Decision making under risk is often studied as a preferential
choice governed by stable individual personality
characteristics, but risky choice can also be viewed as a
dynamic problem of resource accumulation to survive. When
decision makers aim to reach a particular goal in limited time,
such as “earn at least $100 in five choices,” risky choice
becomes a non-trivial planning problem. This problem has an
optimal solution that can differ from immediate expected-value
maximization. We studied the optimality of risky choices under
such minimum goal requirements experimentally and find that
the observed choices under goals approximate the optimal
solution. However, because the optimal model is very complex,
we examine if simpler models can predict people’s choices
better. We test an extended version of prospect theory,
assuming a dynamic reference point that depends on the
distance to the goal. This “dynamic prospect theory” was better
than the alternative model in describing people’s decisions
(i.e., for 63% of the participants, it was the best model). Our
findings show that humans can excel in a highly complex,
dynamic, risky choice problem and that a dynamic version of
prospect theory provides one possible explanation for how
people decide under risk when long-term goals matter.