  A pedagogical formulation of Loschmidt's paradox and H-theorem is presented
with basic notation on occupancy on discrete states without invoking velocity
collision operators. A conjecture, so called H-theorem do-conjecture, is
formulated. Causal inference perspective on the dynamical evolution of
classical many-particle system is invoked. This perspectice introduce a
probabilistic view on the state of the system conditioning on the thermodyamic
ensemble, i.e., function of state-variables representing the ensemble. A
numerical simulation of random walkers for deterministic diffusion demonstrate
the causal effect of interventional ensemble, showing a dynamical behaviour as
a test of the proposed conjecture. Moreover, the chosen game like dynamics
provides an accessible practical example, named Ising-Conway Entropy Game, in
order to demonstrate increase in entropy over time, as a toy system of
statistical physics.
