The mathematical theory entirely based on the opposite statement that some events can be casual (that is controlled by the pure case, uncontrollable, occurring without any specific purpose) had few chances to be published and approved. The mathematician M.G.Candell remarked that «the mankind needed, apparently, some centuries to get used to the idea about the world in which some events occur without the reason or are defined by the reason so remote that they could with sufficient accuracy be predicted with the help of causeless model». The idea of purely casual activity is the foundation of the concept of interrelation between accident and probability.

Equally probable events or consequences have equal odds to take place in every case. Every case is completely independent in games based on the net randomness, i.e. every game has the same probability of obtaining the certain result as all others. Probabilistic statements in practice applied to a long succession of events, but not to a separate event. «The law of the big numbers» is an expression of the fact that the accuracy of correlations being expressed in probability theory increases with growing of numbers of events, but the greater is the number of iterations, the less frequently the absolute number of results of the certain type deviates from expected one.