304 lines
17 KiB
Python
304 lines
17 KiB
Python
#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""清图支配性对账重算工具（行动经济 条款⑤ · 挖穿残余池计价）。
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判式权威 = design/gdd/systems/排雷循环/行动经济.md 条款⑤（公式本体同时内联于本 docstring）：
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主判式 Δ_clear = [R_res + C_eff] − [X_res + Δr × s_ref] ≥ 0
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保守地板 C_eff(min) ≥ X_res + Δr × s_ref
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E[踩雷] = |M| × n_s ÷ (n_s + 1) （均匀交错模型）
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n_s = (1 − ι) × |S| （域守卫 n_s < 1 ⇒ 不评估）
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R_res = n_s × E_dig；X_res = E[踩雷] × V_mine；Δr = ⌈(n_s + E[踩雷]) ÷ AP_r⌉
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s_ref = D_ref；停手侧 RAP 机会收益按零计价（显式假设）。
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本工具是难度曲线调参的常设重跑入口：
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所有输入可经命令行覆盖（--d-ref --c-clear --ap-r --iota ...），
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重跑时按当期 .tres 行值更新默认值即可，公式本体不动。
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单雷代价 / 单格收益的当量换算严格走 战斗结算「效果档位对照表」单一口径：
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flat 类 E = 表值；percent 类 E = |层数×行值|÷100 × D_ref（每结算每层）；
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AC 轴换算 = AC 点数 × 5pp（d20 线性）× D_ref（假设登记，见审计报告）。
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【现行判式口径】
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- 池权重合计 77（含 action 6 / gp 2；clear_blast 系清图槽对象不入格池）。
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- 直伤雷负向三行 6/8/8（backlash/snare/recoil）；
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正向 pierce_strike/magic_bolt 维持 flat 2；heal_minor 2（Package B 第 2 轮）。
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- 清图槽 C_MIN/C_MAX = 24/40（中点 32）；AP_r = 8。
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- off_guard 走 ac 轴 −1（0.2u 模型：点数×5pp×D_ref=0.2 当量/每敌拍）。
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- V_mine 为九型负向字典口径（enrage/off_guard/警觉/backlash/sapped/snare/recoil/
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ap_drain/gp_lose——ap_drain 按 A6 flat 1、gp_lose 按 A5 代理 2 计）。
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- β 比值带判读与逐型净期望输出：
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β(u)=V_mine/E_dig ∈ [1.2, 2.5]；条件一 (1−ρ̂)E_dig−ρ̂V_mine ≥ 0（下限 0，上限归 β_hi）；
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条件二 E[标中兑付] ≥ (1+δ)·E_dig（δ=1.25 provisional，兑付溢价形态 a）。
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"""
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import argparse
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import math
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# ============ 现行值链（出处见各注释；重跑按当期 .tres 更新） ============
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D_REF = 4 # settlement.tres equivalence_ref_damage
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P_PERFECT = 200 # settlement.tres（percent，÷100 = ×2 双份交付）
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C_MIN, C_MAX = 24, 40 # reward.tres clear_blast power_min/max；期望口径 = 中点 32
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AP_R = 8 # action_economy.tres ap_per_round
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DIG_COST = 1 # action_economy.tres dig_ap_cost
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IOTA = 0.88 # board_gen.tres inferability_target（判式 ι 代理）
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# 效果行值（status_effects.tres）
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ATTACK_UP_PCT = 50 # 增伤 +50%，duration 1，hero 侧
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AC_UP_POINT = 1 # 护甲强化 +1 AC，duration 1
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WEAKEN_PCT = 65 # 削弱 −65%（有效拍 1：duration 2 先兑付后衰减）
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ENRAGE_PCT = 25 # 暴走 +25%，enemy 侧 side-wide
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SAPPED_PCT = 25 # 乏力 −25%，hero 侧
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OFF_GUARD_AC = 1 # 失衡 AC −1（0.2u 模型：1 点 × 5pp × D_ref = 0.2 当量/每敌拍）
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ALERT_EQUIV = 0.2 # 警觉（敌 AC+1×1拍）：主角每拍恰 1 攻 × 1 拍寿命 ⇒ 0.2 当量，u 无关（假设 A4）
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# 直伤/群伤 flat 值（reward.tres）
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SPARK_AOE = 1 # 爆裂粉尘（全体存活敌）
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HEAL_MINOR = 2 # 急救敷料（Package B 第 2 轮）
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HEAL_BACKLASH = 6 # 反噬震荡（主角直伤）
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PIERCE_STRIKE = 2 # 穿刺弹（单目标克制直伤，必中全额）
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MAGIC_BOLT = 2 # 魔法矢（同上）
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PIERCE_SNARE = 8 # 穿刺陷阱（主角直伤）
