Evolutionary Transfer Learning for Dragonchess

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 …

Authors: Jim O'Connor, Annika Hoag, Sarah Goyette

Evolutionary Transfer Learning for Dragonchess
Ev olutionary T ransfer Learning for Dragonc hess Jim O’Connor, Annika Hoag, Sarah Go yette, Gary B. P ark er Computer Science Department, Connecticut College, New London, United States {jo conno2, ahoag, sgoy ette, park er}@conncoll.edu Keyw ords: Dragonc hess, transfer learning, CMA-ES, evolutionary computation Abstract: Dragonc hess, a three-dimensional chess v arian t introduced by Gary Gygax, presents unique strate- gic and computational challenges that make it an ideal environmen t for studying the transfer of articial intelligence (AI) heuristics across domains. In this work, we introduce Dragonchess as a no vel testb ed for AI research and provide an op en-source, Python-based game engine for commu- nit y use. Our research inv estigates evolutionary transfer learning b y adapting heuristic ev aluation functions directly from Stocksh, a leading chess engine, and subsequently optimizing them using Co v ariance Matrix Adaptation Evolution Strategy (CMA-ES). Initial trials show ed that direct heuristic transfers were inadequate due to Dragonchess’s distinct multi-la y er structure and mov e- men t rules. Ho wev er, evolutionary optimization signicantly improv ed AI agent p erformance, resulting in superior gamepla y demonstrated through empirical ev aluation in a 50-round Swiss- st yle tournament. This research establishes the eectiveness of evolutionary metho ds in adapting heuristic knowledge to structurally complex, previously unexplored game domains. 1 INTR ODUCTION Game pla ying has pro v en o ver time to be an eec- tiv e testb ed for adv ancemen ts in the eld of arti- cial in telligence (AI). F rom early heuristic-based approac hes in c hess and c heck ers to mo dern deep reinforcemen t learning strategies exemplied by systems like AlphaZero (Silv er et al., 2017a), the eld has progressed signicantly in adapting AI to complex strategic environmen ts. How ev er, the v ast ma jority of researc h has fo cused on games with relatively consistent b oard structures, pri- marily tw o-dimensional lay outs with w ell-dened and static piece mo v ement rules (Hu et al., 2024). As AI tec hniques contin ue to ev olve, there is an increasing ability to extend these metho ds to more intricate game domains that introduce new structural and strategic complexities. Dragonc hess, a game developed by Gary Gy- gax, presents an ideal case for studying AI adap- tation in no vel game environmen ts. Unlike con- v entional c hess, Dragonchess is pla yed on a three- tiered b oard, signicantly increasing the state and action space of the game (Jackman, 1999). The game’s unique structure in tro duces m ulti- lev el in teractions, distinct mo vemen t rules for dif- feren t piece types, and additional strategic depth not presen t in traditional c hess-lik e games. These factors make it a particularly challenging domain for AI researc h, as traditional searc h-based meth- o ds and heuristic ev aluation functions struggle with the game’s heigh tened complexity . In this w ork, we in vestigate ev olutionary transfer learning in the context of Dragonchess b y adapting heuristics from Sto c ksh, the leading op en-source chess engine (Romstad et al., 2025). Sto c ksh heuristics, including piece-square ta- bles, material v alues, and mobility-based ev alu- ations, hav e b een highly optimized for standard c hess but perform p o orly when directly trans- ferred to Dragonc hess due to its distinct b oard structure and mov ement rules. T o address this, w e employ Co v ariance Matrix Adaptation Evolu- tion Strategy (CMA-ES) (Ostermeier et al., 1994) to ev olv e these heuristics, ne-tuning piece v alues and ev aluation functions to b etter t the Drag- onc hess domain. Our exp eriments demonstrate that while di- rect transfer of Stocksh heuristics results in sub- optimal play , evolutionary optimization signi- can tly enhances the agent’s p erformance, surpass- ing standard minimax-based agents and v alidat- ing the ecacy of evolutionary transfer learning in this nov el setting. By integrating