arXiv subjects

Sourish Sarkar

Publications and source records attributed to Sourish Sarkar.

7 recordsLinked to original sources

arXiv2026

Winning Before You Play: An Iterative Capture Algorithm for Pre-Game Dominance Analysis in Three-Player Auction Bridge

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.

cs.GT↗

arXiv2026

A Statistical Analysis of Three Player Auction Bridge

Three-player Auction Bridge is a finite imperfect-information game in which dynamic partnerships create a distinctive interaction between scoring, strategic incentives, and payoff distribution. This paper develops a unified statistical and game-theoretic framework to evaluate a traditional scoring rule against a modified mechanism designed to improve strategic incentives. We first identify a structural defect in the original scheme: a bid-invariant slam bonus can make lower contracts strictly more attractive than higher ones. A bid-dependent correction removes this incentive distortion. We then compare the two schemes using higher-moment analysis, fairness measures, Nash equilibrium analysis, and General-Sum Counterfactual Regret Minimization (GS-CFR). The results show significant differences in the shape of the payoff distributions and reveal that, although both schemes remain highly balanced across physical seats, the modified scheme substantially increases inequality across strategic roles. The game is shown to be neither zero-sum nor constant-sum, motivating a general-sum rather than minimax analysis. Full-game GS-CFR further indicates a substantial increase in the bidder's payoff under the modified scheme, accompanied by a reduction in defender payoff and a shift from separating to partially pooling bidding behavior. These findings demonstrate that scoring-rule design can fundamentally reshape incentives, payoff distribution, and information transmission in imperfect-information games. The proposed framework provides a systematic approach to evaluating such mechanisms from both statistical and strategic perspectives.

cs.GT↗

arXiv2026

Algorithmic Threshold Optimization: Quantitative Modeling of Multiplier Distributions in Crash Games

Crash is a widely played casino game that blends strategic decision-making, probability, and computational analysis, particularly from the perspective of the house. This paper presents an optimization algorithm aimed at minimizing the casino's guaranteed positive earnings while simultaneously maximizing the number of players who win some amount during a given round. Since Crash is inherently a multiplayer game, players place random investment amounts at different points in time, which makes it difficult for any individual player to judge, before the round even begins, whether their intended investment is comparatively high or low, and consequently, how much risk they are actually taking on. The core objective of the proposed algorithm is to determine an optimal stopping multiplier that balances both the casino's and the players' interests. Notably, the algorithm remains unaffected by changes in the number of players or by variation in investment amounts, although in practice casinos typically impose a fixed range on permissible investments. Beyond this, the algorithm can help professional players make more informed decisions about how much to invest and how much risk they are comfortable accepting. We further analyze the algorithm's computational complexity and its stopping-multiplier statistics to give a fuller picture of how it behaves in practice.

cs.GT↗

arXiv2026

3 Players Auction Bridge - Statistical Algorithmic Strategies

Three-player auction bridge is an updated version of the worldwide-recognized auction bridge card game. Dynamic partners and opponents are the key factors in this game. This dynamic property reduces the bias and increases the authenticity of this game. The article provides insight on statistical learning and insight for a three-player auction bridge game. An exact algorithm for various scenarios is developed along with the corresponding winning strategies to explore different game plannings and the computational intelligence involved. Based on the algorithm, we simulate data and define the probabilistic values to win a certain game.

cs.GT↗

arXiv2025

Quantitative Rule-Based Strategy modeling in Classic Indian Rummy: A Metric Optimization Approach

The 13-card variant of Classic Indian Rummy is a sequential game of incomplete information that requires probabilistic reasoning and combinatorial decision-making. This paper proposes a rule-based framework for strategic play, driven by a new hand-evaluation metric termed MinDist. The metric modifies the MinScore metric by quantifying the edit distance between a hand and the nearest valid configuration, thereby capturing structural proximity to completion. We design a computationally efficient algorithm derived from the MinScore algorithm, leveraging dynamic pruning and pattern caching to exactly calculate this metric during play. Opponent hand-modeling is also incorporated within a two-player zero-sum simulation framework, and the resulting strategies are evaluated using statistical hypothesis testing. Empirical results show significant improvement in win rates for MinDist-based agents over traditional heuristics, providing a formal and interpretable step toward algorithmic Rummy strategy design.

cs.AI↗

arXiv2025

A New Three-Players Auction Bridge with Dynamic Opponents and Team Members

This article presents a new three-player version of the bridge playing card game for the purpose of ending fixed partnerships so that the play can be more dynamic and flexible. By dynamically redefining team makeup in real time, this game design increases unpredictability and forces players to repeatedly update strategy. A novel scoring system is introduced to reduce biases present in conventional rule-based games by favoring fairness via reward systems that enforce tactical decision making and risk assessment. Being subject to regular bridge rules, this version tests players to collaborate without fixed friendships, requiring fluid adjustment and adaptive bidding behavior in real time. Strategic issues involve aggressive and defensive bidding, adaptable playing styles, and loss-seeking strategies specific to the three-player structure. The article discusses probabilistic issues of bidding, trump and no-trump declarative effects, and algorithmic methods to trick-taking. Simulation outcomes illustrate the efficiency of diverse strategies. The game's architecture is ideal for competitions and possibly influential in broadening entry pools for tournament card games.

cs.GT↗

arXiv2022

Automatic Detection and Classification of Symbols in Engineering Drawings

A method of finding and classifying various components and objects in a design diagram, drawing, or planning layout is proposed. The method automatically finds the objects present in a legend table and finds their position, count and related information with the help of multiple deep neural networks. The method is pre-trained on several drawings or design templates to learn the feature set that may help in representing the new templates. For a template not seen before, it does not require any training with template dataset. The proposed method may be useful in multiple industry applications such as design validation, object count, connectivity of components, etc. The method is generic and domain independent.

cs.CV↗