赵森烽-克勤概率的赌本分配研究与期望值定理

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Title:

Distribution of gambling capital and expectation value theorem for Zhao Senfeng-Keqin probability

作者:

赵克勤^1,2, 赵森烽¹

1. 诸暨市联系数学研究所, 浙江 诸暨 311811;
2. 浙江大学 非传统安全与和平发展研究中心, 浙江 杭州 310058

Author(s):

ZHAO Keqin^1,2, ZHAO Senfeng¹

1. Zhuji Institute of Connection Mathematics, Zhuji 311811, China;
2. Center for Non-traditional Security and Peaceful Development Studies, Zhejiang University, Hangzhou 310058, China

关键词:

赌本分配; 数学期望; 赵森烽-克勤概率(联系概率); 不确定性; 期望值定理

Keywords:

distribution of gambling capital; mathematical expectation; Zhao Senfeng-Keqin probability (contact probability); uncertainty; expectation value theorem

分类号:

TP18

DOI:

10.11992/tis.201604020

摘要:

针对概率论发展史上合理分配赌本问题，把赵森烽-克勤概率用于合理分配赌本需要的最少赌博次数研究，结果发现，该问题中基于经典概率得出的数学期望不会在实际中出现，实际中出现的是基于赵森烽-克勤概率的"数学期望"的两个极端值。利用赵森烽-克勤概率能客观地反映出给定规则下最少赌博次数与最多赌博次数时的赌博结果，同时刻画出赌博输赢的经典期望值和实际值，从而为有针对性地制定或修改赌博策略和合理地分配赌本提供依据，在此基础上给出期望值不确定定理。文中以机器人服务收费为例说明该定理的现实意义。

Abstract:

With respect to the reasonable distribution of gambling capital in the developmental history of probability theory, Zhao Senfeng-Keqin probability has been used to investigate the minimum number of gambling times necessary for the rational allocation of the minimum amount of gambling capital. Results have shown that the mathematical expectation for this problem, based on classical probability, failed to occur in practice. What appeared instead are two extreme values of "mathematical expectation" based on the Zhao Senfeng-Keqin probability, which can objectively reflect the gambling results within the smallest and largest number of gambling times for a given rule. In addition, it describes both the classic expectation value and the actual value, thereby providing a basis for formulating or amending specific gambling tactics and the reasonable allocation of gambling capital. The result is an uncertainty theorem for the expectation value. In this paper, we illustrate the practical significance of this theorem by giving an example of service charging on a robot.