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Optimistic replication of data is a widely used tool for mobile environments, but the behavior of concurrent conflicting updates caused by the relaxed consistency model is poorly understood. Through analytical modeling, we derive an exact bound for conflict rates for the common case of two replicas. The shape of the two-replica analytic curve matches well with simulation results at 50 replicas. Our result shows that (1) both frequently and infrequently synchronized mobile machines operate in the low regions of the conflict-rate curve; (2) conflict rate is not well suited for comparing systems, since multiple system settings can result in the same conflict rate number; and (3) the conflict rate is highly dependent on the characteristics of data flow paths.