The propensity to make risky choices has a genetic component, and recent studies have identified several specific genes that contribute to this trait. Since risk-taking often appears irrational or maladaptive, the question arises how (or if) natural selection favors risk-taking. Here we show, using a stochastic simulation of selection between two hypothetical species, "R" (risk-seeking) and "A" (risk-averse) that, when expected reproductive fitness of the individual is unaffected by the making of the risky choice (winnings balanced by losses) natural selection (taken to the point of extinction) favors the risk-averse species. However, the situation is entirely reversed if offspring are permitted to inherit a small fraction of the parent's increased or decreased fitness acquired through risk-taking. This seemingly Lamarckian form of inheritance actually corresponds to the human situation when property or culture are transmitted in families. In the presence of this "cultural inheritance", the long-shot risk-taking species was overwhelmingly favored, even when 90% of individuals were rendered sterile by a losing choice. Given this strong effect in a minimal model, it is important to consider the co-evolution of genes and culture when interpreting the genetics of risk-taking. This conclusion applies, in principle, to any species where parental resources can directly affect the fecundity of offspring. It might also be relevant to the effects of epigenetic inheritance, if the epigenetic state of zygotes can be affected by parental experiences.