Appendix C — V5 — Card game substrate validation

Research question. When the BDPD logistic engine is replaced by the Forest of Humbaba card game — stochastic card draws, archetype decks, a hidden Box Reserve — does the aggressive-agent collapse pattern survive the substrate translation?

V1 confirmed that a single aggressive agent in a logistic arena collapses the commons in 5/5 seeds. The baseline paper’s CT1 sweep (Brunelli 2026) ran the same question on the card game substrate: 200 games per matchup across all four archetype pairings (Warrior-King, Stranger-King, Temple Keeper, Merchant), recording collapse rates and wealth distributions.

Setup. We reproduce the headline finding of BDPD$^0$ CT1 rather than running new experiments. The card game differs from the logistic platform in three structural ways: (i) harvest is discrete and drawn from a finite deck, not chosen as a continuous fraction; (ii) a hidden Box Reserve and Forest Die introduce Knightian uncertainty absent from the deterministic platform; (iii) archetype differentiation comes from deck composition (Warrior cards carry high harvest values; Temple cards carry conservation effects), not from a strategy parameter.

Result (BDPD$^0$ CT1, 200 games per cell, 9 rounds).

Matchup	Collapse rate	Note
Warrior vs Warrior	0.815	both aggressive — near-certain collapse
Warrior vs Stranger	0.695	delayed aggression still collapses
Stranger vs Stranger	—	Seneca Clip frequent (0.600)
Temple vs Temple	0.000	two conservators — zero collapse
Merchant vs Merchant	0.000	two conservators — zero collapse
Merchant vs Temple	0.000	two conservators — zero collapse
Stranger vs Temple	$\approx 0$	delayed aggression absorbed by healer

The cliff translates: any matchup involving the Warrior-King collapses the commons at high rates; matchups among conservators never collapse. The probabilistic character of the card game refines the binary platform finding: Warrior vs Warrior yields 81.5% collapse, not 100%, because favourable Box Reserve rolls rescue a minority of games. The qualitative direction — one aggressor suffices — survives intact.

Two additional CT results from BDPD$^0$ sharpen the substrate comparison:

CT3 (observability noise): noise has zero effect in the card game (collapse rate flat from $\sigma/\mu = 0$ to full occlusion), whereas the platform’s P9 sweep shows a significant effect. The mechanism is clear: random card selection renders the observed forest-health signal strategically irrelevant.
CT4 (defection timing): the Stranger-King’s “safe betrayal” replicates — early defection yields the highest stockpile against conservators, mirroring BDPD$^0$’s P8 platform finding.

Reading. The card game substrate serves as an independent validation of V1’s qualitative claim: the cliff is not an artefact of the logistic equation or the continuous-fraction harvest model. A discrete, stochastic substrate with archetype-driven decks reproduces the same pattern. The CT3 null result on noise highlights the converse: findings that depend on agent decision logic (observability response) do not transfer between substrates, while findings that depend on structural asymmetry (aggressive vs conservative composition) do.

The card game predates the governance surfaces (pacts, treaties, meta-agents) and has no analogue for them yet. Adding pact mechanics to the physical game and its simulator is a natural candidate for future work.

# V5 — Card game substrate validation {#sec-card-game} **Research question.** When the BDPD logistic engine is replaced by the Forest of Humbaba card game — stochastic card draws, archetype decks, a hidden Box Reserve — does the aggressive-agent collapse pattern survive the substrate translation? V1 confirmed that a single aggressive agent in a logistic arena collapses the commons in 5/5 seeds. The baseline paper's CT1 sweep [@bdpd-paper-0] ran the same question on the card game substrate: 200 games per matchup across all four archetype pairings (Warrior-King, Stranger-King, Temple Keeper, Merchant), recording collapse rates and wealth distributions. **Setup.** We reproduce the headline finding of BDPD$^0$ CT1 rather than running new experiments. The card game differs from the logistic platform in three structural ways: (i) harvest is discrete and drawn from a finite deck, not chosen as a continuous fraction; (ii) a hidden Box Reserve and Forest Die introduce Knightian uncertainty absent from the deterministic platform; (iii) archetype differentiation comes from deck composition (Warrior cards carry high harvest values; Temple cards carry conservation effects), not from a strategy parameter. **Result (BDPD$^0$ CT1, 200 games per cell, 9 rounds).** | Matchup | Collapse rate | Note | |---|---|---| | Warrior vs Warrior | 0.815 | both aggressive — near-certain collapse | | Warrior vs Stranger | 0.695 | delayed aggression still collapses | | Stranger vs Stranger | — | Seneca Clip frequent (0.600) | | Temple vs Temple | 0.000 | two conservators — zero collapse | | Merchant vs Merchant | 0.000 | two conservators — zero collapse | | Merchant vs Temple | 0.000 | two conservators — zero collapse | | Stranger vs Temple | $\approx 0$ | delayed aggression absorbed by healer | The cliff translates: any matchup involving the Warrior-King collapses the commons at high rates; matchups among conservators never collapse. The *probabilistic* character of the card game refines the binary platform finding: Warrior vs Warrior yields 81.5% collapse, not 100%, because favourable Box Reserve rolls rescue a minority of games. The qualitative direction — one aggressor suffices — survives intact. Two additional CT results from BDPD$^0$ sharpen the substrate comparison: - **CT3 (observability noise):** noise has *zero* effect in the card game (collapse rate flat from $\sigma/\mu = 0$ to full occlusion), whereas the platform's P9 sweep shows a significant effect. The mechanism is clear: random card selection renders the observed forest-health signal strategically irrelevant. - **CT4 (defection timing):** the Stranger-King's "safe betrayal" replicates — early defection yields the highest stockpile against conservators, mirroring BDPD$^0$'s P8 platform finding. **Reading.** The card game substrate serves as an independent validation of V1's qualitative claim: the cliff is not an artefact of the logistic equation or the continuous-fraction harvest model. A discrete, stochastic substrate with archetype-driven decks reproduces the same pattern. The CT3 null result on noise highlights the converse: findings that depend on agent *decision logic* (observability response) do not transfer between substrates, while findings that depend on *structural asymmetry* (aggressive vs conservative composition) do. The card game predates the governance surfaces (pacts, treaties, meta-agents) and has no analogue for them yet. Adding pact mechanics to the physical game and its simulator is a natural candidate for future work.