Research
A formal mathematical model for card effect resolution, balance validation, and the Legacy Operator.
PEER REVIEW PREPRINT · APRIL 2026
A Formal Mathematical Model for Deterministic Card Effect Resolution in Hero-Locked Trading Card Games
The Starfall Effect System (SES) presents a formal algebraic framework for representing trading card game (TCG) effects as structured JSON. Unlike existing TCGs (Magic: The Gathering, Pokémon, Yu-Gi-Oh!), which rely on natural language parsing or per-card scripting, SES defines a single representation from which card text, engine behaviour, and balance simulation are derived. This eliminates text-engine divergence, reduces new card integration time from hours to minutes, and enables Monte Carlo balance validation across all matchups. The paper introduces the Legacy Operator, a conditional bonus mechanism that gives older cards monotonically increasing value against new expansions while preserving bounded balance.
DOWNLOAD PDFSECTIONS 2–4
JSON-driven effect system with determinism proof. O(1) resolution per card play.
SECTION 6
Older cards gain bonuses vs newer expansions. Monotonic collector value growth with bounded balance.
SECTION 9
Comparative analysis of effect systems across the three dominant TCG engines.
SECTIONS 10–11
Denotational semantics, soundness theorem, and empirical elimination of 8 common bug classes.
KEYWORDS
Trading Card Games • Effect Algebra • Game Balance • Monte Carlo Simulation • Legacy Operator • Formal Semantics • JSON Schema • Starfall Catastrophe • Hero-Locked TCG • Deterministic Resolution