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] (co-op; one pool for the split leaders, no alive-player factor — solo keeps ×0.25, flagged [ASSUMED] in data);
• 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 (solo ×0.25), 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; co-op "敌方领袖的总生命值不变"	co-op = bloodPoint, no alive scaling; solo ×0.25 kept [ASSUMED]; the solo 标准 ×0.6 removed
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
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

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]) are the hard part of the solo modes; the solo pool factor is the one open number here (research 08 §8 #2).

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

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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.

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6. Match follow-ups shipped with this pass

• Multi-round bounties ("之后的每场作战") 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 → 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 / “神秘顾客” stay a random bounty, documented in docs/META.md §2.5.