Zweistein: A Dynamic Programming Evaluation Function for Einstein Würfelt Nicht!

Zweistein is a dynamic programming-based evaluation function designed for the stochastic board game EinStein würfelt nicht! (EWN). The primary objective of the research is to eliminate the need for human-crafted parameters and complex manual tuning, which are common in traditional EWN AI development. By simplifying the game rules to create a data-centric model—specifically by calculating the probability of a piece reaching the corner based on its Chebyshev distance—the function provides a robust, automated heuristic for evaluating game positions.

The methodology relies on collapsing the game board into a distance array, which maps the distance of each piece to the goal corner. This approach reduces the state space to 15,625 possible configurations, allowing for the construction of a compact probability density function and cumulative density function database. The evaluation function calculates the win rate by comparing the distance-to-corner random variables of the player and the opponent. This process is computationally efficient, requiring minimal storage and significantly faster execution times compared to existing heuristic-based models.

Empirical testing demonstrates that Zweistein performs competitively against established evaluation functions like ODEMA and EWNNY. While the function exhibits minor inaccuracies in scenarios where piece-capturing is the primary win condition, these are mitigated when integrated into a tree search. The effectiveness of the approach was validated in the 2023 Taiwan Computer Games Association (TCGA) competition, where Zweistein secured first place among eight contestants. The research concludes that this dynamic programming approach offers a scalable, high-performance alternative to traditional parameter-heavy methods, with future potential for further optimization by incorporating partial piece-capturing rules into the database.