prior knowl- edge with adaptiv e optimization, w e provide a comp elling case for ev olutionary computation as a viable path wa y to adapting AI across structurally complex and underexplored game domains. More broadly , this work extends the appli- cabilit y of AI-driven game pla ying techniques to three-dimensional b oard games, underscoring the imp ortance of heuristic adaptation in nov el strategic settings. By demonstrating that evo- lutionary transfer learning can eectiv ely bridge kno wledge across disparate game domains, this researc h contributes to the growing b o dy of work exploring generalizable AI approaches to strategic decision-making. 2 RELA TED WORKS The study of AI in game pla ying con texts has his- torically b een dominated by deterministic, fully observ able domains such as chess, Go, and shogi, where heuristic ev aluation functions and deep searc h metho ds hav e enabled signican t adv ance- men ts in computational pla y . Early chess en- gines such as Deep Blue (Campb ell et al., 2002) demonstrated the ecacy of brute-force searc h when combined with carefully tuned heuris- tics, while later metho ds, such as Monte-Carlo T ree Searc h (MCTS), introduced probabilistic decision-making that pro ved highly eective in games like Go (Gelly et al., 2012). More recent breakthroughs in deep reinforcemen t learning ha ve shifted fo cus to wards self-play and learned ev aluation functions, exemplied b y AlphaZero (Silv er et al., 2017b) and MuZero(Schritt wieser et al., 2020). These metho ds, while highly suc- cessful, require extensive computational resources and training time, making them impractical for man y emerging domains including games with complex three-dimensional structures lik e Drag- onc hess (Silver et al., 2017c). T ransfer Learning is a concept rst in troduced b y Bozinovski and F ulgosi as a metho d for trans- ferring knowledge in neural net works (Bozino vski and F ulgosi, 1976). Over the following decades, researc h has expanded in to v arious domains, in- cluding image recognition and sp eech pro cessing, demonstrating success in a v ariet y of con texts (Bozino vski, 2020). By the 1990s, m ulti-task learning and more sophisticated theoretical foun- dations emerged, further rening the mechanisms b y which kno wledge from one domain could b e lev eraged in another (Caruana, 1997). More re- cen tly , deep learning and large-scale pretraining ha ve shown the ecacy of transfer learning across m ultiple applications (Iman et al., 2023)(Zhuang et al., 2020). F or instance, Braylan and Miiku- lainen applied transfer learning to the problem of training video game agents with limited data (Bra ylan and Miikkulainen, 2016). A related con- cept brough t up by Sno dgrass and Ontanon maps training data from a dierent, similar domain on to the target domain when there is not enough training data to train mo dels within the target domain (Sno dgrass and On tanon, 2016). T ransfer learning has also b een used successfully in video game level design, transferring knowledge ab out the st yle of one lev el in to the style of another (Sarkar and Co op er, 2022). T ransfer learning oers a promising alterna- tiv e for accelerating AI developmen t in no vel game domains b y enabling agen ts to lev erage kno wledge from previously learned tasks, facili- tating adaptation to new environmen ts with re- duced computational ov erhead (Lu et al., 2015). Ev olutionary transfer learning, in particular, has sho wn promise in optimizing AI agents for com- plex strategic tasks by evolving and ne-tuning existing heuristics (Hou et al., 2019). By adapt- ing pre-existing knowledge rather than relying solely on an agent learning from scratch, evolu- tionary approaches allow for ecient parameter tuning and strategic renement in nov el problem spaces. 