65 lines
1.8 KiB
Python
65 lines
1.8 KiB
Python
"""凱利準則（Kelly Criterion）工具。"""
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from __future__ import annotations
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from dataclasses import dataclass
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@dataclass(frozen=True)
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class KellyResult:
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"""凱利投注建議結果。"""
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decimal_odds: float
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win_probability: float
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raw_kelly_fraction: float
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fractional_kelly_factor: float
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risk_tolerance_factor: float
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final_fraction: float
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stake_fraction: float
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def calculate_kelly_fraction(
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decimal_odds: float,
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true_prob: float,
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*,
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bankroll: float,
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fractional_kelly_factor: float = 1.0,
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risk_tolerance_factor: float = 1.0,
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) -> KellyResult:
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"""依凱利準則估算下注比例與建議金額。
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凱利公式：
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f* = (b * p - q) / b
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其中 b = odds - 1，p 為勝率，q = 1 - p。
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"""
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if decimal_odds <= 1:
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raise ValueError('decimal_odds 必須大於 1')
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if bankroll <= 0:
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raise ValueError('bankroll 必須大於 0')
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if not 0 <= true_prob <= 1:
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raise ValueError('true_prob 需介於 0 到 1')
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if not 0 <= fractional_kelly_factor <= 5:
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raise ValueError('fractional_kelly_factor 須介於 0 到 5')
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if not 0 <= risk_tolerance_factor <= 2:
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raise ValueError('risk_tolerance_factor 須介於 0 到 2')
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b = decimal_odds - 1
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raw_kelly = (b * true_prob - (1 - true_prob)) / b
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final_fraction = raw_kelly * fractional_kelly_factor * risk_tolerance_factor
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# 保守處理：避免負值與超過總資金比例（100%）的極端輸出。
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final_fraction = max(0.0, min(final_fraction, 1.0))
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return KellyResult(
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decimal_odds=decimal_odds,
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win_probability=true_prob,
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raw_kelly_fraction=raw_kelly,
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fractional_kelly_factor=fractional_kelly_factor,
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risk_tolerance_factor=risk_tolerance_factor,
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final_fraction=final_fraction,
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stake_fraction=final_fraction,
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)
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__all__ = ['KellyResult', 'calculate_kelly_fraction']
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