133 lines
5.6 KiB
Python
133 lines
5.6 KiB
Python
import math
|
||
from scipy.optimize import fsolve # 导入 fsolve 函数用于数值求解
|
||
|
||
|
||
def moneyline_to_prob(moneyline_odds: int) -> float:
|
||
"""将 Moneyline 赔率转换为隐含概率."""
|
||
if moneyline_odds == 0:
|
||
raise ValueError("Moneyline odds cannot be 0")
|
||
elif moneyline_odds > 0:
|
||
# 正赔率 +X -> 隐含概率 = 100 / (100 + X)
|
||
return 100 / (moneyline_odds + 100)
|
||
else: # moneyline_odds <= 0
|
||
# 负赔率 -X -> 隐含概率 = X / (X + 100)
|
||
return abs(moneyline_odds) / (abs(moneyline_odds) + 100)
|
||
|
||
|
||
def prob_to_moneyline(probability: float) -> int:
|
||
"""将概率转换为 Moneyline 赔率 (四舍五入到最接近的整数)."""
|
||
if not 0 < probability < 1:
|
||
# 概率为 0 或 1 对应无限或 -100 的 Moneyline 赔率，这里简化处理，实际中极少遇到精确的 0 或 1
|
||
if math.isclose(probability, 0):
|
||
return float("inf")
|
||
if math.isclose(probability, 1):
|
||
return (
|
||
-100
|
||
) # 或者 raise ValueError("Probability must be between 0 and 1 (exclusive)")
|
||
raise ValueError("Probability must be between 0 and 1 (exclusive)")
|
||
|
||
if probability <= 0.5:
|
||
# 概率 <= 0.5 对应正 Moneyline 赔率 (Decimal >= 2.0)
|
||
# Decimal Odds = 1 / probability
|
||
# Moneyline = (Decimal Odds - 1) * 100
|
||
return round((1 / probability - 1) * 100, 2)
|
||
else:
|
||
# 概率 > 0.5 对应负 Moneyline 赔率 (Decimal < 2.0)
|
||
# Decimal Odds = 1 / probability
|
||
# Moneyline = -100 / (Decimal Odds - 1)
|
||
return round(-100 / (1 / probability - 1), 2)
|
||
|
||
|
||
def calculate_no_vig_moneyline_power(moneyline_odds_list: list[int]) -> list[int]:
|
||
"""
|
||
使用 Power Method (根据提供的文献描述) 计算无 vigorish 的 Moneyline 赔率。
|
||
该方法通过寻找 k 使得 sum(implied_prob^k) = 1 来调整概率。
|
||
|
||
参数:
|
||
moneyline_odds_list (list): 包含所有可能结果的 Moneyline 整数赔率列表 (例如, [+116, -156])。
|
||
|
||
返回:
|
||
list: 包含所有可能结果的无 vigorish Moneyline 整数赔率列表。
|
||
"""
|
||
if not moneyline_odds_list:
|
||
return []
|
||
|
||
# 1. 将 Moneyline 赔率转换为隐含概率 (pi)
|
||
implied_probabilities = [moneyline_to_prob(odds) for odds in moneyline_odds_list]
|
||
|
||
# 确保所有隐含概率都大于 0，否则无法进行幂运算或取对数 (数值求解时可能涉及)
|
||
if any(p <= 0 for p in implied_probabilities):
|
||
raise ValueError("All implied probabilities must be positive.")
|
||
|
||
total_implied_probability = sum(implied_probabilities)
|
||
|
||
# 如果总概率 <= 1，说明没有 vig 或 vig 极少，直接返回原始赔率
|
||
if total_implied_probability <= 1:
|
||
print(
|
||
"Warning: Input odds already have little or no vig. Returning original odds."
|
||
)
|
||
return moneyline_odds_list
|
||
|
||
# 2. 定义需要找到根的函数 f(k) = sum(pi^k) - 1
|
||
# 我们要找到 k 使得 sum(pi^k) = 1
|
||
# 由于 sum(pi) > 1 且 pi < 1, 我们需要 k > 1 才能让 pi^k < pi, 从而降低总和至 1。
|
||
def sum_pi_pow_k_minus_1(k):
|
||
# fsolve 传入的 k 是一个数组，我们需要取其第一个元素
|
||
k_val = k[0] if isinstance(k, (list, tuple)) else k
|
||
# 计算 sum(pi^k)
|
||
sum_val = sum(p**k_val for p in implied_probabilities)
|
||
return sum_val - 1 # 我们的目标是让这个函数等于 0
|
||
|
||
# 3. 寻找 k 使得 f(k) = 0
|
||
# 我们知道当 k=1 时，总和是 total_implied_probability (>1)。
|
||
# 当 k 增大时，sum(pi^k) 会减小。所以根 k 应该大于 1。
|
||
# 提供一个合理的初始猜测值给 fsolve，例如 1.1 或 1.5
|
||
initial_k_guess = [1.1] # fsolve 期望一个数组作为初始猜测
|
||
|
||
# 使用 fsolve 寻找 k
|
||
# fsolve 返回一个数组，即使只有一个解
|
||
k_solution = fsolve(sum_pi_pow_k_minus_1, initial_k_guess)
|
||
|
||
# 提取求解到的 k 值
|
||
k = k_solution[0]
|
||
|
||
# 4. 计算无 Vig 概率 pi_novig = pi^k
|
||
no_vig_probabilities = [p**k for p in implied_probabilities]
|
||
|
||
# 由于浮点数精度和数值求解的限制，最终的概率之和可能不严格等于 1。
|
||
# 虽然理论上由 k 的定义保证总和为 1，但实践中检查一下是有益的。
|
||
final_sum_check = sum(no_vig_probabilities)
|
||
if not math.isclose(final_sum_check, 1.0, abs_tol=1e-9):
|
||
print(
|
||
f"Warning: Final no-vig probabilities sum to {final_sum_check:.6f}, expected 1.0. Sum may need slight re-normalization."
|
||
)
|
||
# 理论上 Power Method 的定义保证了总和为 1，但如果因为数值误差偏离较多，
|
||
# 可以选择在这里进行最后的比例调整，但严格遵循方法定义是不需要的。
|
||
|
||
# 5. 将无 Vig 概率转换回 Moneyline 赔率
|
||
no_vig_moneyline_odds = [
|
||
prob_to_moneyline(p_novig) for p_novig in no_vig_probabilities
|
||
]
|
||
|
||
return no_vig_moneyline_odds
|
||
|
||
|
||
# 示例
|
||
if __name__ == "__main__":
|
||
odds_list = [+150, -200, +300, -120]
|
||
for odds in odds_list:
|
||
prob = moneyline_to_prob(odds)
|
||
print(f"赔率 {odds}: 概率 {prob:.4f}")
|
||
|
||
odds = [+116, -156]
|
||
# 计算无 Vig 赔率使用 Power Method
|
||
no_vig_odds_power = calculate_no_vig_moneyline_power(odds)
|
||
|
||
print(f"原始 Moneyline 赔率: {odds}")
|
||
print(f"无 Vig Moneyline 赔率 (Power Method): {no_vig_odds_power}")
|
||
|
||
# 可选: 验证无 vig 赔率对应的概率之和是否接近 1
|
||
if no_vig_odds_power:
|
||
novig_probs_power = [moneyline_to_prob(o) for o in no_vig_odds_power]
|
||
print(f"无 Vig 概率之和 (基于计算出的赔率): {sum(novig_probs_power):.6f}")
|