**Abstract.** 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 accumulation a particular resource in limited time, such as “earn at least 32 in five choices,” risky choice becomes a non-trivial planning problem. This problem has an optimal solution that differs from immediate expected-value maximization. We studied the optimality of risky choices under such minimum resource requirements experimentally and find that the observed choices under requirements approximate the optimal solution. However, because the optimal model is very complex, we examine if simpler models can predict people’s choices. We test an extended version of prospect theory, assuming a dynamic reference point that depends on the distance to the requirement. This “dynamic prospect theory” was better than the alternative model in describing people’s decisions (ie, 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 requirements matter.