The Hadamard gate `h` takes |0⟩ to (|0⟩ + |1⟩)/√2: both amplitudes are 1/√2, so a measurement gives 0 or 1, each with probability (1/√2)² = 1/2.

That is a *superposition*: not a qubit that is secretly 0 or secretly 1, but a state with an amplitude for each. The difference is invisible to one measurement, and it is what the lessons on interference use.

The engine does not sample to check a distribution. It computes the state exactly and reads the probabilities from it, so "exactly one half" means one half, not 0.497 from a thousand shots. A run with shots still samples, and its counts scatter around the exact values:

```sh runnable
cat > coin.qasm <<'QASM'
OPENQASM 3.0;
include "stdgates.inc";
qubit[1] q;
bit[1] c;
h q[0];
c = measure q;
QASM
wai-quantum run coin.qasm --shots 1000 --seed 7
```