圣彼得堡悖论之破解

import numpy as np
import pandas as pd

'''圣彼得堡悖论：[1,2,4,8,16,...]'''

class StPetresburg(object):
    def __init__(self, beitou=2, peilv=1.97):
        self.peilv = peilv # 赔率
        self.beitou = beitou   # 倍投倍数

    def set_option(self, *args, **kwargs):
        self.__dict__.update(dict(zip(['beitou', 'peilv'][:len(args)], args)))
        self.__dict__.update(kwargs)
    
    @property
    def df(self):
        period = np.arange(10) # 期数（从0开始）
        touzhu = self.beitou**period # 当期投注 = 倍投倍数 ^ 期数
        prize =  touzhu * self.peilv # 当期奖金 = 当期投注 × 赔率

        earn =  prize - np.cumsum(touzhu) # 累积收益 = 当期奖金 - 累积投注
        yields = earn / np.cumsum(touzhu) # 收益率 = 累积收益 / 累积投注

        #print(np.column_stack((period, touzhu, prize, np.cumsum(touzhu), earn, yields)))
        
        df = pd.DataFrame({
            '期数': pd.Series(period, dtype=int),
            '当期投注': pd.Series(touzhu, dtype=int),
            '当期奖金': pd.Series(prize, dtype=float),
            '累积投注': pd.Series(np.cumsum(touzhu), dtype=int),
            '累积收益': pd.Series(earn, dtype=float),
            '收益率': pd.Series(yields, dtype=float)
        })
        df = df.reindex(columns=['期数','当期投注','当期奖金','累积投注','累积收益','收益率'])
        return df

sp = StPetresburg()
print(sp.df)
sp.set_option(beitou=3)
print(sp.df)