The dynamic problem of choosing subsets of objects or “toolkits” when their value distribution is unknown is a multi-armed bandit problem with non-independent arms. Accordingly, except for very simple specifications, this problem cannot (practically) be solved, either analytically or numerically. Decision makers facing this problem must resort to decision heuristics, employing past experience and, perhaps, what they know about the problem. This paper focuses on prior-free heuristics, the simpler and more naive end of the spectrum of heuristics where the decision maker is guided entirely by past experience. Prior-free heuristics can take a variety of forms, depending on the decision maker’s unit of analysis: tools or toolkits. We examine and compare different prior-free heuristics using both analytical methods and simulations. In a companion paper, Francetich and Kreps (2019), we examine heuristics in which the decision maker engages in Bayesian updating of her prior beliefs about the environment.