3 DRA GONCHESS Dragonc hess, in troduced b y Gary Gygax in Dragon magazine in 1985, is a three-dimensional c hess v ariant designed to in tro duce additional strategic complexit y beyond traditional chess (Jac kman, 1999). The game is play ed on three v ertically stack ed 12×8 b oards, representing dif- feren t terrain t yp es: the top board sym b olizes the sky , the middle b oard represen ts the land, and the b ottom b oard corresp onds to the under- w orld. Each b oard introduces unique mov ement constrain ts and interactions, requiring play ers to think beyond the conv entional t w o-dimensional constrain ts of standard chess. The game features a div erse set of pieces, man y of which hav e asymmetric mov ement pat- terns and inter-board mobility . F or example, the Dragon, a pow erful piece, remains conned to the top board but possesses the unique ability to cap- Figure 1: Each b oard lay er (Sky , Ground, and Un- derground) consists of 8 rows and 12 columns, repre- sen ted by integer indices from 0 to 287. Each array elemen t at a given index stores an integer constan t denoting piece type and ownership (p ositive integers for Gold, negative integers for Scarlet). This index- ing approach enables ecient mov e generation and heuristic ev aluations. ture pieces on the middle b oard without moving. The Basilisk, lo cated on the b ottom b oard, can temp orarily freeze enem y pieces on the middle b oard, adding a nov el strategic dimension. Addi- tionally , pieces such as the Grin and the Hero can trav erse multiple b oards, reinforcing the im- p ortance of vertical p ositioning and inter-board in teractions. One of the primary challenges of Dragonchess lies in its signican tly expanded state space. While standard chess has approximately 10 43 p os- sible positions, the three-tiered nature of Drag- onc hess increases the com binatorial complexity exp onen tially . The game’s additional lay ers of mo vemen t also introduce new strategic consid- erations, such as con trolling vertical lanes to restrict opponent mo vemen t and co ordinating m ulti-b oard attac ks. These factors mak e heuris- tic ev aluation more dicult, as conv entional b oard ev aluation functions struggle to capture the in terplay b etw een b oards. F rom an AI p ersp ective, traditional search tec hniques such as minimax struggle with the sheer num b er of legal mov es p er turn, given that piece interactions occur across three lay ers rather than a single plane. A dditionally , established heuristics for piece mobility and b oard control in c hess do not directly transfer, as the relative v alue of a piece can v ary signicantly dep ending on its b oard lo cation and potential mobility . F or ex- ample, while a Mage (analogous to the Queen in c hess) is highly mobile on the middle b oard, it b ecomes severely restricted when forced onto the top or b ottom b oards, requiring heuristic adjust- men ts to account for these transitions. These complexities make Dragonchess an ideal testb ed for ev aluating heuristic adaptation and ev olutionary optimization techniques. The non- trivial transfer of chess heuristics to Dragonchess necessitates evolutionary ne-tuning to optimize piece v alues, mov ement priorities, and board con- trol metrics. Understanding these challenges not only aids in developing stronger Dragonchess- pla ying AI but also pro vides broader insigh ts in to the adaptability of heuristic-based AI in nov el strategic en vironments. 4 METHODOLOGY In this research, we develop an evolutionary kno wledge transfer approach to AI agen t opti- mization within the challenging game environ- men t of Dragonc hess. Our method consists of three primary phases: developmen t of a nov el Dragonc hess game engine, direct heuristic knowl- edge transfer from Sto cksh, and the evolution- ary adaptation of these heuristics using the Co- v ariance Matrix Adaptation Evolution Strategy (CMA-ES). 4.1 Dragonchess Game Engine Dev elopment T o further supp ort understanding of Drag- onc hess and facilitate broader AI research into the domain, we hav e developed an op en-source Python-based Dragonchess engine. Figure 2 il- lustrates our implementation, highligh ting the m ulti-lay ered b oard structure and clearly display- ing piece p ositions and p otential inter-board in- teractions. The graphical interface, built using the PyGame library , allows visual insp ection of game states and mov es, assisting b oth heuristic ev aluation and qualitative analysis of AI p erfor- mance. Figure 2: Screenshot from our Dragonchess engine’s graphical interface built using PyGame. The visualization sho ws Dragonchess’ characteristic three-lay ered