ark-stronghold-protocol/docs/BALANCE.md

BALANCE.md — difficulty model and measurement (official numbers, no custom tuning)

Owner: match / balance. Tools: tools/balance.mjs (competent-board model — now a measuring tool only), tools/matchrun.mjs (bot matches). Tests: test/match/balance.test.js, test/match/waves-official.test.js, test/match/waves.test.js, test/sim/pathing.test.js.

Every enemy number is the official one; the custom balance layer was removed (user request: rules, numbers, enemy kinds / counts and routes must follow the official game; research 08 §6–§7, DESIGN §14 corrections):

• waves = the client's RandomEnemyGenerater (research 08 §2): a 15-slot type schedule per match (3 types × 3 slots + 6 SPECIAL, shuffled), one weighted special entry per round, each placeholder ACTION replaced by clamp(roundHalfEven(n·P(t)/P(new)), 1, 5) units over the same window, the other movement class not spawned — no k copies, no kept fly placeholders; verified against all 429 official entry × round compositions and the official count distribution (同盟 险境 R3 ≤ 10 enemies, R13 ≈ 37 — the old generator averaged 28 / 81);
• stats = the PRTS per-round enemyScale table only (data/config.json, 终极 ×1.15 speed from R3);
• leader pool = bloodPoint[difficulty] × the players alive when the fight starts — one pool for every boss field; solo × 1 (the owner's decision of 2026-10-06, adopting PR #209: it replaces the fixed pool of DESIGN §20.10, co-op bloodPoint whatever the count and solo × 0.25 [ASSUMED] — config bossHpScale.perPlayer: false, solo: 0.25 restores it; DESIGN §25.13.4). The bots' solo matches got 4× the leader HP: in the golden corpus 4 of the 6 solo matches that reached and won the Final Assault now lose it (team LP 0 with 93k–176k of the pool left);
• leader parts and drones (DESIGN §20.10): a 剑 / 锤 / 碎铳之簧 passes every damage it takes to its leader 1:1 (PRTS "等量的 无来源生命流失"; until 2026-10-01 half, and a 剑 / 锤 only while grounded — the dive hits [ASSUMED], the handbook says "被击落时"); a 胄 drone that dies (whoever kills it, DESIGN §20.13) costs 2 % of the leader's shown max HP = the pool (unchanged from v2.5; which "最大生命值" the official client reads is [ASSUMED] — the review round tried the unit's data 600 000, which made drones 19–78 % of a solo 标准 fight, and went back, bosses.js DRONE_LINK_BASE);
• same-named effects on an enemy: one instance, the strongest — 奥术 (the two players of a pair field compete for it; until 2026-10-01 one per player, multiplied: ×30 arts damage taken on a leader at ~250 layers each), 灵知 坚冰, 莱恩哈特 / 缄默德克萨斯 RES cuts (until 2026-10-01 one per copy of the operator);
• 坚守 thorns: 无来源 but credited to the member hit (until 2026-10-01 nobody's: up to 19 % of a co-op leader pool and 88 % of a solo one missing from the per-player boss damage; kill times unchanged);
• bond layers stop at 999 per bond (BOND_LAYER_CAP, official: the client's MAX_GARRISON_STACK, §7 / research 11; until 2026-10-01 no cap, so per-layer bonuses kept growing past anything the official game reaches);
• player-side "+X%" ATK / DEF / max HP of bonds, strategies, equipment, 机变 cards and per-layer 特质 = 直接乘算, summed with each other and with skills (PRTS 盟约记录 / 游戏数据基础; DESIGN §20.10) — until 2026-10-01 each compounded, which made every measurement below the 2026-10-01 note (§3) too strong for the player side (most in late rounds and leader fights);
• bounties: no extra ×0.7 in solo (the 70 % base is already in enemyScale), spawned with the template's first normal action (research 08 §5);
• routes = the official 4-direction flow field with crates at cost 1000 (research 08 §3), act1 m02 without crates.

Removed: every enemyHpMul / enemyAtkMul / enemySpeedMul / bossHpMul of data/tuning.json (it now holds only the titles.comment_3 rule) and the flyPlaceholders knob. gamedata.js ignores those keys if an old file carries them.

Measured with the official numbers (node tools/balance.mjs --mode all --difficulty ALL --tuning off, 2026-09-28): average capped leaks per board and round R1–R13 (solo 标准 R1–R8) of the competent board of §1.1 —

mode	old generator, research numbers	old generator, tuned (shipped before)	official (now)	LP/rd after 联防
独立 标准	1.3	0.6	0.17	(= leaks)
独立 险境	1.4	0.9	0.19	(= leaks)
独立 绝境	1.8	1.8	0.22	(= leaks)
独立 终极	4.1	3.1	0.65	(= leaks)
同盟 标准	1.4	0.5	0.31	0.13
同盟 险境	2.3	1.3	0.49	0.01
同盟 绝境	5.0	2.7	0.80	0.10
同盟 终极	6.3	4.3	1.96	0.93

The old generator spawned 2–4× the official enemy count (every template enemy × k, plus the other class's placeholders); the tuning of the previous pass only compensated for that. With the official counts the difficulty comes out below the old targets — which is the official game's difficulty as far as this model can tell (the model is a competent, layer-rich board; see §1.2 for what it does not capture). Nothing is tuned from these numbers.

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1. Method — tools/balance.mjs

For every mode (独立 solo / 同盟 multi) × difficulty × round the tool samples whole matches (stage, the 3 factions, bans, boss, band and lineups all vary with the seed), builds a competent board for that round, generates the round's real wave (waves.js: template, the official per-action replacement of the round's pick, enemy scaling, bounties off) and runs the real Battle with full content (kits, talents, bonds with layers, IN_BATTLE 特质, equipment, bands, summons). Co-op rounds field 4 boards against the same wave and then run 联防 exactly like the match (unite.js: ≤ 2 perfect helpers, only the survivors cost their source LP). Boss rounds build the Final Assault fields exactly like Match.startFinalAssault (pairs / _s for a lone player, shared pool GameData.bossPoolHp = bloodPoint × the players alive (solo × 1, §25.13.4), merged team LP of 15 per player, leaks' lpr, −1 LP/s after 150 s) and record the pool damage by 150 s, the kill time and the win rate.

