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The most simple evolutionary algorithm (EA), the so-called (1 + 1) EA, accepts an offspring if its fitness is at least as large (in the case of maximization) as the fitness of its parent. The variant (1 + 1)* EA only accepts an offspring if its fitness is strictly larger than the fitness of its parent. Here, two functions related to the class of long-path functions are presented such that the (1 + 1) EA maximizes one in polynomial time and needs exponential time for the other while the (1 + 1)* EA has the opposite behavior. These results demonstrate that small changes of an EA may change its behavior significantly. Since the (1 + 1) EA and the (1 + 1)* EA differ only on plateaus of constant fitness, the results also show how EAs behave on such plateaus. The (1 + 1) EA can pass a path of constant fitness and polynomial length in polynomial time. Finally, for these functions, it is shown that local performance measures like the quality gain …