The most useful definition that I have run across is:
An inability to predict future outcomes based on previous results.
Outcomes of indivudual events, of course. Averages of future outcomes (and variances, etc.) may be easily predicable. One cannot predict which radioactive atoms will decay, but one can predict how many will decay in a given time.
Likewise, an English actuary can predict how many people will die during the next year, but not which ones; that would take a Sicilian actuary.