发表机构
Indian Statistical Institute（印度统计研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种三玩家拍卖桥牌变体及双算法框架，通过迭代叫牌与预测算法降低复杂度，在10万局模拟中验证了其提升公平性与预测可靠性，并为风险决策提供启示。
AI 中文摘要
本文介绍了一种创新且无偏的三玩家拍卖桥牌变体，该变体专门设计用于解决传统赛制中存在的结构性局限。在标准拍卖桥牌中，赢家搭档在叫牌阶段结束后往往扮演被动角色，对结果的影响力微乎其微。为纠正这一点，我们提出的三玩家模型重新分配了战略主动权，强调无将策略在统计上优于特定将牌选择的框架。本研究的核心是一个基于规则的雙算法框架。首先，我们实现了一种迭代叫牌算法，允许玩家根据不断变化的手牌强度动态校准其叫牌。其次，我们引入了一种预测性迭代算法，旨在计算玩家在首攻牌打出前预期可赢得的墩数。与依赖回溯或高复杂度动态规划的传统方法不同，我们的迭代方法显著降低了时间复杂度。这一效率对于实时游戏至关重要，使玩家能够即时进行复杂的概率评估而无需计算延迟。为验证该模型，我们在一个包含10万局游戏实例的数据集上进行了模拟。这一大规模分析使得能够对初始叫牌、结果和整体叫牌准确性进行精确比较。实证结果表明，我们的算法不仅增强了拍卖桥牌的平衡性和公平性，而且在预测准确性方面表现出高可靠性。超越纸牌游戏的范畴，通过建模不确定性和战略竞争，该算法为波动市场环境中的风险管理和决策提供了宝贵见解。
英文摘要
This paper introduces an innovative and bias-free variant of a three-player auction bridge, specifically designed to address structural limitations found in traditional formats. In a standard auction bridge, the partner of the winning bidder often plays a passive role, possessing minimal influence over the outcome once the bidding phase concludes. To rectify this, our proposed three-player model redistributes strategic agency, emphasising a framework where No Trump strategies statistically outperform specific trump card selections. The core of this research is a rule-based dual-algorithm framework. First, we implement an iterative bidding algorithm that allows players to calibrate their bids dynamically based on evolving hand strengths. Second, we introduce a predictive iterative algorithm designed to calculate the expected number of tricks a player will secure before the lead card is played. Unlike traditional approaches that rely on backtracking or high-complexity dynamic programming, our iterative method significantly reduces time complexity. This efficiency is crucial for real-time gameplay, enabling players to perform complex probability assessments instantly without computational lag. To validate the model, a simulation was conducted on a dataset of 1,00,000 game instances. This large-scale analysis allowed for a precise comparison between initial bidding, outcomes, and overall bidding accuracy. The empirical results demonstrate that our algorithm not only enhances the balance and fairness of the auction bridge but also exhibits high reliability in predictive accuracy. Beyond the realm of card games. By modelling uncertainty and strategic competition, the algorithm offers valuable insights into risk management and decision-making in volatile market environments.
Comments10 pages, 5 figures
