An agent choosing between various actions tends to take the one with the lowest cost. But this choice is arguably too rigid (not adaptive) to be useful in complex situations, e.g., where exploration- exploitation trade-off is relevant in creative task solving or when stated preferences differ from revealed ones. Here we study an agent who is willing to sacrifice a fixed amount of expected utility for adaption. How can/ought our agent choose an optimal (in a technical sense) mixed action? We explore consequences of making this choice via entropy minimization, which is argued to be a specific example of risk-aversion. This recovers the ε-greedy probabilities known in reinforcement learning. We show that the entropy minimization leads to rudimentary forms of intelligent behavior: (i) the agent assigns a non-negligible probability to costly events; but it          (ii) chooses with a sizable probability the action related to less cost (lesser of two evils) when confronted with two actions with comparable costs; (iii) the agent is subject to effects similar to cognitive dissonance and frustration. Neither of these features are shown by entropy maximization.