A test of ve-theories of risk and the effect of the central limit theorem

There are several theories of risk which indicate that risk could be a function only of variance and expectation. A transformation on odds or skewness was constructed which left the variance and expectation of a gamble unchanged. Perceived risk was clearly a function of this transformation as well as variance and expectation, even under multiple play in which the effect of the central limit theorem modifies the effect of skewness but it remains a relevant variable.