Research

The Starfall Effect System

A formal mathematical model for card effect resolution, balance validation, and the Legacy Operator.

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The Starfall Effect System (SES)

A Formal Mathematical Model for Deterministic Card Effect Resolution in Hero-Locked Trading Card Games

Author

Lim Boon Chuan

Affiliation

Independent Researcher, Singapore

Pages

18

Version

6.0

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.

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What's Inside

SECTIONS 2–4

Effect Algebra & Resolution

JSON-driven effect system with determinism proof. O(1) resolution per card play.

SECTION 6

The Legacy Operator

Older cards gain bonuses vs newer expansions. Monotonic collector value growth with bounded balance.

SECTION 9

MTG vs Pokémon vs Yu-Gi-Oh!

Comparative analysis of effect systems across the three dominant TCG engines.

SECTIONS 10–11

Formal Semantics & Bug Data

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