b oard—Sky (top), Land (middle), and Underworld (b ottom)— with distinct piece t yp es and clear depiction of multi-la y er interactions and mov emen ts unique to Dragonchess. Due to the complexity of Dragonc hess, which in volv es three distinct b oards of dimensions 12x8 stac ked vertically , naive chess b oard representa- tions would b e inadequate for our purp oses. T o address this, we developed a no vel represen tation sp ecically tailored for Dragonc hess, in which eac h square on the three b oards is assigned a unique integer index. These indices are used as direct positions within a NumPy arra y , where eac h elemen t stores an in teger constan t represen t- ing the t yp e of piece o ccup ying that square. Posi- tiv e in tegers indicate pieces belonging to the Gold pla yer, while negative in tegers indicate Scarlet pieces. This indexed in teger representation allows ecien t and rapid state ev aluations, simplies mo ve generation, and enables straigh tforward p o- sition queries. By using integer-based indexing for each piece and b oard lo cation, heuristic ev al- uations transferred from Sto cksh can b e com- puted eciently , despite the increased complex- it y and dimensionalit y of Dragonc hess. Repre- sen ting each piece type distinctly within the in- dexed array enables streamlined calculations for threat detection, mobility assessment, and p o- sitional heuristics. The clarit y and computa- tional eciency of this approac h were critical in supp orting the integration and evolutionary op- timization of chess heuristics within the unique strategic environmen t presented b y Dragonchess. The engine manages the complexities asso ci- ated with inter-board mov es, piece-sp ecic rules, and sp ecial abilities unique to Dragonchess. This includes logic for pieces like the Dragon and the Basilisk, whose mov es inv olve interactions across m ultiple lay ers, capturing pieces from range, or temporarily disabling opp onent pieces. Ef- cien t mov e-generation and state-up date algo- rithms were implemented to handle these com- plex dynamics without sacricing computational p erformance. 4.2 T ransfer of Sto cksh Heuristics The core innov ation in our metho dology inv olves transferring heuristic ev aluation functions from Sto c ksh, a leading op en-source c hess engine, directly to the Dragonchess domain. Sto c k- sh employs a suite of sophisticated heuristics, eac h nely tuned for classical chess, including piece v aluations, p ositional heuristics, mobility metrics, threat detection, king safety ev alua- tion, passed pawn assessments, material scor- ing, and imbalance corrections. These heuristics w ere transferred directly , without mo dication, to ev aluate ho w standard chess heuristics perform within the structurally distinct and strategically in tricate Dragonchess environmen t. Sp ecically , the heuristics we implemen ted in- clude: 4.2.1 Material V alues Sto c ksh assigns numeric v aluations to c hess pieces based on their strategic importance and a verage mobility within traditional c hess. These standard v aluations, derived by a communit y of c hess play ers based on extensive empirical tun- ing, were transferred directly to analogous Drag- onc hess pieces to establish a baseline ev alua- tion. The initial mappings w ere established based on the closest approximate role and mobility of Dragonc hess pieces relative to traditional chess coun terparts: • P a wn (100 p oints): Applied to Dragonchess pieces fullling similar roles as low-v alue, fron t-line infantry , including the Sylph, W ar- rior, and Dwarf. These pieces act as funda- men tal units, capturing and con trolling space analogously to c hess pawns. • Knigh t (320 p oints): Sto cksh’s knight v alue w as directly assigned to Dragonchess pieces with comparable strategic function, sp eci- cally the Unicorn and Basilisk. These pieces p ossess distinctive mo vemen t abilities, inv olv- ing jumps or sp ecial inter-la yer maneuvers reminiscen t of knight mov es. • Bishop (330 p oints): Assigned to Dragonc hess pieces primarily v alued for ranged con trol and diagonal mobility , such as the Cleric, and the Mage. These pieces mirror chess bishops b y exerting long-range p ositional inuence, though