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

TL;DR

The paper tackles designing an evaluation function for Einstein Würfelt Nicht! (EWN) without manual parameter tuning. It presents Zweistein, which collapses EWN-simple boards to distance-to-corner arrays and models players as random-variable DTC distributions, enabling win-rate estimation via PDFs and CDFs. A compact pdf/cdf database is built with exhaustive tree search across 15625 distance arrays per side, and the win rate is computed as $P(X<Y)$ by summing $P(X\le i-1)P(Y=i)$ for $i=1..19$. Empirical results include competitive performance against traditional functions, alignment with exact win rates on simple boards, and first place in TCGA 2023, with a fast, parameter-free evaluator serving as a strong baseline and potential for extending to capture rules.

Abstract

This paper introduces Zweistein, a dynamic programming evaluation function for Einstein Würfelt Nicht! (EWN). Instead of relying on human knowledge to craft an evaluation function, Zweistein uses a data-centric approach that eliminates the need for parameter tuning. The idea is to use a vector recording the distance to the corner of all pieces. This distance vector captures the essence of EWN. It not only outperforms many traditional EWN evaluation functions but also won first place in the TCGA 2023 competition.

Figures (12)

• Figure 1: The initial board.
• Figure 2: An example showing the piece selection and movement
• Figure 3: Another example showing the piece selection and movement
• Figure 4: An example showing the win conditions. On the left side, red reaches the corner and wins. On the right side, red captures all blue pieces and wins.
• Figure 5: The first table shows the Chebyshev distance to the goal corner from the red side's perspective. The second table provides a similar view from the blue side's perspective.