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MAGIC_RECOIL = 8 # 魔法反噬（主角直伤）
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AP_UP = 1 # 行动点 +1（当量 = flat 表值 1，机会成本口径更高仅登记——假设 A6）
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GP_COIN = 3 # GP 袋 +3 GP（gp 当量 = flat power 代理——假设 A5，口径空白登记）
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GP_LOSE = 2 # 破财 −2GP（同上代理）
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# 甲效矩阵（settlement.tres，加法核点数）：基础值 + 点数，damage_floor=1
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ARMOR_EFFECT = { # attack_type → {armor_type: 点数}；切片 L1 全轻甲 / L2 除 Boss 全轻甲
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"pierce": {"light": -1, "ward": 1, "heavy": 0},
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"magic": {"light": 0, "ward": -1, "heavy": 1},
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"normal": {"light": 0, "ward": 1, "heavy": -1},
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}
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# 格面资源池正向权重（reward.tres，合计 77）
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# 类型 → (权重)；负向行 weight=0 不参与摇号，类型分布 = 正向权重
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# clear_blast pool_tag=clear_default 系清图槽对象，不入格池（地图战斗资源.md §清图槽）。
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POOL_WEIGHTS = {"attack": 14, "defense": 11, "blast": 16, "heal": 4,
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"weaken": 8, "pierce": 8, "magic": 8, "action": 6, "gp": 2}
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# β 比值带 [1.2, 2.5]（u=3 登记态 1.17 微破下限=点名不强制回滚）
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BETA_LO, BETA_HI = 1.2, 2.5
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# δ 旗溢价（形态 a 兑付溢价，δ=1.25 provisional ⇒ 兑付按同型正向 ×(1+δ)）
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DELTA = 0.25
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# 板形（|M| 幸存雷 / |S| 安全格）双口径
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# 名义 = density×(W×H−9) 初布值（参考板形口径，连续性参照）
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# 实测 = sim/board_stat_probe.gd 200 样本/行均值（"先布后删"落地值，主流读数）
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# （实测值沿用 board_stat_probe 读数；板形行值未变，不强制复跑）
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BOARDS = {
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"L1前段·名义(10x10)": {"M": 23, "S": 77},
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"L1后段·名义(12x12)": {"M": 34, "S": 110},
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"L2·名义(12x12)": {"M": 34, "S": 110},
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"L1前段·实测(10x10)": {"M": 12.91, "S": 87.09},
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"L1后段·实测(12x12)": {"M": 22.61, "S": 121.39},
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"L2·实测(12x12)": {"M": 22.39, "S": 121.61},
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}
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def e_dig(u: float, d_ref: float, aoe_per_unit: bool = True) -> float:
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"""单安全格期望收益（当量），格子池 77 权重加权。
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u = 敌方单位数。hero 侧单目标效果不随 u 缩放（主角每轮出手一次）；
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enemy 侧 side-wide 效果（ac_up 承伤面 / spark_aoe 群伤 / weaken 全体减伤）随 u 缩放。
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"""
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w = POOL_WEIGHTS
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total = sum(w.values())
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attack = w["attack"] * ATTACK_UP_PCT / 100 * d_ref # 主角下一拍增伤
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ac_up = w["defense"] * AC_UP_POINT * 0.05 * d_ref * u # 每个来敌拍 −5pp 命中
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spark = w["blast"] * (SPARK_AOE * u if aoe_per_unit else SPARK_AOE) # 全体存活敌
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heal = w["heal"] * HEAL_MINOR
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weaken = w["weaken"] * WEAKEN_PCT / 100 * d_ref * u # 全体敌拍 ×0.35
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pierce = w["pierce"] * max(1, PIERCE_STRIKE + ARMOR_EFFECT["pierce"]["light"]) # 轻甲口径
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magic = w["magic"] * max(1, MAGIC_BOLT + ARMOR_EFFECT["magic"]["light"])
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action = w["action"] * AP_UP
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gp = w["gp"] * GP_COIN
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return (attack + ac_up + spark + heal + weaken + pierce + magic + action + gp) / total
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def v_mine(u: float, d_ref: float) -> float:
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"""现行极性矩阵加权口径（九型负向字典）——踩雷兑付 = 该格类型负向行，按 77 权重池加权。
