A Mathematical Analysis and Simulation-Based Evaluation of Local Decision Rules in Skyjo

Skyjo is a simple stochastic card game with partial information, local replacement decisions, and score-reducing column removal events. This paper develops a formal mathematical model of the game, derives expected-score rules for turn-level actions, proves several dominance and threshold results, and evaluates a family of heuristic strategies through Monte Carlo simulation. The focus here lies on local optimality under explicit belief assumptions rather than a full equilibrium solution of the multiplayer game. Finally a simulation code is provided for reproducibility.