Metrics: capped leaks = min(leaks, 10) per board and round (what that board alone would lose; the targets below use it — raw means are dominated by swarm rounds that cap at 10 anyway), LP/rd after 联防 (co-op), perfect-round share, the enemies that leak most, clear time; bosses: share of the pool dealt by 150 s, win rate, kill time.

1.1 The competent board of round r

R	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
shop level	1	1	2	2	3	3	4	4	4	5	5	6	6	6	6
units	2	4	5	7	8	8	8	8	8	8	8	8	8	8	8
elites (精锐)	0	0	0	0.5	1	1.5	2	3	3.5	4	4.5	5	6	6.5	7
equipment	0	0.5	1	1.5	2	3	3.5	4	5	5.5	6	7	8	9	9
core bond members	–	–	3	3	3	3	3	3	4	5	6	6	6	6	6
core bond layers	0	2	6	12	20	28	38	50	65	80	95	110	130	150	170
add-on layers (each)	0	1	4	8	12	17	23	30	38	46	55	65	75	90	100

(fractional values: that many on average.) Sources: income 4, 5, 6 … min(3 + r, 12) and upgrade prices 5 / 8 / 11 / 12 / 13 with −1 per round (research 00-INDEX §3) → L2 at R3, L3 at R5, L4 at R7, L5 at R10, L6 at R12; the board is full from R5; elites ≈ 0 at R3 → 3 at R8 → 6+ at R13; 1–2 add-on bonds; the layer pace reaches Σ active layers ≈ 330 at R14 — the solo Hidden Core threshold is > 350 (research 02 §2.3), i.e. these are boards of players who regularly reach the Hidden Core. Units are drawn from the match's pool (bans respected) with a tier mix per shop level, around a core bond with enough members, plus the roles a player reads from the wave preview: 2 blockers, anti-air by the share of flyers, arts dealers by the armour of the enemies (arts anti-air when the flyers are armoured, e.g. 寒霜 DEF 600), a medic from R5. Equipment: passive combat items of tier ≤ shop level (golden from R7) on the damage dealers. Layers: the core curve on the core bond, the add-on curve on every other bond the lineup activates. Placement: the bot's layout planner with rehearsal of its 5 variants (a player adapts the layout to the previewed wave). Not modeled: bounties, 机变 cards, prep-only effects (their value is folded into the curves). --profile weak|strong scales elites, items and layers ×0.6 / ×1.4.

1.2 Reference levels (informative — nothing is tuned against them any more)

The previous pass tuned the waves toward: 标准 ≤ 1 capped leak per board and round, 险境 ≤ 2, 绝境 ≈ 2–3.5, 终极 ≈ 3–5. They are kept only to read the measurement. What the model does NOT capture (so real matches are harder than the table): imperfect economy and placement, bans hitting the planned bonds, 机变 / bounty choices (bounties add enemies), the preview being read by a human in 90 s, and losing LP early (fewer rounds to build layers).

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2. What the numbers were checked against (research first)

