Case-based Decision Theory (CBDT) suggests that decisions under ucnertainty are made by analogies to previously-encountered problems. The theory postulates a similarity function over decision problems and a utility functionon outcomes, such that acts are evaluated by a similarity-weighted sum of the utility othey yielded in past cases in which they were chosen. It gives rise to the concept of "aspiration level" in the following sense: if this level is attained by some acts, the decision will only choose among them, and will not even experiment withothers. Thus a case-based decision maker may be "satisficed" with a choice, and will not maximize his/her utility function even if the "same" problem is encountered over and over again. In this paper we discuss the process by which the aspiration level is updated. An adjustment rule is "realistic" if the aspiration level is (almost always) set to be an average of its previous value and the best average-performance so far encountered. It is "ambitious" if at least one of the following holds: (i) the initial aspiration level is set at a high level, or (ii) the aspiration level is set to exceed the maximal average performance by some constant infinitely often. While we propose realistic-but-ambitious adjustment rules for decision under uncertainty at large, we focus here on the case in which the decision maker is repeatedly faced with the "same" problem, assuming that each choice yields an independent realization of a given random variable. We show that if the adjustment rule is realistic-but-ambitious in the sense of (i), then with arbitrarily high probability the decision maker will asymptotically choose only expected-utility maximizing acts. Ambitiousess in the sense of (ii) above guarantees the same result with probability 1, and for all underlying payoff distributions. Hence, case-based decision makers who are both ambitious and realistic will "learn" to be expected-utility maximizers, provided that the decision problem is repeated long enough.