their mo vemen t and capture rules ha ve notable domain-sp ecic dierences. • Rook (500 p oints): The ro ok’s v aluation was applied to Dragonc hess’s Hero, Thief, and Oliphan t pieces, reecting their higher mo- bilit y , vertical trav ersal abilities, and strate- gic impact on b oard control similar to chess ro oks. • Queen (900 points): The p o werful Dragon w as assigned Sto cksh’s queen v aluation due to its dominating p ositional strength, signif- ican t mobility , and ability to control mul- tiple squares from afar. This mapping ac- kno wledges the Dragon’s high-impact p oten- tial analogous to the chess queen. • King (20,000 points): Dragonchess retains the singular strategic signicance of the king, th us directly inheriting Stocksh’s substantial king v aluation. This extremely high n umeric v alue reects the criticalit y of king safet y and chec k- mate preven tion, consistent with traditional c hess heuristics. These direct v aluations provided a base- line for testing heuristic eectiveness in Drag- onc hess. How ever, due to substantial dierences in piece mobility , capturing mechanics, and the m ulti-lay ered nature of Dragonc hess, experiments sho wed that these direct v aluations required sig- nican t evolutionary adjustment to achiev e com- p etitiv e gameplay . 4.2.2 Piece-Square T ables (PSQT) Piece-square tables (PSQT) enco de positional heuristics by assigning b onuses or p enalties to pieces dep ending on their specic locations on the c hessb oard. Although Dragonchess diers signif- ican tly in its three-lay ered b oard structure and v arying board sizes, w e initially applied Sto ck- sh’s classical 8 × 8 PSQT without adaptation. Eac h Dragonchess b oard was ev aluated indep en- den tly using the standard tables, despite p oten- tial mismatches in board geometry causing a lac k of information on the sides of the Ground b oard and in total for the Sky and Underw orld b oards. 4.2.3 Mobilit y Metrics Mobilit y heuristics quantify the strategic ad- v antage gained from increased p otential mov es a v ailable to each piece. W e directly incorpo- rated Sto cksh’s mobility calculations into Drag- onc hess, considering the num ber of legal mov es eac h piece could make. This metric w as imple- men ted separately for eac h piece type, and trans- ferred without considering special Dragonchess rules, such as multi-lev el mov ement or b oard transitions. 4.2.4 King Safet y Ev aluation The king safety heuristic estimates vulnerability based on pro ximity to enemy pieces, av ailable es- cap e routes, and defensive pawn structure in clas- sical chess. W e directly integrated this heuris- tic into Dragonchess, ev aluating the king’s exp o- sure and threat-lev el across the three boards with- out adapting the rules to consider unique Drag- onc hess features suc h as v ertical threats or remote attac ks. 4.2.5 Threat Detection Sto c ksh assesses threats based on p otential cap- tures and attacks, assigning p enalties for p osi- tions where pieces are vulnerable. This heuristic w as directly transferred by ev aluating threatened squares and capturing p otential across each indi- vidual Dragonchess b oard. W e purp osely did not accoun t for inter-la yer threats unique to Drag- onc hess to main tain the eect of the Sto cksh orien ted set of heuristics. 4.2.6 P assed Pa wns (Passed Pieces) In chess, passed pa wn heuristics ev aluate the strategic adv antage of pawns unopp osed in their adv ancement to ward promotion. F or Drag- onc hess, we transferred this concept directly as ”passed pieces,” ev aluating p ositional b onuses for an y pieces facing limited opp osition in their di- rect line of adv ancement, despite dierences in the promotion rules and b oard geometry of Drag- onc hess. 4.2.7 P awn Count Sto c ksh’s heuristic calculates the n umber of pa wns on the b oard, regardless of their p osition. The algorithm then provides a score calculated b y the ratio of one play er’s pawns to another. This heuristic was conceptually transferred directly to Dragonc hess, with the heuristic tracking the im- balance of Sylphs, W arriors, and Dwarv es. These pieces were determined to b e closest in b oth abil- it y and strategic imp ortance to the chess pawn. 4.2.8 Im balance T otal Sto c ksh incorp orates heuristics that ev aluate im balances in material distributions, particularly the strategic consequences of uneven piece ex- c hanges like bishop-pair adv antages. This imbal- ance heuristic was transferred directly into Drag- onc hess, pro viding the strategic implications of asymmetric piece distributions without adapta- tion to Dragonchess-specic asymmetries or v er- tical interactions. 