{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T14:05:06Z","timestamp":1785333906049,"version":"3.55.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":0,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.uspto.gov\/ip-policy\/copyright-policy\/copyright-basics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We present the Starfall Effect System (SES), a formal mathematical framework for defining, resolving, and generating card effects in hero-locked trading card games. SES introduces a structured JSON effect algebra where every card effect is expressed as a sequence of atomic operations with typed conditions and modifiers, enabling: (1) deterministic resolution by the game engine with formal guarantees, (2) automated generation of human-readable card text with multi-language support, (3) cross-linguistic publishing from a single data source, and (4) rigorous Monte Carlo balance validation. We further introduce the Legacy Operator, a conditional modifier that monotonically increases the strategic and collector value of cards from earlier expansions when played against heroes from later sets. We provide formal proofs of determinism, define condition evaluation semantics, and include a complete reference implementation in pseudocode. The model is implemented and validated in Starfall Catastrophe (572 cards, 14 heroes, 2 books) and is presented as a general framework applicable to any hero-locked TCG system.<\/jats:p>","DOI":"10.2139\/ssrn.6566539","type":"posted-content","created":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T13:20:00Z","timestamp":1785331200000},"source":"Crossref","is-referenced-by-count":0,"title":["The Starfall Effect System (SES) A Formal Mathematical Model for Deterministic Card Effect Resolution in Hero-Locked Trading Card Games"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-8477-9393","authenticated-orcid":true,"given":"Boon Chuan","family":"Lim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T13:20:00Z","timestamp":1785331200000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ssrn.com\/abstract=6566539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2139\/ssrn.6566539","relation":{},"subject":[],"published":{"date-parts":[[2026]]},"subtype":"preprint"}}