Suspect	Research	Verdict
Enemy multipliers (config.modes[m].enemyScale, k exponents)	A3 table (PRTS 下半, user-sourced) — 01-core-rules.md A3 / _criticAddendum.enemyStatMultipliers	match exactly (every mode, every round incl. ABYSS HP k and ×1.08); kept as the base
Wave templates / counts	level data (maxPlayTime, spawns, routes) — DATA	match the official levels; kept
Faction replacement	was: each template enemy × k [ASSUMED]	replaced by the official per-action rule (research 08 §2.3, client code)
Fly placeholders without a FLY faction	was: kept (寒霜 / 暴鸰 / 妖怪, the #1 leak source) [ASSUMED]	official: the other movement class is not spawned (research 08 §2.3 + the PRTS screenshots)
Faction mixing	was: every round a ground entry + a FLY entry	official: one entry per round from a 15-slot type schedule
MOVE_SCALE 0.5	every level's moveMultiplier 0.5 (05 §2.2)	kept
Combat time limit unit	maxPlayTime read as game seconds [ASSUMED]	wrong — real seconds; fixed (§2.1)
Boss pool	bloodPoint DATA = the current game data (activity_table act2autochess bossInfoDict; the local cache equals upstream ArknightsGameData master, checked 2026-10-01). PRTS 盟约记录's leader table is the older 11月18日 revision: it matches 常规 and most of 险境, but differs for 铳 险境 (450 000 vs 400 000) and 胄 / 铳 / 萨米 绝境 (1 600 000 / 870 000 / 1 800 000 vs 1 800 000 / 800 000 / 2 000 000), and has no 终极 column or 卢西恩 row; one pool for every field ("所有人将一起对敌方领袖造成伤害"); "敌方领袖的总生命值不变" = the mirrored copies of a pair field share it (notice 5114)	co-op = bloodPoint whatever the alive count; × alive / 4 is a config switch (aliveScaling, off: 巴哈姆特 12294 "聯機隊友…變少，最後boss血條也會變少" is one community note without a proportion, awaiting the user's recall); solo ×0.25 kept [ASSUMED]; the solo 标准 ×0.6 removed
Leader parts / 胄 drones / same-named debuffs / 坚守 thorns	PRTS 碎铳之簧, “斩胄之剑”, “破胄之锤” "受到伤害时令…受到等量的无来源生命流失"; PRTS 假想敌：胄 "该妖怪死亡时令假想敌：胄受到最大生命值2%的真实伤害" (which max HP: [ASSUMED]); PRTS 作战机制 同名buff默认只表现出一个, 巴哈姆特 12316 "共享型buff會跟對面搶"; 坚守 "伤害来源受到(850+10×L)点法术伤害"	parts 1:1 (was ½, 剑/锤 only grounded); drone 2 % of the pool (unchanged; the unit-HP reading was tried and reverted); 奥术 / 灵知 坚冰 / 莱恩哈特 & 缄默德克萨斯 RES cut: one instance per target (was one per player / copy); thorns credited to the member (was to nobody) — 2026-10-01, DESIGN §20.10
Bonus stacking	was: each bond / strategy / item / 机变 / 特质 "+X%" its own ×(1 + x) (research 02 §2.1)	official 直接乘算: summed with each other and with skill "+X%" (PRTS 盟约记录 "…属性加成均为直接乘算", 游戏数据基础 D_t = Σtᵢ); 2026-10-01, DESIGN §20.10
Solo bounties ×0.7	上半 11/18 note = the global solo base	removed (already in enemyScale)
Bounty spawn timing	was: the bounty units appended after the host action's own units	official: inserted among them at floor((i+1)·len/(n+1)), then the list spread over the window (client _InsertSpActionToNormal + _CalculateActionPredelay, decoded; waves.js withBounties)
联防 spawn timing	was: owner k at +min(0.5·k, 5) s, each owner's units over the whole window [ASSUMED]	official (decoded _CalculateActionPredelayConsiderUid): owner k at +0.5·k s, unit step min(max(W/M, 0.05·W), 5 s), M = largest owner group — a lone leaker's units now come 5 s apart instead of up to 40 s
Leader / leader-part multipliers	was: leaders and their parts never scaled	official: the round multipliers are the ENEMY effects 攻坚装备 / II / III / 补给线 / 急行军 (enemy_attribute_mul; enemy_exclude = 炎佑 — plus the TIMES tokens for 补给线 — never a leader) ⇒ parts take HP/ATK/speed, the leader ATK/speed; only the leader's HP (the server pool) is exempt ("领袖单位于服务器的生命值加成不受上述加成影响"). Co-op 终极 R14: leader ATK ×2.14; solo 标准: ×0.7
频次 器物 and leader summons (0.2.1, PR #272 by @CXUtk)	was: a 器物's hit count was the data's whatever the difficulty (the spawn's HP multiplier was overwritten); a leader's mid-fight summons (死亡集群's 妖怪, 刺胄之弹, 余音, 不祥幻影) took no round effect	official data: 攻坚装备 / II / III leave out only 炎佑, 补给线 / 补给线II also the 14 器物 keys (activity_table aceffect_enemy_2 / 2_2 enemy_exclude) ⇒ a 器物 needs data × hp / supplyHp hits (config supplyHp: co-op 终极 R5–R15, the HP-only 1.2 steps and the 1.08), rounded [ASSUMED]; the summons take the round's HP (a hit count too) / ATK / speed through the boss field's flags.enemyScale, 死亡集群's summon.hp_ratio on top. Solo 标准 青铜镜 30 → 23 hits, co-op 终极 R14 30 → 129; 炎佑 is an ally here, never scaled. The 逐火 / 再生 husk counts (talent Revive[Trigger].prop_max_hp) stay as they were [open]
Ground routes	was: 8-dir A*, m02 crates active	official 4-dir SPFA + smoothing, crates cost 1000, m02 without crates (research 08 §3)
Income / upgrade curve	R1–R3 VERIFIED, +1/round cap 12 ASSUMED	kept (the model's level curve follows it)
Operator stats per tier	chess status T1 E1 L55 … T6 E2 L1, elites E2 + skill 7 (03) — DATA	faithful: power comes from layers, elites and skills, which is why the model carries them
Player power in the bots	bots fielded T1-heavy boards with 0–3 elites and 20–70 layers per bond at R13	bot fixes (§5)

2.1 Combat time limits are real seconds (fidelity fix)

maxPlayTime counts real seconds of the forced 2× battle. Read as game seconds (the old assumption) the rounds' own spawn schedules do not fit: R2 spawns its last flyer at 43 s of a 45 s limit, R3 its last enemies at 60–62 s of a 55 s limit (they could never be killed, or never even spawned). As real seconds (× 2 in game seconds) every limit is ≈ the last spawn + one flyer crossing of the board (≈ 44 s serpentine at 0.45 tiles/s): R2 43 + 44 ≈ 90, R3 62 + 44 ≈ 110, R5 38 + 67 ≈ 110 (暴鸰 at 0.3 tiles/s).

R	1	2	3	4	5	6	7	8	9	10	11	12	13
maxPlayTime (real s)	45	45	55	55	55	70	85	85	95	95	115	115	115
last spawn (game s)	15	43	62	39	38	42	56	67	75	59	68	60	73
slack, old reading	30	2	−7	16	17	28	29	18	20	36	47	55	42
slack, fixed (× 2)	75	47	48	71	72	98	114	103	115	131	162	170	157

Before the fix 90–100 % of the early "leaks" were enemies still alive (often just spawned) at the limit, not enemies that reached the objective. gd.combatTimeLimit(r) now returns game seconds (config.combatTimeScale, default 2); the player-facing combat countdown is unchanged (= maxPlayTime real seconds). Research 00-INDEX §8 #10 should be updated by its owner.

2.2 The fly placeholders (resolved)

The previous pass measured that the kept fly placeholders (寒霜 DEF 600, 暴鸰) were the most frequent leakers and left a flyPlaceholders knob for experiments. The official client settles it: a placeholder whose class differs from the round's pick is isValid = false — not spawned, not sent, not previewed (research 08 §2.3). The knob is gone.

