乒乓球单淘汰赛赛制的数学原理与抽签的操作策略

Research on Mathematical Principles and Drawing Lots Operation Strategies of Table Tennis Single Tournament System

从继承和扬弃乒乓球单淘汰赛赛制传统理论和操作方法的目标出发,对这一赛制的数学原理和抽签的操作策略进行了系统的、多层次探讨。提出了运动员入区约束条件排序、运动员序与入区理想概率对应关系、抽签顺序与运动员类型影响相消长等原则,提出了概率归一、区域差数、"剧场寻座"等规律,并提出了轮空数和机动数的计算公式。认为抽签操作应以"分型抽签"和"逐级入区"作为核心理念,同时,在不同层级入区时,要在保证相关队友合理分开的前提下,最大限度地实现运动员的理想概率或最佳概率。具体而言,在各个相应层级入区时,只可能有3种类型的运动员:同型相关队友、混合型相关队友、落单运动员。针对"同型相关队友",提出在不需机动数的情况下各类型运动员直接随机到底进入相应层级的区;针对"混合型相关队友",提出"红黑不等"布签模式、"一抽一跟"并"抽后不放"的抽签模式;针对落单运动员,应放在这一层级的最后集群抽,提出续用"混合型相关队友"抽签之后的布签形式,采用"抽后不放"的抽签模式。

This paper, from the inheritance and abandoned table tennis single tournament system traditional theory and method of operation of the objectives, tries to give a system and multi- level study to its mathematical principles and drawing lots operation strategies. And it attempts to made three strategies and three rules including the strategy of sorting the contestant entering zone＇s constraints, the strategy of corresponding relationships between member sequences and ideal probability, the strategy of influence between the drawing lots order and the member type, the probability normalizing rule, the region difference rule and the ＂seeking seats in the theater＂ rule, and draw the bye number and the mobile number formula. The drawing lots operation should take ＂variety drawing lots according to different member type＂ and ＂step by step into the zone＂ as core idea, and when entering different level zones, should maximum a- chieve member＇s idea/or the best probability under the premise of ensuring reasonable separated the teammates. Specifically speaking, the same type related teammates should use ＂equal red lots and black lots＂ and ＂draw out a lot with another＂, or in the no motor, several different types of players random to the ＂end＂ directly, into the corresponding level of the district. The mixed type related teammates should use ＂unequal red lots and black lots＂,＂ draw out a lot with another＂ and ＂draw out but not return lot＂ model; the remaining individual contestants should use ＂unequal red lots and black lots＂ and ＂draw out but not return lot＂ model.