Mathematics of Mafia and Werewolf: Periodic Random-Elimination Benchmarks—Schedule Order, Residue-Class Limits, and Protection Thresholds

This Version 2 working paper studies periodic two-type finite-population elimination processes motivated by the mathematical literature on Mafia and Werewolf. For a fixed period of length r containing d uniformly random removals, machine-checked finite certificates identify the subcritical/supercritical transition scale M_c(R) asymptotic to R^(d/r); the classical alternating day–night square-root law is the case r=2, d=1. Beyond the exponent, the paper proves an exact order-dependent falling-factorial invariant, identifies the first schedule correction, gives adjacent-exchange and state-specific ranking certificates, and shows by an explicit reversal that there is no population-independent best order. Residue classes and schedule phase remain visible at criticality: the alternating cyclic orders realize distinct Gaussian profiles on a common even-population sequence. A separate protection mechanism yields a survival-weight exponent 1/(2-g), with matching zero/one laws for the actual guarded executor at exact hunter rates. A version-pinned audit covers six retained sources, identifies five localized statement, model-connection, or approximation-boundary issues, and closes one limitation explicitly stated by Migdal under matched assumptions. These results concern specified random-elimination kernels, not the unrestricted strategic value of Mafia or Werewolf.