Risk and Uncertainty

Uncertainty is measurable as a probability when all outcomes of certainty are defined. A probability of certainty is uncertainty, the entropy. Uncertainty is the randomness among certain outcomes.

Uncertainty is distinct from risk. If risk is a quantity susceptible of measurement, then risk is a measurable uncertainty. Risk that is un-measurable is not in effect an uncertainty at all but a result of any number of random unknowns.

Risk is defined as uncertainty only when it can be based on (quantitative) probability. It must by definable with an uncertainty, or variability of returns measured by a standard deviation of returns around a mean.

Risk can not assign such a probability if it can not be reduced significantly by attempts to gain all information about the phenomena in question and their causes or a defined uncertainty.

Risks of stock investments guess at immeasurable possibilities.
Risks of games of chance are uncertain at measurable probabilities.

Probabilities of measurable risks exactly predict every uncertainty in a game chance.
Randomness of real-world risks use mathematical models that attempt to predict immeasurable estimates of unknown situations as if it were a probability in a game of chance. The result is occasionally a good example of Feynman’s Cargo Cult Science.