Results of game AI experiments are comparable only when the underlying decision problem exposed by different implementations is identical. Seemingly minor representation choices can silently alter that problem by changing action probabilities or by merging states that lead to different outcomes. This paper investigates the issue using CoToan, an executable specification and representation contract for Vietnamese Mathematical Chess that bridges the Game Description Language (GDL) with OpenSpiel. CoToan represents actions by their state transitions rather than by arithmetic witnesses, and treats remaining time and victory configuration as part of the task identity. The game is a useful testbed because a single capture may have multiple arithmetic justifications, outcomes depend on scoring rules, and the horizon is finite. Cross‑representation tests on hundreds of sampled and constructed positions show agreement in legal actions, successor states, and terminal outcomes, complemented by exhaustive checks of all 32 operator masks and 512 opposing‑material subsets. Controlled diagnostics reveal that uniform sampling at the witness level alters endpoint‑action probabilities, while omitting time or victory settings merges states with different terminal behavior. These findings demonstrate that action semantics, time, and victory configuration are not mere implementation details; they belong to the experimental task itself and must be represented explicitly for reproducible game AI evaluation.
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