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3. Measurement per round (official numbers)

Capped leaks per board (16 solo samples / 6 co-op matches × 4 boards per round), --tuning off (identical: the tuning file holds only titles), seed 1, rehearsal 5. Leader columns: win rate, share of the pool dealt by 150 s, mean kill time (8 samples). Re-measured after the review fixes (decoded 联防 timing; leaders take the round ATK / speed multipliers, their parts all of them): normal rounds unchanged, leader rounds and LP/rd as below.

mode	R1	R2	R3	R4	R5	R6	R7	R8	R9	R10	R11	R12	R13	avg	LP/rd
独立 标准	0.13	0.06	0.00	0.13	0.63	0.00	0.25	0.19	–	–	–	–	–	0.17	0.17
独立 险境	0.00	0.00	0.00	0.31	0.00	0.00	0.63	0.19	0.06	0.00	0.00	0.63	0.63	0.19	0.19
独立 绝境	0.00	0.00	0.00	0.00	0.38	0.00	0.00	0.25	0.63	0.50	0.44	0.63	0.00	0.22	0.22
独立 终极	0.13	0.00	0.19	0.25	1.00	0.88	0.44	0.81	1.50	0.94	1.13	0.06	1.19	0.65	0.65
同盟 标准	0.00	0.54	0.00	0.00	1.13	0.00	1.25	0.13	0.88	0.04	0.00	0.04	0.00	0.31	0.13
同盟 险境	0.00	0.00	0.83	0.17	0.00	0.00	0.17	0.25	1.58	0.04	0.46	2.21	0.71	0.49	0.01
同盟 绝境	0.00	0.00	0.38	1.00	0.71	1.17	0.50	0.92	1.88	2.50	0.63	0.71	0.00	0.80	0.10
同盟 终极	0.00	0.04	0.21	0.92	0.83	2.79	4.00	6.00	3.83	1.29	3.71	0.83	0.96	1.96	0.93

mode	最终攻势 (R14; solo 标准 R9)	隐秘核心 (R15)
独立 标准	pool 64k · win 50 % · 80 % by 150 s · 89.8 s	–
独立 险境	pool 169k · win 88 % · 97 % · 19.5 s	pool 237k · win 100 % · 100 % · 22.2 s
独立 绝境	pool 456k · win 63 % · 86 % · 57.0 s	pool 869k · win 50 % · 70 % · 71.1 s
独立 终极	pool 899k · win 38 % · 79 % · 42.0 s	pool 1.63M · win 25 % · 48 % · 44.9 s
同盟 标准	pool 224k · win 100 % · 100 % · 18.0 s	–
同盟 险境	pool 550k · win 100 % · 100 % · 22.0 s	pool 919k · win 100 % · 100 % · 37.8 s
同盟 绝境	pool 1.68M · win 88 % · 99 % · 32.6 s	pool 3.42M · win 88 % · 94 % · 100.9 s
同盟 终极	pool 3.70M · win 88 % · 95 % · 41.9 s	pool 6.08M · win 75 % · 87 % · 92.6 s

2026-10-01 — 假想敌：胄 audit (content/bosses.js kitHelm / kitBlade, PRTS): one 刺胄之弹 below 20 % as well (能力修正), shells only at operators in range (boss_1 too), any drone death costs 2 %, 剑 / 锤 sorties per PRTS (【瘫痪】 10 s instead of 20 s, 100 % of their damage passed to 胄 also during the dive instead of 50 % while grounded, a fresh copy after every sortie, so 掷 comes back after its initial 25 / 55 s instead of the 80 s cooldown; 锤 hits 150 % ATK). Same-seed --boss-only before → after: boss_1 unchanged (≤ 0.5 s); boss_8 独立 绝境 44.7 → 45.2 s, 独立 终极 win 2/3 → 3/3, 同盟 绝境 23.3 → 23.7 s, 同盟 终极 72.0 → 64.2 s (n = 3–5 per cell). The leader columns above are from an earlier commit (a current run differs for every leader) and were not refreshed here.

Reading: the early game is easy everywhere (official R1–R3 bring 3–10 enemies); leaks concentrate on the second-half specials (深池逐火 TIMES embers, stealth 隐形弩手组长 / 重弩突袭者, 疯狂的逐腐兽, 掠海漂移体) and 终极 R6–R11, where co-op boards still leak 3–6 and 联防 halves the LP cost. Solo leaders (bloodPoint × 0.25 [ASSUMED] when these tables were measured; × 1 since the owner's decision of 2026-10-06, §25.13.4) are the hard part of the solo modes.

Reproduce: node tools/balance.mjs --mode all --difficulty ALL --tuning off [--bots 5] [--json].

2026-10-01 — 直接乘算 stacking and the leader pool (DESIGN §20.10). The tables above were measured while every bond / strategy / item "+X%" compounded. With the official summing, leader rounds of the same model (--boss-only --boss-samples 8 --rehearsal 0, mean kill time in game seconds; 2× = real): 同盟 终极 35.6 → 59.7 (隐秘核心 104.9 → 143.9, win 100 → 88 %), 同盟 绝境 25.1 → 37.0 (38.5 → 80.8), 同盟 险境 14.0 → 17.8, 独立 终极 91.1 → 128.5, 独立 绝境 42.0 → 73.7. Replaying the same R14 lineups of 4-AI 终极 matches (seeds 1–3, every leader; the fights dumped with the old code and replayed with both): median kill 175 → 247 real s at the bots' own layers (Σ 36–361 per player), 65 → 109 s at +100 layers per active bond, 37 → 61 s at +200, 25 → 40 s at +400; 绝境 97 → 106, 25 → 43, 16 → 28, 10.5 → 19.7 s. Bot matches (matchrun, 8 seeds) pass fewer rounds: 同盟 险境 14.0 → 13.6, 绝境 12.0 → 11.4, 终极 10.1 → 9.9; 独立 险境 13.5 → 12.6 (wins 6 → 3 of 8), 绝境 12.9 → 12.6, 终极 9.5 → 9.1.

