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We present results from nine simulations that compare the standard Lambda cold dark matter cosmology (ΛCDM) with counterfactual universes, for approximately 100Gyr using the Enzo simulation code. We vary the value of Λ and the fluctuation amplitude to explore the effect on the evolution of the halo mass function (HMF), the intergalactic medium (IGM), and the star formation history (SFH). The distinct peak in star formation rate density (SFRD) and its subsequent decline are both affected by the interplay between gravitational attraction and the accelerating effects of Λ. The IGM cools down more rapidly in models with a larger Λ and also with a lower σ8, reflecting the reduced SFRD associated with these changes – although changing σ8 is not degenerate with changing Λ, either regarding the thermal history of the IGM or the SFH. However, these induced changes to the IGM or ionizing background have little impact on the calculated SFRD. We provide fits for the evolution of the SFRD in these different universes, which we integrate over time to derive an asymptotic star formation efficiency. Together with Weinberg’s uniform prior on Λ, the estimated probability of observers experiencing a value of Λ no greater than the observed value is 13 per cent, substantially larger than some alternative estimates. Within the Enzo model framework, then, observer selection within a multiverse is able to account statistically for the small value of the cosmological constant, although Λ in our universe does appear to be at the low end of the predicted range.