72 lines
3.1 KiB
Python
72 lines
3.1 KiB
Python
from typing import List, Dict
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import math
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class SGPCorrelationEngine:
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"""
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同場串關 (Same Game Parlay) 關聯性與價值探測引擎
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"""
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@staticmethod
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def calculate_joint_probability(prob_A: float, prob_B: float, correlation_coeff: float) -> float:
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"""
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計算兩個事件的聯合機率 (考慮相關係數)。
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使用簡化的二元正態分佈/Copula近似邏輯。
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:param prob_A: 事件 A 獨立發生的真實機率
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:param prob_B: 事件 B 獨立發生的真實機率
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:param correlation_coeff: 相關係數 (-1.0 到 1.0)
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"""
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if not (-1.0 <= correlation_coeff <= 1.0):
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raise ValueError("相關係數必須介於 -1.0 與 1.0 之間")
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# 獨立發生的聯合機率
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independent_joint_prob = prob_A * prob_B
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# 理論最大與最小邊界
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max_joint_prob = min(prob_A, prob_B)
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min_joint_prob = max(0.0, prob_A + prob_B - 1.0)
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if correlation_coeff == 0:
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return independent_joint_prob
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elif correlation_coeff > 0:
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# 正相關：使用 Fréchet–Hoeffding 上界與獨立機率的非線性加權，避免極端值的線性失真
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return independent_joint_prob + (max_joint_prob - independent_joint_prob) * (correlation_coeff ** 1.5)
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else:
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# 負相關：使用 Fréchet–Hoeffding 下界與獨立機率的非線性加權
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return independent_joint_prob - (independent_joint_prob - min_joint_prob) * (abs(correlation_coeff) ** 1.5)
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@staticmethod
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def find_sgp_value(events: List[Dict], bookmaker_sgp_odds: float) -> Dict:
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"""
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評估 SGP 注單是否具備正期望值。
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events 範例: [{'prob': 0.6}, {'prob': 0.4}] 且需自帶兩兩相關係數矩陣 (此處簡化為平均相關性)
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"""
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if len(events) < 2:
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raise ValueError("SGP 必須至少包含兩個事件")
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# 假設外部特徵工程已經給出了這組事件的平均正相關係數 (例如 0.4)
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# 實務上會透過更複雜的 Monte Carlo 計算，此為展示核心邏輯
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avg_correlation = events[0].get('correlation_with_others', 0.0)
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current_joint_prob = events[0]['prob']
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for i in range(1, len(events)):
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current_joint_prob = SGPCorrelationEngine.calculate_joint_probability(
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current_joint_prob,
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events[i]['prob'],
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avg_correlation
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)
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# 計算莊家隱含機率
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implied_prob = 1.0 / bookmaker_sgp_odds
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# 計算 EV
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ev_percentage = (current_joint_prob * bookmaker_sgp_odds) - 1.0
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is_profitable = ev_percentage > 0.05 # 設定 5% 的 EV 門檻
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return {
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"true_joint_probability": round(current_joint_prob, 4),
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"bookmaker_implied_probability": round(implied_prob, 4),
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"ev_percentage": round(ev_percentage, 4),
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"is_profitable_sgp": is_profitable,
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"fair_odds": round(1.0 / current_joint_prob, 2) if current_joint_prob > 0 else 0
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}
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