2026-10-01 (review rounds) — 奥术 and the other same-named debuffs one instance, leader parts 1:1, fixed pool, 坚守 thorns credited. Replays of the R14 boards of 4-AI co-op matches (seeds 7–9 × boss_1…7 × 终极 / 绝境 = 21 fights per row, both pair fields on one pool, +L layers on every active bond; real seconds, ∞ = not killed in 200 s), v2.5 → 直接乘算 → now — measured on the boss-HP workstream's boards, before the elite-to-board merge (DESIGN §20.11) changed what the bots build; the integrated build's numbers are in the 2026-10-02 table below:

mode	+L	Σ active layers / player	median kill	fastest	kills < 10 s	kills < 20 s
终极	0	251 (210–404)	∞ → ∞ → ∞ (8 → 6 → 6 kills)	90.7 → 126.5 → 126.5	0	0
终极	100	892 (793–1204)	61.4 → 85.8 → 102.6	20.0 → 22.5 → 54.7	0	0
终极	200	1532 (1343–2004)	30.9 → 43.4 → 56.0	9.2 → 9.7 → 20.1	1 → 1 → 0	9 → 4 → 0
终极	400	2813 (2443–3604)	16.4 → 23.9 → 23.9	2.6 → 2.7 → 9.0	7 → 4 → 1	13 → 10 → 8
绝境	0	257 (224–423)	66.5 → 81.3 → 81.3	21.7 → 41.0 → 41.0	0	0
绝境	100	900 (824–1277)	16.0 → 23.5 → 23.5	10.8 → 11.7 → 11.7	0	13 → 8 → 8
绝境	200	1543 (1424–2177)	11.7 → 14.2 → 14.2	7.4 → 7.8 → 8.8	5 → 5 → 5	19 → 16 → 16
绝境	400	2829 (2624–3977)	8.4 → 9.2 → 9.2	2.1 → 2.0 → 2.7	16 → 12 → 12	21

The 奥术 fix moves the fields where both players run 奥术 (终极 seed 7: leader arts damage taken ×40 → ×7.6 at +400, kills 2.7 → 9.0 s; 9.7 → 20.1 s at +200). 胄's drones stay at 2 % of the pool (v2.5; 12–44 % of the pool damage at the bots' layers, 2–16 % at +200): the second review round's unit-HP reading (12 000 per drone) is reverted — it made a drone 19 % of a solo 标准 bar (solo 胄 replays, seeds 13 / 21 / 31: drones 10 → 78 % of the pool, kill 144 → 78 s); with the pool reading the solo fights are back at v2.5 (drones 4–30 %) and only 直接乘算 slows them (标准 none / +100 / +200: kill times = v2.5 or up to +4 s; 终极 / 绝境 +100: 16 → 25 s, 69 → 101 s, 90 → 135 s). 坚守 thorns now count for the member's player: on the second reviewer's 28 co-op boards the unattributed share of the leader damage drops from up to 27 % (58 % with each player's main bond at 999) to 0, a solo 标准 胄 fight's from 88 % to 0; kill times are unchanged. What still kills a 绝境 leader in 3 s at Σ ≈ 3000 layers per player is official per-layer scaling without caps (炎 +0.9 %/layer ATK, 维多利亚 ×(1.25 + 0.008 L), 精准 +1.2 %/layer, 坚守 thorns 850 + 10 L every 0.2 s) — the community reports the same in the official game (巴哈姆特 12522: 999 谢拉格 + 301 灵巧 + 122 炎 at R14 "boss一秒死"). Since 2026-10-01 a bond stops at 999 layers (BOND_LAYER_CAP, official: the client's MAX_GARRISON_STACK, research 11 §1 and §7 below — the game data has no such constant, and the community never names a count above 999: 巴哈姆特 12534 "每把都能999层", "沒999層的盟約情況下"; v2.5 kept growing). On the 42 boards of the table above it changes nothing up to +400 (no bond passes 568); with each player's top bond at 1500 it holds that bond at 999: 终极 median 82.1 → 101 s (16–17 of 21 killed), fastest 19.9 → 31.4 s; 绝境 median 12.2 → 19.6 s, fastest 6.7 → 8.6 s (uncapped at 2500: 终极 median 54.9 s, fastest 12.0 s; 绝境 8.2 s / 3.4 s). "限傷" (巴哈姆特 12316 "999謝絕對不要亮奧術…大初雪會被限傷 打不出來") is the official boss-hit limit, not an overflow: the client cancels a single leader hit of ≥ 300000 in boss battles (MAX_BATTLE_DAMAGE, research 11 §2, BOSS_HIT_LIMIT — §7). An earlier reading of this note (an engine fixed-point overflow at 2³¹, not modelled) is superseded by that binary evidence. The largest damage instance on a leader in all the measurements here is 144 000 (a hidden 胄 drone at 终极; from an operator 141 323 at +400 layers; 245 493 with an uncapped 2500-layer bond), below the line, so the limit leaves these numbers unchanged — for these profiles (up to +400 per bond, a top bond at 999); with two bonds or every bond at 999 it cancels hits and changes the kill times (the 2026-10-02 table below). Hidden Core (36 fights, boss_8–10, +30 / +100 at R14): hidden 铳 kills 5 → 3 → 5 of 12 (pool dealt by 200 s 82 → 61 → 80 %; the springs' 1:1 transfer is 55–85 % of its damage); hidden 胄 10 → 6 → 9 of 12 (drones median 16–33 % of the pool damage, v2.5 12–32 %; 剑 / 锤 transfer 10–11 → 22–25 %); hidden 管 12 → 11 → 11 of 12.

2026-10-02 — the integrated build (QA 6b, cca11e6: boss HP + elite to the board + official limits + the 胄 audit). The R14 boards of real 4-AI co-op matches, seeds 7 / 8 / 9 / 12 × boss_1…7 (28 Final Assaults per row; Hidden Core boss_8–10, 12 per row), both pair fields on one pool, the same boards replayed on v2.5 → now. Real seconds (the QA tables are in game seconds: ÷ 2); "cancelled" = hits stopped by 限伤 on the integrated build. Profiles: own = the bots' layers (Σ ≈ 230 active per player), +L on every active bond (Σ ≈ 1500 / 2650–2960), top-2 = each player's two highest bonds at 999 (Σ ≈ 2050), all = every active bond at 999 (Σ ≈ 6000–7000).

