AI Teaches Humans to Handle Complexity in the Game of Go
Authors: Adamo Cerioli, Vito D. P. Servedio, Gabriele Cerioli, Antonio Villani, Carlo Metta
Organizations: Department of Mathematics, Physics and Computer Science, University of Parma, Parco Area delle Scienze, 7/A, 43124, Parma, Italy · Complexity Science Hub, Metternichgasse 8, 1030, Vienna, Austria · Department of Physics, University of Trieste, Via A. Valerio 2, 34127 Trieste, Italy · Center for Nanotechnology Innovation (NEST-IIT), P.zza San Silvestro 12, 56127 Pisa, Italy
Strategic decision-making in complex environments requires balancing local stability against global coordination. Using the game of Go as a bounded empirical testbed, we investigate how biological and artificial agents navigate this trade-off by formalizing a network-derived metric of strategic tension defined via the spectral radius of spatial dependency matrices. Across human skill progression, tension systematically decays from novices to masters as uncoordinated tactical skirmishes give way to disciplined territorial stabilization. However, a longitudinal analysis of professional play spanning 1980--2026 reveals a striking historical paradox: following the superhuman breakthrough of AlphaGo in 2016, elite human matches display a marked surge in sustained tension. A two-dimensional projection based on move distance and captures places modern professionals close to neural engines, separating their tension from the local contact fighting of novices and from random noise. Consequently, strategic tension acts as a macroscopic order parameter for decision paradigms rather than raw computational strength. Beyond the game of Go, these findings establish a constructive paradigm for human-AI interaction, indicating how artificial systems can act as cognitive scaffolding that expands biological heuristics and elevates human capacity to navigate higher-order complexity across professional training and decision-making domains.
Domain terminology provides concise descriptions of game states and strategic relationships, but whether game-playing language models can accurately recognize these concepts and relate them to move evaluation remains unclear. We construct a controlled evaluation set centered on atari and its relationship to sente in Go, examining terminology recognition under local board changes and move evaluation under different strategic conditions. We conduct our tests on LoGos, a Go language model, after fine-tuning it with terminology and commentary supervision. The model struggles to recognize changes in the atari relationship and assess its strategic implications. Its terminology predictions are associated with move preferences even when those preferences contradict the reference evaluation. Our controlled tests provide a framework for examining whether language-based Go agents connect domain terminology with precise board relationships and strategic move values.
Recent advancements in Computer Go, driven by AlphaZero and MuZero, rely heavily on Monte Carlo Tree Search (MCTS) to correct the errors of the neural network policy. While effective on massive computational clusters, this dependence creates a critical bottleneck on consumer-grade hardware, where the computational cost of tree management severely limits inference rates. Furthermore, without deep search, these models suffer from hallucination, proposing moves with high confidence that are strategically fatal. This paper introduces a novel Belief-Guided architecture that disentangles the Policy head from a distinct Belief head. Unlike traditional value functions, the Belief head acts as an internal simulator and independent critic, modeling epistemic uncertainty and strategic stability. By integrating memory mechanisms (Transformer/GRU) to handle long-term dependencies and the Ko rule, and utilizing a gating mechanism to filter overconfident policy errors, our model shifts the burden of intelligence from runtime search to parametric "intuition." Experimental results demonstrate that this approach significantly improves search-free win rates and reduces hallucination, enabling professional-level play on limited hardware where massive MCTS is infeasible.
Mehrad Yaghoubi, Azam Bastanfard, Abbas Jalilvand +1
Department of Computer Engineering, Ka.C, Islamic Azad University, Karaj, Iran
The emergence of large language models (LLMs) has spurred economists to study how humans and LLMs behave in strategic settings. We organized a series of round-robin tournaments in the Colonel Blotto game. This game attracts game theorists' attention due to high-dimensional action space and the absence of pure strategy Nash equilibria. In the first tournament, more than 200 human participants competed against one another. In the second tournament, several popular LLMs were invited to submit strategies. In the third tournament, we matched the number of LLM strategies to the number submitted by humans. We find that humans more often employ better-calibrated intermediate-level allocation heuristics and outperform the simpler, more stereotyped strategies submitted by LLMs. Strategic sophistication is key to success if and only if the necessary level of reasoning depth is reached, while lower and higher levels of reasoning offer no clear advantage over the primitive strategies. Among humans, field of study weakly predicts success: participants with STEM backgrounds perform better in the first tournament. Surprisingly, humans almost do not adjust their strategies across tournaments with different sets of opponents. This result suggests that humans base their choices primarily on the game's rules rather than on the identity of their opponents, treating LLMs much like human competitors.
Dmitry Dagaev, Egor Ivanov, Petr Parshakov +2
HSE University · New Economic School · Central Economic Mathematical Institute, Russian Academy of Sciences +3