9.2 方差与体验

#!/usr/bin/env python3
# file: sim/gd_mech_09_variance.py
# tier: S
# verify: /opt/homebrew/bin/python3 sim/gd_mech_09_variance.py
"""9.2 方差与体验（S 层）。

9.1 比的是「单次抽样的分布形状」，本节比的是**同一条体验代理量在两套发牌结构下
的离散程度**。体验代理量取**起手 5 张的总伤害**（开局压制力）：

  - bag      真实发牌：Fisher-Yates 打乱 12 张牌库，取前 5 张（不放回）
  - replace  假想发牌：每次 rng_next % 12 独立抽一张（可放回，允许重复）

对 200 组显式种子各算一次起手伤害，用**整数与千分比**度量离散程度：

  - range   极差 = max - min（整数）
  - avg     均值（整数地板除）
  - varPm   方差代理量 = Σ(x-avg)² ×1000 // (S·avg)（χ² 型千分比）
  - lowPm   起手伤害 < 20 的「哑火局」占比（千分比）
  - hiPm    起手伤害 >= 45 的「爆开局」占比（千分比）

体验代理量只用于**相对比较**，禁绝对化：它回答的是「可放回比不放回宽多少」，
不是「多少伤害最好玩」。
"""
from __future__ import annotations

import os
import sys

import ashlib

HERE = os.path.dirname(os.path.abspath(__file__))
ROOT = os.path.dirname(HERE)

DECK = [6, 6, 6, 6, 6, 14, 14, 14, 3, 3, 0, 0]  # strike×5 heavy×3 jab×2 guard×2
HAND = 5
SEEDS = list(range(1, 201))
LOW = 20
HIGH = 45
HEADER = ["structure", "minD", "maxD", "range", "avg", "varPm", "lowPm", "hiPm"]


def bag_hand(seed: int) -> int:
    """真实发牌：洗牌袋取前 5 张，总伤害。"""
    cards = [{"d": d} for d in DECK]
    shuffled = ashlib.shuffle_deck(cards, seed)
    return sum(c["d"] for c in shuffled[:HAND])


def replace_hand(seed: int) -> int:
    """可放回发牌：每次独立抽一张，允许重复。"""
    state = seed % ashlib.RNG_MOD or 1
    total = 0
    for _ in range(HAND):
        state = ashlib.rng_next(state)
        total += DECK[state % len(DECK)]
    return total


def stats(vals: list) -> dict:
    s = len(vals)
    avg = sum(vals) // s
    var_pm = sum((x - avg) ** 2 for x in vals) * 1000 // (s * avg)
    low = sum(1 for x in vals if x < LOW)
    hi = sum(1 for x in vals if x >= HIGH)
    return {
        "min": min(vals), "max": max(vals), "range": max(vals) - min(vals),
        "avg": avg, "varPm": var_pm,
        "lowPm": low * 1000 // s, "hiPm": hi * 1000 // s,
    }


def main() -> int:
    bag = [bag_hand(s) for s in SEEDS]
    rep = [replace_hand(s) for s in SEEDS]
    rows: list = []
    for name, vals in (("bag", bag), ("replace", rep)):
        st = stats(vals)
        rows.append([name, st["min"], st["max"], st["range"], st["avg"],
                     st["varPm"], st["lowPm"], st["hiPm"]])

    out = os.path.join(ROOT, "out", "mech09_variance.csv")
    n = ashlib.write_csv(out, HEADER, rows)

    print(f"seeds={len(SEEDS)} hand={HAND} lowThresh={LOW} highThresh={HIGH} deckSum={sum(DECK)}")
    print(" ".join(HEADER))
    for r in rows:
        print(" ".join(str(x) for x in r))
    print(f"bagRange={stats(bag)['range']} replaceRange={stats(rep)['range']}")
    print(f"wrote out/mech09_variance.csv rows={n}")
    return 0


if __name__ == "__main__":
    sys.exit(main())

seeds=200 hand=5 lowThresh=20 highThresh=45 deckSum=78
structure minD maxD range avg varPm lowPm hiPm
bag 12 54 42 32 2505 70 80
replace 6 70 64 32 3878 110 135
bagRange=42 replaceRange=64
wrote out/mech09_variance.csv rows=2

bag     avg = 32   Σ(x-avg)² = 16033   16033 × 1000 // (200 × 32) = 2505
replace avg = 32   Σ(x-avg)² = 24825   24825 × 1000 // (200 × 32) = 3878