4.2.9 Space Control The space heuristic quan ties the strategic ad- v antage of con trolling more squares, and conse- quen tly restricting opp onent mobility . Directly transferred from Sto cksh, our space heuristic simply coun ted empty squares controlled by each pla yer, neglecting the vertical dimension and in ter-b oard spatial interactions that distinguish Dragonc hess. 4.2.10 Board Activit y Penalties Sto c ksh ev aluates b oard activity b y penalizing certain pieces o ccup ying sub optimal or restricted p ositions. W e incorp orated these p enalties di- rectly into Dragonc hess without mo dication, as- sessing p enalties uniformly across b oards regard- less of lay er-sp ecic strategic nuances or sp ecial piece abilities unique to Dragonchess. 4.2.11 Dragon Center Bonus (Adapted Queen Cen tralization) In classical chess, Sto c ksh assigns positional b on uses for centralized queens due to increased con trol. F or Dragonchess, w e adapted this heuris- tic to grant p ositional b onuses sp ecically for Dragons p ositioned centrally on the Sky b oard, directly transferring the centralization logic with- out extensive mo dication. 4.2.12 Heuristic T otal In this Sto cksh-based assessment, all previous heuristics are added together to form a heuristic total. This v alue can b e directly transferred to Dragonc hess. 4.3 Initial T ransfer P erformance Up on directly transferring these heuristics, our initial tests demonstrated that unmodied Sto ck- sh heuristics p erformed p o orly when directly applied to Dragonchess. The distinctiv e three- dimensional nature of the Dragonchess b oards, coupled with unique piece mov ements and in ter- b oard in teractions, created critical mismatches in heuristic ev aluations. P ositional heuristics, particularly piece-square tables and threat ev al- uations, frequently underestimated or misjudged strategic opp ortunities and vulnerabilities. Mo- bilit y calculations and passed-piece heuristics also pro ved inadequate due to the unique vertical and in ter-lay er interactions present in Dragonchess. These initial observ ations underscored the need for adaptiv e heuristic optimization. Conse- quen tly , the transferred heuristics formed an ef- fectiv e baseline from whic h our ev olutionary opti- mization pro cess b egan. W e then used CMA-ES to adapt these heuristics to b etter t the complex and no vel dynamics presented by Dragonchess. 4.4 Evolutionary Optimization via CMA-ES T o impro ve the eectiveness of these transferred heuristics, w e employ ed an evolutionary opti- mization pro cess using Cov ariance Matrix Adap- tation Evolution Strategy (CMA-ES). CMA-ES is an evolutionary algorithm designed for the opti- mization of complex, high-dimensional, contin u- ous parameter spaces, making it particularly suit- able for adjusting heuristic parameters. Our evolutionary strategy targeted a param- eter vector comprising 25 numerical scaling fac- tors. This vector enco ded adjustments for piece v alues, p ositional heuristics, and other strategic factors originally derived from Sto cksh. The sp ecic parameterization was chosen based on preliminary analysis, which indicated sensitivity of Dragonchess heuristics to certain p ositional and material features. F ormally , w e dene our ev olutionary ob jective as maximizing the p erformance of the agen t: maximize θ W ( θ ) (1) Where W ( θ ) represents the exp ected win-rate of the Dragonsh agen t with heuristic parameters θ , measured via win rate ov er simulated games. The parameter v ector ev olved by CMA-ES is rep- resen ted as: θ = [ w 1 , w 2 , w 3 , . . . , w 25 ] (2) These weigh ts modify v arious heuristic com- p onen ts. Specically , the rst p ortion of weigh ts ( w 1 through w 14 ) correspond are used to scale the piece v aluations, while the remainder ( w 15 to w 25 ) are directly applied to the elev en previously listed dynamic p ositional ev aluation comp onents (mo- bilit y , threats, etc.). 