In Nobunaga’s Ambition the binding constraint is the action slot, not the efficiency of any one action: a fief gets one command a season, so the strategy lives in which command, not in squeezing more out of it. From that follow three of Chris’s quantitative claims, made playing Tokugawa in Mikawa (May 2026): an Economic Index that measures a clan’s compounding capacity, a Winning-Position Theorem (the game is decided once your index exceeds everyone else’s combined), and a ~10% CAGR with a per-slot hurdle rate.
Links: NA1 — A Game-Design Crucible (the specimen) · The MIRR 4X Framework (the hurdle-rate engine this instantiates) · The Dead-Verb Test (verbs priced against this compounding) · The Hollow Opponent · The Multiplayer Coalition Problem (boom vs rush, coalitions) · The Dominance-Frontier Lens
Grounding: the mechanics cited (one command per fief per season, the develop formulas, the caps) are bytecode-verified in the na1-decompiler repo (docs/appendix-formulas.md, checked against the ROM by na1sim.oracle). The index, the theorem and the CAGR are play observations and Chris’s theory, not ROM-derived; the game-specific doctrine built on them is the repo’s docs/synthesis-frontier.md #35. Promoted from session memory 2026-11-02.
A fief issues one command per season, four a year. Doubling an income matters less than what one more slot buys, so optimization happens at the allocation layer, not the production layer. The strategy frontier is therefore at least four-dimensional: terrain (each fief’s tactical map), force count, force quality (skill, morale, arms) and economic runway (town, output, dams, wealth). A 5-year opening is 20 decisions per fief. (Corrected: the May notes tied each season to one verb — Spring give, Summer build — which the game has no rule for: ch.11 gives one command per fief per turn.)
Chris’s index for a clan: E = Σ over owned fiefs of ∛(town × output × wealth) — a constant-returns Cobb-Douglas form that rewards balanced development and adds across fiefs, so it compounds through territory. Its fast-moving twin is the Combat Index, Σ(men × skill).
Theorem (Chris, 2026-05-22). A player is in a winning position once E(self) > Σ E(all others): no alliance of the rest can out-compound the leader, so the outcome is decided by execution, not contention. Observed, Fall 1597 (Tokugawa playthrough): Tokugawa 10,009 against Oda 3,971 + “Uewa” 885 (as recorded) + Hojo 676 = 5,532, a ratio of 1.81 — over the threshold. Analogues: a dominant market position, a winning coalition, a material-won chess endgame.
| Vector | Index | Time scale | |—|—|—| | Boom | Σ ∛(town · output · wealth) | decades | | Rush | Σ (men · skill) | seasons | | Survival floor | the minimum defense that buys time to boom | — |
The winning line was boom with minimum viable defense: Mikawa held, the rear developed. Over 20 years of that playthrough every capability metric compounded at ~9.5–11.7% a year (combat capacity 6.1×, town 8.1×, output 6.5×, rice and gold ~9×), which puts the per-slot hurdle at about 2.4%: an action returning less is a drag on the baseline, so waiting while neighbours destroy each other is a positive-return choice. Each conquered fief raises the cap and with it the sustainable rate. This is the MIRR argument on a game with hard per-fief caps.
The two scenarios encode two unification scopes: the 17-fief map is central Honshu around Kyoto (what Oda achieved before Honnō-ji, 1582); the 50-fief map adds the periphery Oda never reached (Mōri, Ryūzōji, Kyushu) — Hideyoshi’s and Tokugawa’s project. The boom line is Tokugawa’s: patient development while neighbours exhausted each other, then a territorial advantage no rival could match by Sekigahara. The rush line is Oda’s. That a game built in 1986 reproduces this ordering is part of why NA1 earns its crucible.
synthesis-frontier #36).