribution