The pioneering model of Henri, Michaelis, and Menten was based on the fast equilibrium assumption: the substrate binds its enzyme reversibly, and substrate dissociation is much faster than product formation. Here, we examine this assumption from a somewhat different point of view, asking what fraction of enzyme-substrate complexes are futile, i.e., result in dissociation rather than product formation. In Knowles' notion of a "perfect" enzyme, all encounters of the enzyme with its substrate result in conversion to product. Thus, the perfect enzyme's catalytic efficiency, kcat/KM, is constrained by only the diffusion on-rate, and the fraction of futile encounters (defined as φ) approaches zero. The available data on >1000 different enzymes suggest that for ≥90% of enzymes φ > 0.99 and for the "average enzyme" φ ≥ 0.9999; namely, <1 of 10(4) encounters is productive. Thus, the "fast equilibrium" assumption holds for the vast majority of enzymes. We discuss possible molecular origins for the dominance of futile encounters, including the coexistence of multiple sub-states of an enzyme's active site (enzyme floppiness) and/or its substrate. Floppiness relates to the inherent flexibility of proteins, but also to conflicting demands, or trade-offs, between rate acceleration (the rate-determining chemical step) and catalytic turnover, or between turnover rate and accuracy. The study of futile encounters and active-site floppiness may contribute to a better understanding of enzyme catalysis, enzyme evolution, and improved enzyme design.