Dragonchess, a three-dimensional chess variant introduced by Gary Gygax, presents unique strategic and computational challenges that make it an ideal environment for studying the transfer of artificial intelligence (AI) heuristics across domains. In this work, we introduce Dragonchess as a novel testbed for AI research and provide an open-source, Python-based game engine for community use. Our research investigates evolutionary transfer learning by adapting heuristic evaluation functions directly from Stockfish, a leading chess engine, and subsequently optimizing them using Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Initial trials showed that direct heuristic transfers were inadequate due to Dragonchess's distinct multi-layer structure and movement rules. However, evolutionary optimization significantly improved AI agent performance, resulting in superior gameplay demonstrated through empirical evaluation in a 50-round Swiss-style tournament. This research establishes the effectiveness of evolutionary methods in adapting heuristic knowledge to structurally complex, previously unexplored game domains.
Figures & tables
Figure 1: Each board layer (Sky, Ground, and Underground) consists of 8 rows and 12 columns, represented by integer indices from 0 to 287. Each array element at a given index stores an integer constant denoting piece type and ownership (positive integers for Gold, negative integers for Scarlet). This indexing approach enables efficient move generation and heuristic evaluations.
Figure 2: Screenshot from our Dragonchess engine’s graphical interface built using PyGame. The visualization shows Dragonchess’ characteristic three-layered board—Sky (top), Land (middle), and Underworld (bottom)—with distinct piece types and clear depiction of multi-layer interactions and movements unique to Dragonchess.
Agent
Wins
Losses
Draws
Elo Rating
Dragonfish (post-evolution)
32
17
1
1665.8
Jackman Minimax
28
21
1
1604.7
Gygax Minimax
28
22
0
1539.9
Dragonfish (pre-evolution)
24
26
0
1488.6
Random Agent 1
21
23
6
1439.9
Random Agent 2
20
24
6
1449.7
Table 1: Results of the 50-Round Swiss-system Tournament
Our research investigates how two adaptive AI methods, evolutionary transfer learning and TD(lambda), perform in the three-dimensional chess environment Dragonchess. The game challenges players with its unique board structure and computational load, making it an ideal setting to study how adaptive methods can update evaluation heuristics in novel environments. In this work we re-implement the Dragonchess engine, changing it from a PyGame engine to C++. This enables faster gameplay, allowing us to run 10,000 games with confidence intervals and significance tests, rather than a single small tournament. Both adaptive methods outperform all other agents in the round-robin tournament. Our results showed that there is no significant difference in the performance between the evolved and learned evaluations. This research establishes the efficacy of adaptive methods in structurally complex, novel game domains.
Chess is a two player strategic game that is embedded in classical AI culture as it was once the frontier for intelligent behaviour. There was the silent assumption that the advent of computer engines that play better than the best humans will extinguish interest in the game. However, the opposite has come to pass, with a growing following for the game. A lot of the computational resources are now centered around training of players, where the engine output is just one aspect. Access to past games is also an essential part, both in knowing what games a specific player has played previously, and also which continuations at a certain position have led to victory more often for each of the two colour players. We present Chess_db a suite of logic programming tools that can effectively manipulate games both in memory and via creating back end databases. In particular, we provide versatile code that creates databases from PGN (portable game notation) game files and explore the suitability of open source key-value databases for storing position tables that provide near-instant access to information pertaining to substantially large number of games.
Nicos Angelopoulos, Jan Wielemaker
University College & Imperial College, London UK · University College & Imperial College London, UK · SWI-Prolog solutions +1
Rating systems such as Elo serve as the gold standard for matchmaking in competitive chess. However, they inherently suffer from response lag due to their exclusive reliance on match outcomes, neglecting the granular quality of gameplay. Nevertheless, incorporating move-by-move information into rating adjustments presents a significant challenge given the substantial noise and the vastness of the game-state space. To address this, we propose the Drift-Diffusion-Enhanced Elo Rating System (DD-Elo), a novel skill assessment framework inspired by the drift diffusion model (DDM) from cognitive neuroscience. By modeling skill expression as a decision-making process, our model integrates move-level data to capture rapid skill fluctuations. We provide a rigorous mathematical derivation proving that DD-Elo maintains a bounded deviation from the traditional Elo system, ensuring theoretical alignment. Extensive experiments demonstrate that DD-Elo adapts to skill changes faster than Elo. Our findings suggest that DD-Elo offers an explainable, highly responsive, and backward-compatible solution for chess rating ecosystems. The implementation code is publicly available at https://github.com/Aquila-zhou1/DD-Elo .
Tianyuan Zhou, Zhizheng Fu, Tianming Yang
School of Intelligence Science and Technology Nanjing University Suzhou, China · Center for Excellence in Brain Science and Intelligence Technology Institute of Neuroscience Chinese Academy of Sciences Shanghai, China