In a major extension of previous work, we model the putative hydrothermal rock pore setting for the origin of life on Earth as a series of coupled continuous flow units (the toy train). Perfusing through this train are reactants that set up thermochemical and pH oscillations, and an activated nucleotide that produces monomer and dimer monophosphates. The dynamical equations that model this system are thermally self-consistent. In an innovative step that breaks some new ground, we build stochasticity of the inputs into the model. The computational results infer various constraints and conditions on, and insights into, chemical evolution and the origin of life and its physical setting: long, interconnected porous structures with longitudinal non-uniformity would have been favourable, and the ubiquitous pH dependences of biology may have been established in the prebiotic era. We demonstrate the important role of Gaussian fluctuations of the inputs in driving polymerization, evolution and diversification. In particular, we find that the probability distribution of the resulting output fluctuations is left-skewed and right-weighted (the loaded dice), which could favour chemical evolution towards a living RNA world. We tentatively name this distribution ‘Goldilocks’. These results also vindicate the general approach of constructing and running a simple model to learn important new information about a complex system.