Draw procedures for balanced 3-team group rounds in sports competitions
提出了一种抽签程序，通过高效算法找出所有平衡分组方案，确保三人小组实力均衡，提升比赛公平性和观赏性。
Abstract We propose procedures for draws in sports tournaments that will achieve balanced groups of size 3. We start by developing an efficient algorithm that finds all possible balanced groupings; that is, allocations of teams to groups such that the strength of all groups lies between two bounds. The algorithm uses comparison results to discard large sets of unfeasible allocations and backtracking. We then define pot-and-ball draws that randomly pick one of the balanced groupings. Our draw procedures ensure that all groups are of (virtually) identical competitive levels, thereby enhancing the overall fairness and interest of the tournament.