A magician asks you to run one of two programs on a computer with a single bit of memory. One picks the bit’s value at random; the other always sets the same value. You run whichever you like and hand him the bit. He tells you which program you ran, and he is right every time. He should not be able to do this. Whether a value was picked at random or fixed in advance is a property of a collection of runs, not of a single bit. Yet real machines do this daily: a quantum computer is a statistical device, and a single instruction in one behaves one way when the instructions before it picked the bit at random, and another when they set it deterministically, though the bit handed to it is only ever a 0 or a 1, with nothing on it to say which. The usual answers go one of two ways. Some add something to the world: a wave that really collapses when anyone looks, a wave that steers the bit, a universe that splits at every measurement. Others remove something from it, holding that there is no fact about the bit’s value at all until someone looks. We take neither route. The only waves are patterns in the collective behavior of bits, not extra entities in the world, and what has to change is the form of the stochastic law those bits obey, which consults the system’s history and not only its present. The experiments and theorems said to forbid this are met one by one: the double slit, Kochen–Specker and Bell, Wigner’s friend, Frauchiger–Renner and Pusey–Barrett–Rudolph. We demonstrate that not one of them contradicts the traditional realist picture, where objects possess properties whether or not anyone is looking. What they constrain is the laws, which must be contextual, non-local and non-Markovian, and which need a preferred ordering of events in time.