  If an artificial intelligence aims to maximise 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 (${\Upsilon}$) 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 give an
algorithm for estimating ${\Upsilon}$ and ${p_U}$ in finite cases and discuss
how to deal with infinite strategy spaces. We show how this principle can be
used to help detect unethical strategies and to estimate ${\eta}$. Finally we
sketch some policy implications of this work.