4.5 Evolutionary Optimization Pro cedure The evolutionary pro cess inv olv ed the following iterativ e steps: 1. Initialize a CMA-ES p opulation from the direct-transfer heuristic parameters derived from Sto c ksh. 2. Ev aluate each candidate heuristic v ector b y sim ulating m ultiple Dragonchess games against standard baseline agents and record- ing win-loss-draw ratios. 3. Select the highest-p erforming candidates based on their win rate and Elo ratings, up- dating the CMA-ES co v ariance matrix ac- cordingly . 4. Con tin ue evolving heuristics ov er multiple generations, perio dically ev aluating against baseline agents to assess impro vemen t and con vergence. CMA-ES was chosen due to its robustness in handling high-dimensional contin uous optimiza- tion problems, enabling ecien t heuristic tuning without the need for gradien t computations or explicit deriv ative information. 5 Results T o quan tify the eectiv eness of our ev olved heuristics, we p erformed an empirical ev aluation through a Swiss-style tournamen t inv olving sev- eral AI agents, each given exactly three seconds p er mov e to main tain fair computational condi- tions. The tournament was conducted ov er 50 rounds, to provide statistically signican t results. The agents ev aluated included: • Dragonsh (p ost-ev olution): The agent em- plo ying evolv ed heuristics from CMA-ES. • Dragonsh (pre-evolution): Baseline agent utilizing unmo died Sto cksh heuristics. • Jac kman Minimax: A standard minimax agen t using piece weigh ts recommended b y Edw ard Jac kman specically for Dragonchess. • Gygax Minimax: A baseline minimax agent using Gary Gygax’s original prop osed weigh ts. • Random Agen ts: Standard agents that se- lected mov es randomly , serving as a low er- p erformance b enchmark. T o ev aluate AI agent performance, w e em- plo yed multiple complementary metrics. T our- namen t Elo ratings were calculated after each round using the standard Elo system, oering a quan tiable and standardized measure of relative agen t strength. Win, loss, and draw ratios were recorded to directly assess p erformance improv e- men ts resulting from heuristic evolution. The results of the 50-round Swiss-system tour- namen t are summarized in T able 1. Elo ratings, whic h quantify relativ e play er strength based on matc h outcomes, w ere calculated after eac h round to pro vide clear comparative analysis. 6 CONCLUSIONS In this paper, we introduced an ev olutionary transfer learning approac h to adapt heuristics from the w ell-established Sto cksh chess engine to the complex, three-dimensional domain of Dragonc hess. Our metho d demonstrated that, while direct transfer of chess heuristics provides a functional baseline, the unique strategic com- plexit y and three-dimensional structure of Drag- onc hess require adaption or tuning to achiev e comp etitiv e p erformance. By employing the Co- v ariance Matrix Adaptation Evolution Strategy (CMA-ES), w e successfully evolv ed the initially transferred heuristic v alues, signicantly enhanc- ing agen t p erformance and achieving sup erior tournamen t results. The evolv ed Dragonsh agen t demonstrated the strongest p erformance in our empirical ev alu- ation, attaining an Elo rating substan tially higher than agen ts employing directly transferred heuris- tics or handcrafted heuristic v alues. Our results underscore the viability and eectiveness of evo- lutionary transfer learning, highlighting its p o- ten tial as an eective approach for adapting ex- T able 1: Results of the 50-Round Swiss-system T ournamen t Agen t Wins Losses Dra ws Elo Rating Dragonsh (p ost-ev olution) 32 17 1 1665.8 Jac kman Minimax 28 21 1 1604.7 Gygax Minimax 28 22 0 1539.9 Dragonsh (pre-ev olution) 24 26 0 1488.6 Random Agen t 1 21 23 6 1439.9 Random Agen t 2 20 24 6 1449.7 Random Agen t 3 20 26 4 1420.2 Random Agen t 4 16 30 4 1337.2 isting heuristic knowledge across structurally dis- tinct and strategically complex game domains. By contributing b oth a nov el domain and an accessible implementation, this research lays the groundw ork for future in