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hero 侧固定（直伤三类 heal_backlash/snare/recoil + 乏力 sapped + ap_drain + gp_lose）；
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enemy 侧 side-wide（enrage 每敌拍 / off_guard 每敌拍命中上浮）随 u 缩放；
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警觉按 0.2 当量固定（假设 A4）。
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"""
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w = POOL_WEIGHTS
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total = sum(w.values())
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enrage = w["attack"] * ENRAGE_PCT / 100 * d_ref * u
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off_guard = w["defense"] * OFF_GUARD_AC * 0.05 * d_ref * u # AC−1 → 每敌拍 +5pp 命中
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alert = w["blast"] * ALERT_EQUIV
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backlash = w["heal"] * HEAL_BACKLASH
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sapped = w["weaken"] * SAPPED_PCT / 100 * d_ref # 主角下一拍 −25%
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snare = w["pierce"] * PIERCE_SNARE
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recoil = w["magic"] * MAGIC_RECOIL
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ap_drain = w["action"] * AP_UP
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gp_lose = w["gp"] * GP_LOSE
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return (enrage + off_guard + alert + backlash + sapped + snare + recoil
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+ ap_drain + gp_lose) / total
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def w_flag_hit(u: float, d_ref: float, prem_pct: int = 125) -> float:
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"""标中旗兑付聚合当量 W(u)——整数量级实现口径（与机制同式：各型四舍五入取整后折算）。
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条件二常设判读式：条件二 = W(u) ≥ (1+δ)·E_dig(u)。
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取整跟随机制（GDScript round=半分远离零），非 Python banker's rounding。
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1 点量纲行（ac_up/action/spark）取整地板=×1.0——u=3 聚合微欠的成因（登记面）。
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"""
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w = POOL_WEIGHTS
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total = sum(w.values())
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def sc(x: float) -> int:
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return int(math.floor(x * prem_pct / 100.0 + 0.5))
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attack = w["attack"] * sc(ATTACK_UP_PCT) / 100 * d_ref
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ac_up = w["defense"] * sc(AC_UP_POINT) * 0.05 * d_ref * u
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spark = w["blast"] * (sc(SPARK_AOE) * u)
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heal = w["heal"] * sc(HEAL_MINOR)
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weaken = w["weaken"] * sc(WEAKEN_PCT) / 100 * d_ref * u
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pierce = w["pierce"] * max(1, sc(PIERCE_STRIKE) + ARMOR_EFFECT["pierce"]["light"])
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magic = w["magic"] * max(1, sc(MAGIC_BOLT) + ARMOR_EFFECT["magic"]["light"])
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action = w["action"] * sc(AP_UP)
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gp = w["gp"] * sc(GP_COIN)
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return (attack + ac_up + spark + heal + weaken + pierce + magic + action + gp) / total
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def per_type_table(u: float, d_ref: float) -> list:
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"""逐型 P_t/N_t 明细（当量），供条件净期望计算。返回 [(型, P_t, N_t)]。"""
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return [
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("attack", ATTACK_UP_PCT / 100 * d_ref, ENRAGE_PCT / 100 * d_ref * u),
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("defense", AC_UP_POINT * 0.05 * d_ref * u, OFF_GUARD_AC * 0.05 * d_ref * u),
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("blast", float(SPARK_AOE * u), ALERT_EQUIV),
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("heal", float(HEAL_MINOR), float(HEAL_BACKLASH)),
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("weaken", WEAKEN_PCT / 100 * d_ref * u, SAPPED_PCT / 100 * d_ref),
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("pierce", float(max(1, PIERCE_STRIKE + ARMOR_EFFECT["pierce"]["light"])), float(PIERCE_SNARE)),
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("magic", float(max(1, MAGIC_BOLT + ARMOR_EFFECT["magic"]["light"])), float(MAGIC_RECOIL)),
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("action", float(AP_UP), float(AP_UP)),
