▷ impossibility of a gambling system principle

Principle of the impossibility of a gambling system:

Principle that a properly defined collective (see frequency theory of probability) will be random in a sense that makes it impossible to construct a system for predicting results with any greater probability than would be possible without the system.

The principle was named by the German mathematician and philosopher Richard von Mises (1883-1953).

The key condition is that the limiting frequency of the characteristic concerned should be the same for all partial sequences we could select from the collective, provided only that whether a given term in the collective is taken into a partial sequence is independent of whether that term manifests the characteristic concerned.

Source:
R von Mises, Probability, Statistics and Truth 2nd edn (1939), 30-35

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