Although the adaptive algorithm produced improvements in the rate of equilibration, we found no clear differences between the uncertainty in the free energy estimates at equivalent computational effort either within stages (Figure ), or over entire calculations (Figure ). This likely reflects two facts: that the √ t λ σ ∂H ∂λ λ -based improvement factors are fairly close to 1 (Figure ), indicating little scope for improvement with adaptive time allocation; and that allocating time to problematic windows often does not reduce uncertainties because individual runs become stuck in local minima, indicating that the timescales of sampling issues are too long. An alternative approach would be to allocate more replicates to problematic λ windows, but this would reduce the rate of equilibration. Despite the lack of uncertainty reduction, the algorithm successfully allocated sufficient time to achieve equilibration in the bound vanish legs, while allocating dramatically less time to most free stages. This again suggests a correlation between slow equilibration and large inter-run uncertainty.