Adaptive AI for the King of Diamonds Game: A Bayesian Approach to Imperfect Information and 0.8-Average Dynamics

This research delves into the algorithmic complexities of the King of Diamonds game from Alice in Borderland II, a unique variant of the Keynesian Beauty Contest. This game features imperfect information, dynamic player elimination, and a critical rule where the objective is to choose a number closest to 80% of the average of all chosen numbers. We propose and evaluate a Bayesian Learning Agent designed to adapt its strategy against diverse opponents. The BLA employs Bayesian inference to dynamically update its beliefs about opponent behaviors, integrating these predictions into a Keynesian Beauty Contest decision-making framework. Through extensive simulations, the BLA consistently demonstrates superior performance. For instance, in games against four random opponents, the BLA achieved a survival rate of 67.00%, significantly outperforming the random players' combined 33.00% survival rate, and consistently maintained an average absolute distance to the target of 10.59 units across rounds. Notably, against four naive Fifty players, the BLA achieved a 100.00% survival rate with an extremely low average distance of 0.08 units, concluding games in a single round. Furthermore, the study provides a specialized algorithmic analysis for the game's challenging two-player endgame, where it exhibited a 1.30% draw rate in relevant scenarios. Our findings offer novel insights into designing adaptive AI agents for complex, imperfect information games with unique convergence dynamics, extending the understanding of computational strategies in evolving competitive environments.