fight	profile	median kill	fastest	kills < 5 s	cancelled	biggest landed hit
终极 最终攻势	own	206 → 258	88 → 114	0 → 0	0	72k → 72k
终极 最终攻势	+200	24.5 → 42.1	8.2 → 18.9	0 → 0	0	180k → 72k
终极 最终攻势	+400	11.3 → 16.8	3.7 → 9.2	2 → 0	0	402k → 114k
终极 最终攻势	top-2	28.5 → 47.8	4.2 → 7.5	2 → 0	6	828k → 274k
终极 最终攻势	all	5.0 → 8.3	1.2 → 3.4	14 → 9	18	2.38M → 300k
绝境 最终攻势	own	79 → 99	19 → 32	0 → 0	0	44k → 36k
绝境 最终攻势	+200	11.6 → 14.8	1.9 → 7.3	3 → 0	0	148k → 51k
绝境 最终攻势	+400	6.1 → 8.6	0.8 → 3.6	7 → 1	0	347k → 108k
绝境 最终攻势	top-2	9.7 → 10.0	1.1 → 2.6	9 → 7	7	398k → 267k
绝境 最终攻势	all	2.4 → 3.7	0.2 → 1.7	26 → 20	10	1.76M → 266k
终极 隐秘核心	own	345 → 352	138 → 167	–	0	144k drone
终极 隐秘核心	+200	49 → 80	25 → 42	–	0	144k drone
终极 隐秘核心	+400	18.6 → 27.3	10 → 20	–	0	144k drone
终极 隐秘核心	all	7.2 → 14.7	3.7 → 8.0	–	77	–
绝境 隐秘核心	+200	20 → 34	–	–	0	–
绝境 隐秘核心	+400	10 → 15	–	–	0	–
绝境 隐秘核心	all	4.3 → 7.8	0.3 → 2.1	–	14	–

Each player's top bond requested at 1500 (held at 999 now): 终极 median 53 → 95 s, 绝境 17.5 → 33 s. Same boards: now is 1.2–2.1× slower in every row. On each version's own bot boards the medians moved only ×1.0–1.2 (终极 own 256 → 258 s, +200 47 → 54 s; 绝境 own 81 → 99 s, +200 13 → 15 s; defeats at 终极 own 4 → 3 of 28, all boss_4 昆图斯), because the elite-to-board rule gives the bots slightly stronger R14 boards (终极 2.12 → 2.26 elites per player, 绝境 2.14 → 2.51; 绝境 6.0 → 6.9 active bonds). Pool composition now: Final Assault drone link 3.7 % at own / 0.8 % at +400, the rest direct, 0 % unattributed; Hidden Core drones 20.7 % / 1.8 %, 剑 / 锤 and spring transfers 16.3 % / 21.1 %. What still kills in seconds at ≈ 2000+ layers per player is official uncapped per-layer scaling (谢拉格 vs cold ×11.34, 奥术 ×15.7, 精准 +1208.8 % ATK at 999), which 限伤 bounds per hit only. Matchrun (co-op 4 AI, rounds passed v2.5 → now): 标准 14.00 → 14.00, 险境 13.81 → 13.88, 绝境 12.41 → 12.06 (Final Assault wins 8 → 5 of 32), 终极 9.47 → 9.47.

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4. The tuning — removed

The previous pass layered per-round enemy HP × s / ATK × √s (all 8 modes, e.g. 同盟 险境 R13 HP × 0.55) and the solo 标准 leader pool × 0.6 on top of the research numbers, to compensate for the old generator's 2–4× enemy counts. Research 08 decoded the official generator, so the compensation is gone together with its cause: data/tuning.json keeps only titles.comment_3 (坚若磐石 = least LP lost), gamedata.js has no multiplier layer (enemyScale(r) = the config table, bossHpMul() = 1, bossPoolHp() = the official pool). Difficulty questions are now answered by measuring (§3), not by tuning. tools/balance.mjs --tuning remains accepted and has no effect on the numbers.

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5. Bots (server/match/bot.js)

As found the bots lost every merge reward made while buying (the free pick-one offer queued by a merge expires at prep end; they only looked at offers when the prep opened), levelled late (L2 at R4 … L6 at R13), valued a T6 barely above a T1 and ignored the 特质 that produce layers — at R13 they fielded T1-heavy boards with 0–3 elites and 20–70 layers per bond (model: 6 elites, 130 / 75). Changes: offers are taken after every buy loop, the level curve is the competent one (early levels only with a full board), tier power 10 → 25 (was 19.5 for T6), recurring layer 特质 (every prep / refresh) and 获得时 layer / economy 特质 add value, and boss rounds are planned against the boss field (the leader counts as 10 tough enemies with a 30 s dwell on its first tiles, so stationary leaders such as 阿利斯泰尔 get hit).

mode	as found (before the fixes*)	research + time fix	tuned	official waves (now, seeds 1–5)
独立 标准 (1 AI)	6.7 rounds · 3/10 wins · [5 5 9 9 5 7 6 8 4 9]	8.1 rounds · 5/10 wins · [7 7 9 9 6 8 9 9 8 9]	8.9 rounds · 9/10 wins · [9 9 9 9 8 9 9 9 9 9]	8.8 · 4/5 · [9 9 9 9 8]
独立 险境 (1 AI)	6.5 rounds · 1/10 wins · [5 4 11 4 5 9 3 7 3 14]	8.4 rounds · 1/10 wins · [7 6 13 6 8 11 6 8 5 14]	10.1 rounds · 3/10 wins · [9 14 14 7 9 11 9 9 5 14]	13.2 · 3/5 · [14 14 13 14 11]
独立 绝境 (1 AI)	6.9 rounds · 1/10 wins · [5 5 11 5 5 7 3 14 3 11]	8.6 rounds · 1/10 wins · [7 5 12 8 13 8 6 9 4 14]	8.6 rounds · 1/10 wins · [7 5 12 8 13 8 6 9 4 14]	13.2 · 1/5 · [13 14 13 13 13]
独立 终极 (1 AI)	5.0 rounds · 0/10 wins · [4 4 7 3 3 7 3 7 3 9]	5.9 rounds · 0/10 wins · [5 4 8 5 5 7 4 7 4 10]	6.1 rounds · 0/10 wins · [5 4 10 5 4 7 4 7 4 11]	11.4 · 0/5 · [13 8 13 11 12]
同盟 标准 (4 AI)	9.1 rounds · 2/10 wins · [9 4 14 11 9 11 6 8 5 14]	11.6 rounds · 3/10 wins · [11 8 14 12 13 14 8 11 11 14]	14.0 rounds · 10/10 wins · [14 14 14 14 14 14 14 14 14 14]	14.0 · 5/5 · [14 14 14 14 14]
同盟 险境 (4 AI)	6.6 rounds · 0/10 wins · [9 4 8 7 8 6 5 6 4 9]	9.3 rounds · 0/10 wins · [10 6 12 11 10 7 7 9 9 12]	11.1 rounds · 2/10 wins · [11 8 14 11 12 7 13 10 11 14]	14.0 · 5/5 · [14 14 14 14 14]
同盟 绝境 (4 AI)	4.9 rounds · 0/10 wins · [6 4 6 4 6 6 5 4 3 5]	7.0 rounds · 0/10 wins · [7 5 8 7 7 7 6 8 5 10]	8.9 rounds · 0/10 wins · [9 6 10 9 9 8 8 11 7 12]	11.2 · 0/5 · [12 9 13 10 12]
同盟 终极 (4 AI)	5.2 rounds · 0/10 wins · [6 4 6 5 5 6 5 5 4 6]	6.3 rounds · 0/10 wins · [6 5 7 6 6 7 6 6 5 9]	7.2 rounds · 0/10 wins · [6 5 9 6 8 7 7 8 6 10]	9.8 · 0/5 · [10 7 13 8 11]