vestigations into evolu- tionary heuristic adaptation, kno wledge trans- fer metho ds, and AI strategies for complex, m ulti-lay ered game environmen ts. F uture direc- tions may include further renemen t of heuris- tic functions, exploration of deep learning-based approac hes, and comparative analyses using additional evolutionary optimization tec hniques within the Dragonchess environmen t. REFERENCES Bozino vski, S. (2020). Reminder of the rst paper on transfer learning in neural netw orks, 1976. Informatica, 44(3). Bozino vski, S. and F ulgosi, A. (1976). The inuence of pattern similarity and transfer learning up on training of a base p erceptron b2. In Pro ceedings of symp osium informatica, volume 3, pages 121– 126. Bra ylan, A. and Miikkulainen, R. (2016). Ob ject- mo del transfer in the general video game do- main. In Pro ceedings of the AAAI Conference on Articial Intelligence and Interactiv e Digital En tertainment, volume 12, pages 136–142. Campb ell, M., Hoane Jr, A. J., and Hsu, F.-h. (2002). Deep blue. Articial intelligence, 134(1-2):57– 83. Caruana, R. (1997). Multitask learning. Machine learning, 28:41–75. Gelly , S., Kocsis, L., Schoenauer, M., Sebag, M., Sil- v er, D., Szep esv ári, C., and T eytaud, O. (2012). The grand challenge of computer go: Monte carlo tree search and extensions. Communica- tions of the ACM, 55(3):106–113. Hou, Y., Ong, Y.-S., T ang, J., and Zeng, Y. (2019). Ev olutionary multiagen t transfer learn- ing with mo del-based opp onent behavior predic- tion. IEEE transactions on systems, man, and cyb ernetics: Systems, 51(10):5962–5976. Hu, C., Zhao, Y., W ang, Z., Du, H., and Liu, J. (2024). Games for articial in telligence researc h: A review and p ersp ectives. IEEE T ransactions on Articial Intelligence. Iman, M., Arabnia, H. R., and Rasheed, K. (2023). A review of deep transfer learning and recent adv ancements. T echnologies, 11(2):40. Jac kman, E. (1999). Dragonchess. https://www. chessvariants.com/3d.dir/dragonchess.html [A ccessed: 3/15/2025]. Lu, J., Behbo o d, V., Hao, P ., Zuo, H., Xue, S., and Zhang, G. (2015). T ransfer learning using com- putational intelligence: A survey . Kno wledge- Based Systems, 80:14–23. Ostermeier, A., Gaw elczyk, A., and Hansen, N. (1994). A derandomized approac h to self- adaptation of evolution strategies. Evolutionary Computation, 2(4):369–380. Romstad, T., Costalba, M., and Kiiski, J. (2025). Sto c ksh. https://stockshc hess.org/. Accessed: 2025-06-12. Sarkar, A. and Co op er, S. (2022). tile2tile: Learn- ing game lters for platformer style transfer. In Pro ceedings of the AAAI Conference on Arti- cial Intelligence and In teractive Digital Enter- tainmen t, volume 18, pages 53–60. Sc hrittwieser, J., Antonoglou, I., Hubert, T., Si- mon yan, K., Sifre, L., Schmitt, S., Guez, A., Lo c khart, E., Hassabis, D., Graep el, T., et al. (2020). Mastering atari, go, chess and shogi b y planning with a learned model. Nature, 588(7839):604–609. Silv er, D., Hub ert, T., Schritt wieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Ku- maran, D., Graep el, T., et al. (2017a). Master- ing c hess and shogi by self-play with a general reinforcemen t learning algorithm. arXiv preprint Silv er, D., Hub ert, T., Schritt wieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Ku- maran, D., Graep el, T., et al. (2017b). Master- ing c hess and shogi by self-play with a general reinforcemen t learning algorithm. arXiv preprint Silv er, D., Sc hrittwieser, J., Simony an, K., An tonoglou, I., Huang, A., Guez, A., Hub ert, T., Baker, L., Lai, M., Bolton, A., et al. (2017c). Mastering the game of go without h uman kno wl- edge. nature, 550(7676):354–359. Sno dgrass, S. and Ontanon, S. (2016). An approach to domain transfer in pro cedural conten t gener- ation of tw o-dimensional videogame levels. In Pro ceedings of the AAAI Conference on Arti- cial Intelligence and In teractive Digital Enter- tainmen t, volume 12, pages 79–85. Zh uang, F., Qi, Z., Duan, K., Xi, D., Zhu, Y., Zhu, H., Xiong, H., and He, Q. (2020). A comprehen- siv e survey on transfer learning. Pro ceedings of the IEEE, 109(1):43–76.

Original Paper

Loading high-quality paper...

Comments & Academic Discussion

Loading comments...

Leave a Comment