Verdict

half of these stamps are yours.

stop the flickering die, then say whether the mark was your thumb or the machine

A die flickering between two faces is stopped by a press. Half the time the face that was showing is the face that lands; the other half a face was drawn when the form arrived and the press only plays along. Both settle identically, and nothing about the descent differs between them, so the only information is the face that was showing when your thumb landed against the face that locked. Whether you can hold on to the first one depends on how long it was there: at twelve flickers a second it is gone before the press finishes and the score comes out near chance. Slow the flicker down on ?tune and the difference becomes plain, which is the whole of it: whether a control is real is a fact about the machine, and whether it feels real is a fact about how fast it is moving.

Concepts: perception, randomness, illusion.

An interactive you play with one thumb, on Wundr.