  Under the assumption that the quantum random number generator Quantis by Id
Quantique is a fair quantum coin, experimental indications of the fact that
independent tosses of a quantum coin don't pass the Iterated Logarithm
Randomness' Test are shown.
  The consequential observed experimental violation of the Martin L\"{o}f -
Solovay - Chaitin Axiom of Reduction of Quantum Mechanics is then interpreted
as the indication of the necessity of replacing it with the weaker Von Mises -
Church Axiom of Reduction whose Game Theoretic meaning is explained.
