Multi-turn LLM evaluation is typically reported as a single win-rate scalar, conflating distinct capabilities. We introduce AIDG (Adversarial Information Deduction Game), formalizing multi-turn adversarial dialogue as a two-player partially observable stochastic game (POSG) and decomposing performance along Seeker (extraction) and Holder (containment) roles. The decomposition isolates three failure modes: cooperative-prior leakage, constraint–reasoning interference, and inefficient hypothesis-space traversal. Across 439 games over six frontier LLMs, defensive performance is tightly clustered (σ = 1.9 ELO) while offensive performance varies substantially (σ = 53.3 ELO); confirmation framing increases extraction odds 7.75× over uninformed deduction (p < 0.00001); and constraint violations account for 41.3% of deductive failures, uncorrelated with scale (ρ = 0.0). We position the containment-over-extraction gap not as a surprising finding but as a measurable consequence of locally-resolvable defensive decisions versus globally-coupled offensive planning, and use the decomposition to attribute the gap per model. All design choices, including turn-decay weighting and the Bradley–Terry rating model, are derived from explicit assumptions.

We audit a multilingual affective generation benchmark eight instruction-tuned LLMs producing emoji summaries for 17,100 Bangla, English and Hindi sentences, with 6,960 human judgements and find its headline conclusions to be artefacts of the measurement instrument rather than properties of the systems. Treating annotators as a random rather than a fixed factor, no system differs significantly from any other (F(7,14)=0.59, p=0.76), although the conventional analysis declares 19 of 28 pairwise differences significant. Annotator identity explains far more rating variance than system identity, and the winning system changes whenever any single annotator is removed. The ordering that does emerge tracks output length: mean emoji count explains 78.7% of between-system variance, and a within-item length-matched comparison over 2,599 pairs reverses the leaderboard. We further show that cross-provider anisotropy differences vanish under mean-centring, that per-language token costs change sign with the normalising unit, and that multi-view row-wise splits inflate macro-F1 by 3.1 points and change the top-ranked system. In place of preference scoring we propose **emoji-affect decodability**, a reference-based probe whose rankings are stable to ±0.003 macro-F1 across seeds.