Self-Play Calibration of Heuristic Agents for Mexican Train Under Competing Objectives

Mexican Train dominoes is commonly played under two incompatible victory conditions: points (lowest pip total when the round ends) and go-out (first player to empty their hand). This paper describes the development, calibration, and empirical validation of AI agents for both objectives in Warp 12, an open-source Mexican Train implementation. We introduce the Tactical Effectiveness Index (TEI), a dual-track OpenSkill-based rating system with gamified grade display, anchored to fixed AI reference tiers. Empirical results from thousands of self-play games show that skill ordering is stable under the points objective (consistent rating gaps between tiers), while go-out exhibits higher variance and compressed skill gaps. We demonstrate that search algorithms provide different advantages depending on context: expectimax wins in 2-player points (64% vs heuristics), while ISMCTS excels in 4+ player go-out (31% vs 23% baseline). A 285,000-game points self-play campaign across 570 configuration cells (4 Warp factors × every legal fleet size × 15 module configs) is our sole skill/luck instrument for board choice and module taxonomy. From the baseline cells alone we find that skill expression increases with both tile set size and player count, contradicting the intuition that larger games devolve into luck, and that Warp factor 12 is the empirically optimal choice for competitive rating. Across the full matrix, most optional modules preserve the baseline skill ceiling; Module Iota (Double Down) slightly raises it. Module Epsilon (Drafting) collapses it (1.08/4 indicators) — counter-intuitively, choosing your hand makes outcomes more luck-dominated mid-game — and is therefore designated Warped / party. Module Zeta (Squadrons) also preserves skill (2.94/4); it never writes free-for-all (FFA) TEI — rated Warp 12 crew sectors update a dedicated Squad TEI track (squadRating) after team-track calibration (SQUADRONS RATING CALIBRATED), not because Zeta is luck-dominant. Finally, we report on Class Ω, a neural self-play agent that achieves parity with heuristic baselines in small games and outperforms in large fleets. All code, data, and reproduction scripts are available as open source.