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We analyze how the choice of the sampling weight affects the efficiency of the Monte Carlo evaluation of classical time autocorrelation functions. Assuming uncorrelated sampling or sampling with constant correlation length, we propose a sampling weight for which the number of trajectories needed for convergence is independent of the correlated quantity, dimensionality, dynamics, and phase-space density. In contrast, it is shown that the computational cost of the "standard" intuitive algorithmdoi:10.1063/1.4820420 pmid:24050326 fatcat:g4n6nmvp45cqhlrdnthuhvuagu