Official-waves column: node tools/balance.mjs --mode all --difficulty ALL --bots 5 (rounds passed avg · wins · per seed), measured before the review's leader-multiplier / 联防-timing fixes (§2; not re-run); the other columns are the previous pass (old generator), kept for history. * the bot code of this pass (§5) with the old time reading and no tuning; the originally reported bots (old bot code) survived ≈ 6.5 rounds on 险境 and won 1/20 on 标准.

Player feedback after 0.1.0 (#10 "人机有点太笨了"). Measured first (tools/botbench.mjs): the 0.1.0 bots refreshed 0–2 times a prep and bought side-grade singles they sold again at a loss (every sale returns 1), so they merged ≈ 2 times a match and fielded ≈ 2 elites at R13; in co-op 绝境 ≈ 1 in 2 of their bounty picks leaked (solo 10 of 80; the old score ignored the enemy); 信标 went on the best operator (it destroys its carrier) and a level-up could spend the funds a third copy in the shop needed. Changes (server/match/bot.js header, META §1.5): refresh-vs-buy by the shop odds of completing held pairs, the freeze for an unaffordable third copy, merges before level-ups, a committed focus / second bond (a teammate's main bond read from its bond strip), armour-aware DPS, bounty picks by expected value from the exposure model, item carriers by effect, 坎诺特 banking its interest capital, a tactician's 援军 inside its range. Same seeds (1–40) old → new, the match's default rehearsal (3):

config	wins	rounds passed	LP left	leaks / match	bounty enemies leaked	merges / bot	elites at R13
独立 标准 (1 AI)	35 → 35 / 40	8.80 → 8.80	29.9 → 28.6	2.5 → 3.3	1 → 1	1.40 → 2.25	– (R7: 0.7 → 1.0)
独立 绝境 (1 AI)	19 → 26 / 40	13.05 → 13.35	14.3 → 16.6	26.5 → 19.7	10 → 8 of 80 picks	2.33 → 4.10	1.8 → 2.2
同盟 标准 (4 AI)	40 → 40 / 40	14.00 → 14.00	110.0 → 112.2	39.4 → 33.1	6 → 6	2.59 → 4.10	1.9 → 2.3
同盟 绝境 (4 AI)	5 → 12 / 40	11.85 → 12.32	5.1 → 12.7	224.6 → 212.6	155 → 148 of ≈ 310 picks	2.00 → 2.97	2.3 → 2.8

绝境 leaks per alive bot in R12 / R13: solo 8.0 / 9.2 → 5.7 / 4.8, co-op 20.5 / 20.7 → 18.5 / 15.8. Co-op bounty leaks are bound by the drafts, not the pick: in 223 of the 312 co-op 绝境 bounty picks no card still on offer had a kill chance ≥ 0.5 (solo 22 of 80), and only 5 picks (solo 0) took a card below 0.5 while one ≥ 0.5 was on offer — re-measure after the bounty-half fix (player report #2). Strategies played alone (solo 绝境, seeds 201–220, forced with --band): 坎诺特 9 → 14 wins of 20, 昆图斯 9 → 11, 杜宾 8 → 9 (keeping an unused 教鞭 vs dropping it: 11 vs 11 wins over 24 杜宾 matches — kept, as it costs nothing but a hand slot). Decision time per bot prep is unchanged (one thread, back to back on a quiet host, seeds 1–6, solo 绝境 / co-op 绝境; the rehearsal included): wall clock p50 / p95 94 / 191 → 89 / 205 ms and 86 / 175 → 83 / 162 ms, CPU 131 / 314 → 124 / 329 ms and 97 / 209 → 91 / 188 ms; the heuristics alone (CPU) 31 / 74 → 28 / 70 ms and 17 / 39 → 17 / 38 ms (the lineup search tries identical pieces once and reuses the lineup across refreshes); a 机变 pick 0.07 → 0.15 ms (p50). Over the 40-seed A/B the summed prep CPU per match moved −6 % … +2 %. The tuning sweeps used seeds 101–148 with the rehearsal off; the tables above are separate seed ranges.

