A mathematical model is constructed to predict the probability that a collision between two activated platelets results in doublet formation mediated by fibrinogen cross-bridges. The model is used to explore the effect of time from activation, looking at both simultaneous and non-simultaneous activation times. Also considered are the impact of blood fibrinogen concentration and various shear rates. The idea of hydrodynamic efficiency [Tandon & Diamond (1997) Biophys. J.73, 2819-2835] is extended by varying the separation distance which is considered to be a collision. From fitting the model to data [Xia & Frojmovic (1994) Biophys. J.66, 2190-2201], it is found that the hydrodynamic efficiency corresponds to short interaction distances ( approximately 14 nm). The model predicts that the probability of forming a doublet increases quickly after activation, remains near its maximum for a significant time interval, and then declines. This may contribute to the regulation of the time and location of platelet aggregation, by ensuring that platelets are more likely to aggregate near an injury, rather than downstream in the vascular system. A newly activated platelet has a high probability of cross-bridging with an already activated platelet. Fibrinogen concentration strongly affects the time course and the equilibrium values of the aggregation probability. These results indicate the importance of considering the progression of the reaction between solution fibrinogen and surface receptors in determining a platelet's ability to aggregate.