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("gp", float(GP_COIN), float(GP_LOSE)),
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]
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def audit_shape(name: str, m: float, s: float, u: float, c_clear: float,
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d_ref: float, ap_r: int, iota: float, v_mine_v: float,
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e_dig_v: float, dig_cost: int) -> dict:
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"""单板形单语境全量计算，返回判式各腿与判定。"""
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n_s = (1 - iota) * s
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if n_s < 1:
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return {"name": name, "skip": True}
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e_mine = m * n_s / (n_s + 1)
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r_res = n_s * e_dig_v
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x_res = e_mine * v_mine_v
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dr = math.ceil((n_s + e_mine * dig_cost) / ap_r)
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c_eff_normal = c_clear
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c_eff_perfect = c_clear * P_PERFECT / 100
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d_normal = (r_res + c_eff_normal) - (x_res + dr * d_ref)
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d_perfect = (r_res + c_eff_perfect) - (x_res + dr * d_ref)
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floor_req = x_res + dr * d_ref # 保守地板需求（对 C_eff）
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return {
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"name": name, "skip": False, "n_s": n_s, "e_mine": e_mine,
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"r_res": r_res, "x_res": x_res, "dr": dr, "dr_cost": dr * d_ref,
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"floor_req": floor_req, "gap_normal": floor_req - c_eff_normal,
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"gap_perfect": floor_req - c_eff_perfect,
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"d_normal": d_normal, "d_perfect": d_perfect,
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}
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def main() -> None:
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ap = argparse.ArgumentParser(description="清图支配性（条款⑤）对账重算 + 判式换代面板（条款3）")
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ap.add_argument("--d-ref", type=float, default=D_REF)
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ap.add_argument("--c-clear", type=float, default=None,
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help="清图奖励当量 C（默认 = (C_MIN+C_MAX)/2 = 32；传 24 得保守地板口径）")
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ap.add_argument("--ap-r", type=int, default=AP_R)
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ap.add_argument("--iota", type=float, default=IOTA)
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ap.add_argument("--rho-nominal", type=float, default=0.25, help="名义雷率（判式主口径）")
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ap.add_argument("--rho-measured", type=float, default=0.129, help="实测幸存雷率（10×10 包络口径）")
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ap.add_argument("--delta", type=float, default=DELTA, help="旗溢价系数 δ（兑付溢价形态 a）")
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ap.add_argument("--e-dig-discount", type=float, default=1.0,
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help="E_dig 实现率折减（legacy 敏感性口径传 0.6）")
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args = ap.parse_args()
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c_clear = args.c_clear if args.c_clear is not None else (C_MIN + C_MAX) / 2
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print(f"现行值链快照：D_ref={args.d_ref:g} C={c_clear:g}（min {C_MIN}/max {C_MAX}） "
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f"AP_r={args.ap_r} ι={args.iota} p_perfect={P_PERFECT} RAP零价假设照旧")
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print(f"E_dig（77权重池加权当量）: u=1 {e_dig(1, args.d_ref):.3f} · u=2 {e_dig(2, args.d_ref):.3f} · "
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f"u=3 {e_dig(3, args.d_ref):.3f}（折减 ×{args.e_dig_discount:g} 后同乘）")
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print(f"V_mine（九型矩阵加权）: u=1 {v_mine(1, args.d_ref):.3f} · "
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f"u=2 {v_mine(2, args.d_ref):.3f} · u=3 {v_mine(3, args.d_ref):.3f}")
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print()
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print("### 条款3 判式换代面板（β 比值带 + 条件一聚合健康式 + 条件二旗溢价）")
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print(f"β 带 = [{BETA_LO:g}, {BETA_HI:g}]（2026-10-04 用户裁 P4） 兑付溢价 ×(1+δ) = ×{1 + args.delta:g}（形态 a）")