0.1.1 integration (DESIGN §21.6). With all 18 workstreams merged (the official bounty draft structures, the AoE, displacement and enemy fixes) the same bot on the same seeds wins 27 / 40 solo 绝境 and 9 / 40 co-op 绝境 (co-op bounty enemies leaked 120 of 380 picks: 232 drafts offered no card at a kill chance ≥ 0.5 — the R9 boss groups). The bot was then reconciled with the merged rules: it plans each unit with the range it is deployed with (rangeRec: attackRangeGrid, the server's summonRange grid — no outcome changed on these seeds) and values an attack on every enemy in range ×2 (阵法术师 / 轰击术师, now rangeAoe), a splash ×1.3 and a chain ×1.4 [ASSUMED] (CROWD). Seeds 1–40, rehearsal 3, before → after: solo 绝境 27 → 27 wins, LP left 17.9 → 18.4, bounty enemies leaked 8 → 5 of 104; co-op 绝境 9 → 11 wins, LP left 14.8 → 14.1, leaks per match 215 → 220 — within the noise of 40 seeds (the ×2-only variant: 25 / 11 wins). Decision time stays at the WF numbers (one thread, back to back, seeds 1–6): heuristics CPU p50 / p95 25 / 59 → 24 / 57 ms solo and 16 / 36 → 16 / 36 ms co-op; the whole prep with its rehearsal wall clock 80 / 148 → 78 / 153 ms and 74 / 152 → 73 / 151 ms.

0.1.1 after the QA (DESIGN §21.6, §21.19). Seeds 1–40, rehearsal 3 (wins solo 绝境 / co-op 绝境, 4 AI): the merged build dbd45c8 27 / 11; with WB's 22-match bounty lists (a rule change: R11 is a 悬赏决策 in 14 of 22 and every R11 bounty list holds a 特异III giant) the same bot 22 / 9 (LP left 16.3 / 10.9); the residual sim fixes change no outcome (22 / 9); the bench-shed fix (the buy loop's shed never sells a piece that came this prep) 24 / 10 (LP left 17.4 / 13.1, co-op leaks per match 217 → 210). 0.1.0 on the same seeds: 19 / 5; 0.1.0's bot on the final 0.1.1 rules: 23 / 7 (LP left 14.6 / 5.2, merges per bot 2.2 / 2.0 — the solo gain over 0.1.0 is mostly the rules, the co-op one the bot). The 29 same-prep buy → sell of co-op 绝境 (2 AI 托管 + 2 bots, seeds 21–26) drop to 3 (a reward pick's room, arrange, sellJunk). Decision time unchanged (one thread, seeds 1–3, both builds side by side): the whole prep p50 / p95 81 / 187 → 81 / 184 ms solo and 71 / 153 → 71 / 129 ms co-op, heuristics CPU 36 / 88 → 35 / 86 ms and 16 / 40 → 16 / 40 ms.

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6. Match follow-ups shipped with this pass

• Bounties with battles left (multi-round cards — "之后的每场作战" — last two battles since playtest #6, META §1.2) also spawn in the Final Assault / Hidden Core, on the owner's half (route to its goal), are shown in the boss-round preview, and the boss battle uses up one of their battles (kill coins, and a perfect-payout 战术特训 card's coins when the player's own field is perfect and the team wins → pending funds for the Hidden Core prep).
• A 驰援 card is never offered when its bond has no chess left in the match's pool (every member banned).
• docs/META.md §2.6 example guards ctx.source.kind === 'choice' (its EffectRef reuses the handler's key).
• 坚若磐石 = least LP lost (titles.comment_3 { stat: 'lpLost', rule: 'min' } in tuning.json; results.js supports rule: 'min' among the players still alive).
• 教鞭 offers a personal choice of three 战术特训 cards (a bot picks by the bounty scorer, the prep's deadline at random); “神秘顾客” stays a random bounty — docs/META.md §2.5.

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7. Official limits: 999 layers per bond, 限伤 300000 (research 11, DESIGN §20.12)

Two official caps, now in the sim and the match (shared/constants.js BOND_LAYER_CAP / BOSS_HIT_LIMIT, 0 / Infinity = off): a bond's layers stop at 999 (MAX_GARRISON_STACK); in the Final Assault / Hidden Core a single hit of ≥ 300000 on a leader is cancelled (MAX_BATTLE_DAMAGE: 0 damage, nothing to the pool — not a clamp).

• Effect on the measurements above: none. The competent board of §1.1 carries ≈ 150 core layers at R14, far below 999, and its biggest leader hits stay far under the line — probe of 2026-10-01 (runBoss with every leader hit recorded, 2 seeds each): 同盟 终极 R14 competent max 37k (2481 hits), 同盟 终极 R15 strong (×1.4) max 72k (4669), 独立 终极 R14 strong max 28k (1201); no hit reached 200k, none was cancelled. §3 stays valid. The co-op replay profiles of §3 with two bonds or every bond at 999 per player do reach the line (6–77 cancelled hits per row, the 2026-10-02 table).
• Where they bind: the late boards the community describes — 999-layer 谢拉格 (×11.34 vs cold / frozen), 奥术 (×11.19 arts taken, a debuff a teammate's board also applies), 炎 (ATK ×10.22) — whose single hits run from 160k to past 300k. There the limit makes the official co-op leaders as hard to kill as the user asked: a hit past the line deals nothing, so extra multipliers can lower the damage, the reason players avoid lighting more damage bonds at 999 layers. Pools: 200k (卢西恩 FUNNY) … 7.6M (假想敌：管 hidden ABYSS) — in the easy modes one cancelled hit would have been the whole pool.
• Bots read the capped ps.layers; their boards never come near either line (§5), so their play is unchanged.
• The tools stop at the cap too: balance.mjs applyBoard clamps the profile-scaled layer curves (a numeric --profile above ≈ 4.9 would have pushed the 170-layer R15 core curve, +20 % jitter, past 999) and matchrun.mjs --layers N adds at most the room left under 999, so --check stays clean on a boosted run.
• Pool size and the line: a drone that dies (whoever kills it, DESIGN §20.13) costs 假想敌：胄 0.02 × the pool max (【死亡集群】, boss_1 / boss_8; bosses.js DRONE_LINK_BASE 'pool'). With the pool per player alive (§25.13.4) the hidden 胄 终极 pool is 21.6M / 28.8M at 3 / 4 players, so a drone is 432000 / 576000 — above the line; the link is a share, no hit, and passes it (Battle.loseHp noHitLimit [ASSUMED]: research 11 §2.1 checks every damage modifier, but which max HP the official link reads is not documented). Re-check this whenever the pool size changes (research 11 §6).