Card Tournaments (CT1–CT5)¶

Card tournament sweeps replicate the platform's thematic clusters on a fundamentally different substrate: a stochastic, discrete engine where the hidden Box Reserve and Forest Die replace the logistic model, and four archetypal decks replace homogeneous strategy classes. All sweeps use 200 games per data point; error bars show 95% bootstrap confidence intervals (10,000 resamples).

CT1 — Collapse-Rate Matrix: Archetype vs. Archetype¶

Attribute	Detail
Design	Round-robin of all 12 ordered archetype pairs, 2-player, 9 rounds
Result	The Warrior-King is the dominant driver of collapse. Warrior vs. Warrior: 81.5% collapse. Matchups excluding the Warrior-King (Temple/Temple, Temple/Merchant, Merchant/Merchant): 0% collapse. Stranger-King dual nature: vs. Temple = 0%, vs. Warrior = 69.5%.

	Warrior	Stranger	Merchant	Temple
Warrior	81.5%	69.5%	71.5%	54.5%
Stranger	69.5%	56.0%	39.5%	0.0%
Merchant	71.5%	39.5%	0.0%	0.0%
Temple	54.5%	0.0%	0.0%	0.0%

: Collapse rate matrix (row = Player 1 deck). {#tbl-ct1-matrix}

Key insight: Unlike the platform's binary gate passage (0% or 100%), the stochastic Forest Die introduces a probabilistic collapse frontier. The threshold is not binary but probabilistically dominant — the Warrior-King makes collapse near-certain, not inevitable in every single game.

| Figure | CT1_collapse_matrix__light_paper.png |

CT2 — Game-Length Sweep: Temporal Horizon and Collapse¶

Attribute	Detail
Design	All 6 unordered pairs at 9, 12, and 15 rounds
Result	Game length acts as an amplifier of structural asymmetries. Warrior vs. Temple: collapse rises from 0.05 (9 rounds) to 0.79 (15 rounds). Merchant vs. Temple: 0.0 at all lengths. Wealth divergence grows with length in asymmetric pairs. Temporal extension benefits the extractor, not the conservator.
Figure	`CT2_gamelength_sweep__light_paper.png`

CT3 — Observability Noise: The Irrelevance of Fog¶

Attribute	Detail
Design	Warrior vs. Temple; \(\sigma/\mu \in \{0.0, 0.1, 0.2, 0.3, 0.4, 0.5\}\) + hidden; 9 rounds
Result	Zero effect. Collapse rate flat from 0.405 (transparent) to 0.41 (hidden). Gini flat at 0.484–0.490. Stockpiles unaffected. Heuristic archetypes do not condition on exact stock values — information fidelity only matters if agents possess the cognitive architecture to act on it.
Figure	`CT3_noise_sweep__light_paper.png`

Platform vs. Cards

This starkly contrasts with P9, where moderate noise improved welfare and full occlusion was disastrous. The dual-mode result — noise matters on one substrate, not the other — is itself a finding about the role of cognitive architecture.

CT4 — Defection Timing: Safe Betrayal Against Conservators¶

Attribute	Detail
Design	Stranger-King vs. Temple Keeper and vs. Warrior-King; forced defection at turns 3–11; 12 rounds
Result	Against Temple Keeper: defection at any turn yields higher stockpile (18.18–20.90) than the no-defection baseline (16.51) — a +27% gain at T=3. Defection slightly reduces collapse below baseline (0.05–0.10 vs. 0.105). Against Warrior-King: collapse near-certain (0.975–1.0) at all timings.

| Figure | CT4_defection_timing__light_paper.png |

Safe betrayal: A defector profits from a conservator's healing without triggering collapse. The Temple Keeper's regeneration acts as an implicit subsidy to the Stranger-King's aggression. This maps onto the dilemma of early movers in climate negotiations — conservation without exclusion transforms the commons into a subsidised extraction ground.

CT5 — Stranger-King Deep Dive¶

Three complementary sub-sweeps against the Warrior-King (12 rounds, 200 games/point):

CT5a — Patience Accumulation¶

Attribute	Detail
Result	Patience accumulates linearly with cooperative turns (0.45 at T=3 → 2.93 at T=11) but provides no survival benefit against the Warrior-King. Collapse ≥ 0.975 regardless. Structural depletion overwhelms accumulated potential.
Figure	`CT5a_patience_at_defection__light_paper.png`

CT5b — Aggression Nudge¶

Attribute	Detail
Result	Nudge parameter 0.8–2.0 has no measurable effect on collapse, stockpile, or Gini. Deterministic strategic pressure overwhelms marginal changes in assertiveness — soft guidance does not work.
Figure	`CT5b_aggression_nudge__light_paper.png`

CT5c — Hand Composition at Defection¶

Attribute	Detail
Result	Stranger-King consistently holds 5 cards with ~11 cedars of aggressive potential at every defection turn. The weapon is always loaded — its efficacy is gated by opponent pressure, not readiness.
Figure	`CT5c_hand_composition__light_paper.png`

Together, CT5 confirms that structural position dominates strategic intent.

CT6 — LLM Qualitative Case Studies (Preliminary)¶

Single-model (DeepSeek v4-flash), fixed-seed case studies of LLM Stranger-King play against Temple Keeper and Warrior-King. Three observations:

Safe betrayal emerged spontaneously. The LLM defected at T=3 when the forest reached maximum health — triggered by the conservator's success.
Awareness without restraint. Against the Warrior-King, the LLM verbalised imminent collapse yet continued extracting aggressively.
Nominal cooperation is functionally aggressive. In a 20-game sweep, the LLM's no-defection stockpile (25.6) was nearly identical to defection outcomes (24.6–26.2) — its "cooperation" was cooperation in name only.

Full prompt/response logs and analysis in Prompt Design. Systematic multi-model validation remains future work.