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print("| u | E_dig | V_mine | β=V/E | 带判定 | 条件一 盲挖净期望(名义ρ) | 条件一 盲挖净期望(实测ρ̂) | 条件二 W(u) | 条件二 阈值(1+δ)E_dig | 条件二判定 |")
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print("|---|---|---|---|---|---|---|---|---|---|")
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for u in (1, 2, 3):
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ed = e_dig(u, args.d_ref)
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vm = v_mine(u, args.d_ref)
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beta = vm / ed
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verdict = "✓带内" if BETA_LO <= beta <= BETA_HI else (
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"✗破下限(登记态)" if beta < BETA_LO else "✗破上限")
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blind_nom = (1 - args.rho_nominal) * ed - args.rho_nominal * vm
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blind_meas = (1 - args.rho_measured) * ed - args.rho_measured * vm
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# 条件二（机制在位）：W=整数量级标中兑付聚合（取整跟随机制），阈值 =(1+δ)·E_dig
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wfh = w_flag_hit(u, args.d_ref, int(round((1 + args.delta) * 100)))
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thresh = (1 + args.delta) * ed
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cond2 = "✓转绿" if wfh >= thresh else "✗微欠(整数量级取整地板，登记面)"
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print(f"| {u} | {ed:.3f} | {vm:.3f} | {beta:.2f} | {verdict} | "
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f"{blind_nom:+.2f} | {blind_meas:+.2f} | {wfh:.3f} | {thresh:.3f} | {cond2} |")
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print()
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print("### 逐型条件净期望 (1−ρ)P_t − ρN_t（当量/格，u=1，名义 ρ 与实测 ρ̂ 双列）")
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print("| 型 | P_t | N_t | 净期望(名义ρ) | 净期望(实测ρ̂) | 判(名义) |")
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print("|---|---|---|---|---|---|")
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for t, p, n in per_type_table(1, args.d_ref):
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net = (1 - args.rho_nominal) * p - args.rho_nominal * n
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net_m = (1 - args.rho_measured) * p - args.rho_measured * n
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verdict = "✓" if net > 1e-9 else ("踩线" if abs(net) <= 1e-9 else "✗破线")
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||
print(f"| {t} | {p:g} | {n:g} | {net:+.2f} | {net_m:+.2f} | {verdict} |")
|
||
for u in (2, 3):
|
||
cells = " · ".join(f"{t}({(1 - args.rho_nominal) * p - args.rho_nominal * n:+.2f})"
|
||
for t, p, n in per_type_table(u, args.d_ref))
|
||
print(f"u={u} 净期望: {cells}")
|
||
print()
|
||
|
||
print(f"### 主判式（条款⑤）· 九型矩阵加权 V_mine · C={c_clear:g}")
|
||
print("| 板形 | u | n_s | E[踩雷] | R_res | X_res | Δr(代价) | Δ_clear 非完美 | Δ_clear 完美 | 判定 |")
|
||
print("|---|---|---|---|---|---|---|---|---|---|")
|
||
for bname, b in BOARDS.items():
|
||
for u in (1, 2, 3):
|
||
ed = e_dig(u, args.d_ref) * args.e_dig_discount
|
||
r = audit_shape(bname, b["M"], b["S"], u, c_clear, args.d_ref,
|
||
args.ap_r, args.iota, v_mine(u, args.d_ref), ed, DIG_COST)
|
||
if r["skip"]:
|
||
continue
|
||
verdict = "✓" if r["d_perfect"] >= 0 and r["d_normal"] >= 0 else (
|
||
"完美✓" if r["d_perfect"] >= 0 else "✗")
|
||
print(f"| {bname} | {u} | {r['n_s']:.2f} | {r['e_mine']:.2f} | {r['r_res']:.1f} | "
|
||
f"{r['x_res']:.1f} | {r['dr']}({r['dr_cost']:.0f}) | {r['d_normal']:+.1f} | "
|
||
f"{r['d_perfect']:+.1f} | {verdict} |")
|
||
print()
|
||
|
||
print("### 保守地板（C_eff(min)=C_MIN）需求与缺口")
|
||
print("| 板形 | u | 地板需求 X_res+Δr×s_ref | 缺口(对 min) | 缺口(对完美 ×2) |")
|
||
print("|---|---|---|---|---|")
|
||
for bname, b in BOARDS.items():
|
||
for u in (1, 3):
|
||
ed = e_dig(u, args.d_ref) * args.e_dig_discount
|
||
r = audit_shape(bname, b["M"], b["S"], u, float(C_MIN), args.d_ref,
|
||
args.ap_r, args.iota, v_mine(u, args.d_ref), ed, DIG_COST)
|
||
if r["skip"]:
|
||
continue
|
||
print(f"| {bname} | {u} | {r['floor_req']:.1f} | +{r['gap_normal']:.1f} | +{r['gap_perfect']:.1f} |")
|
||
print()
|
||
|
||
# 护栏 B（防钓鱼——退化板刷清图奖励上界）：⌈(|S|min − |R0|max) ÷ AP_r⌉ × s_ref ÷ 2
|
||
# |S|min = min_safe_count 当期行集（50/60）；|R0|max = 20 经验值（无登记供给方）
|
||
print("### 护栏 B 复核（防钓鱼上界，D_ref 口径）")
|
||
for s_min in (50, 60):
|
||
ub = math.ceil((s_min - 20) / args.ap_r) * args.d_ref / 2
|
||
print(f"|S|min={s_min}: 上界 = ⌈({s_min}−20)/{args.ap_r}⌉×{args.d_ref:g}÷2 = {ub:g}"
|
||
f" → C={c_clear:g} {'✓' if c_clear <= ub else '越 %.1f×' % (c_clear / ub)}"
|
||
f" / 完美 C_eff={c_clear * P_PERFECT / 100:g} "
|
||
f"{'✓' if c_clear * P_PERFECT / 100 <= ub else '越 %.1f×' % (c_clear * P_PERFECT / 100 / ub)}")
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|