Collapse of Determinism

FOR a profound study, of the question of determinism in physics, reference may be made to Prof. J. von Neumann's ``Mathematische Grundlagen der Quantenmechanik'', p. 157 et seq. I doubt if any very simple treatment can be quite rigorous; but in connexion with Mr. Barkas's point, the following line of thought might be profitable. If a coin is tossed a thousand times and the number of occurrences of heads recorded, and if this experiment is repeated a very great number of times, there will be a statistical regularity in the records, which may be calculated by the ordinary theory of probability. Does the calculation at any stage involve the assumption that the tossing of coins is crypto-deterministic, or does it involve only the assumption (as regards the tossing) that there is symmetry in the system, so that there is no reason to expect heads rather than tails in a single trial?