If an artificial intelligence aims to maximize risk-adjusted return, then under mild conditions it is disproportionately likely to pick an unethical strategy unless the objective function allows sufficiently for this risk. Even if the proportion eta of available unethical strategies is small, the probability p(U) of picking an unethical strategy can become large; indeed, unless returns are fat-tailed p(U) tends to unity as the strategy space becomes large. We define an unethical odds ratio, Upsilon (capital upsilon), that allows us to calculate p(U) from eta, and we derive a simple formula for the limit of Upsilon as the strategy space becomes large. We discuss the estimation of Upsilon and p(U) in finite cases and how to deal with infinite strategy spaces. We show how the principle can be used to help detect unethical strategies and to estimate eta. Finally we sketch some policy implications of this work.