136 lines
3.9 KiB
Python
136 lines
3.9 KiB
Python
"""莊家抽水（Vig）去除工具。"""
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from __future__ import annotations
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from typing import Callable, List, Sequence
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import numpy as np
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from scipy.optimize import minimize_scalar
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def calculate_overround(odds: Sequence[float]) -> float:
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"""計算莊家總水位（Overround）。
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Overround = Σ(1 / odds_i)。
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若結果 > 1 表示含有抽水。
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"""
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if not odds:
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raise ValueError('odds 不可為空')
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_odds = np.asarray(odds, dtype=float)
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if np.any(_odds <= 1):
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raise ValueError('賠率必須全部大於 1')
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return float(np.sum(1.0 / _odds))
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def remove_margin_basic(odds: Sequence[float]) -> List[float]:
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"""等比例剝除抽水。
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先轉換為 implied probability，再除以 overround 讓機率總和為 1。
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"""
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implied = np.array([1.0 / x for x in odds], dtype=float)
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overround = implied.sum()
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if overround <= 0:
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raise ValueError('無效 odds，無法計算去水')
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true_probs = implied / overround
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return [float(x) for x in true_probs]
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def _shin_objective(z: float, observed: np.ndarray) -> float:
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"""Shin 模型中，透過 z 估計真實機率，使每個結果有一致修正。
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模型假設：
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q_i(z) = max((p_i - z/(k-1)) / (1 - k/(k-1)*z), 1e-12)
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其中 q_i 為觀察值 implied probability，p_i 為解構後真實機率。
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透過約束 Σp_i=1 搜尋最小平方誤差。
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"""
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k = observed.size
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if not 0.0 <= z < 1:
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return 1e9
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denom = 1.0 - k / max(k - 1, 1) * z
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if denom <= 0:
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return 1e9
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raw = (observed - z / max(k - 1, 1)) / denom
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raw = np.clip(raw, 1e-12, None)
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normalized = raw / raw.sum()
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return float(np.sum((normalized - observed / observed.sum()) ** 2))
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def remove_margin_shin(odds: Sequence[float]) -> List[float]:
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"""Shin 方法去水。
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流程：
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1) 觀察賠率轉 implied probability。
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2) 用單參數 z 做最小化，推回一組更接近無套利的真實機率。
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3) 回傳機率正規化結果。
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"""
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odds_array = np.asarray(odds, dtype=float)
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if odds_array.size == 0:
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raise ValueError('odds 不可為空')
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if np.any(odds_array <= 1):
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raise ValueError('賠率必須全部大於 1')
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implied = 1.0 / odds_array
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if implied.size == 2:
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# 二元市場可直接利用近似閉式解，穩定性較佳
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q1 = implied[0] / implied.sum()
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q2 = implied[1] / implied.sum()
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z = max(0.0, min(0.49, (q1 + q2 - 1.0) * 0.5))
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else:
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# 多項市場，使用數值搜尋
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result = minimize_scalar(
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_shin_objective,
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args=(implied,),
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bounds=(0.0, 0.49),
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method='bounded',
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)
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z = float(result.x if result.success else 0.0)
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k = implied.size
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denom = 1.0 - k / max(k - 1, 1) * z
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if denom <= 0:
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return remove_margin_basic(odds)
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raw = (implied - z / max(k - 1, 1)) / denom
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raw = np.clip(raw, 1e-12, None)
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true_prob = raw / raw.sum()
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return [float(x) for x in true_prob]
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def prob_to_decimal_odds(true_probs: Sequence[float]) -> List[float]:
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"""真實機率轉換回無水賠率。
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p 轉賠率公式：odds = 1 / p。
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"""
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probs = np.asarray(true_probs, dtype=float)
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if np.any(probs <= 0):
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raise ValueError('機率需大於 0')
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total = probs.sum()
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if not np.isclose(total, 1.0, atol=1e-6):
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probs = probs / total
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return [round(float(1.0 / p), 4) for p in probs]
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def compare_bookmaker_true_prob(
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implied_odds: Sequence[float],
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transform: Callable[[Sequence[float]], Sequence[float]] = remove_margin_shin,
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) -> dict[str, list[float]]:
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"""比對原始賠率與去水後真實賠率，可直接提供前端展示。"""
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true_probs = transform(implied_odds)
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return {
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'implied_prob': [float(1.0 / x) for x in implied_odds],
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'true_implied_prob': true_probs,
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'true_decimal_odds': prob_to_decimal_odds(true_probs),
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}
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