Chess variation entropy and engine relevance for humans

Marc Barthelemy

Home/Archive/arXiv

arXiv · 2505.03251

Chess variation entropy and engine relevance for humans

Marc Barthelemy

View original source ↗Read source document ↗Export metadata ↓

Abstract

Modern chess engines significantly outperform human players and are essential for evaluating positions and move quality. These engines assign a numerical evaluation $E$ to positions, indicating an advantage for either white or black, but similar evaluations can mask varying levels of move complexity. While some move sequences are straightforward, others demand near-perfect play, limiting the practical value of these evaluations for most players. To quantify this problem, we use entropy to measure the complexity of the principal variation (the sequence of best moves). Variations with forced moves have low entropy, while those with multiple viable alternatives have high entropy. Our results show that, except for experts, most human players struggle with high-entropy variations, especially when $|E|<100$ centipawns, which accounts for about $2/3$ of positions. This underscores the need for AI-generated evaluations to convey the complexity of underlying move sequences, as they often exceed typical human cognitive capabilities, reducing their practical utility.

Explore related subjects

physics.soc-ph cond-mat.dis-nn cs.HC

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Marc Barthelemy. 2025-05-06. Chess variation entropy and engine relevance for humans. https://arxiv.org/abs/2505.03251

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantifying the Dynamics of Innovation Abandonment Across Scientific, Technological, Commercial, and Pharmacological Domains

Despite the vast literature on the diffusion of innovations that impacts a broad range of disciplines, our understanding of the abandonment of innovations remains limited yet is essential for a deeper understanding of the innovation lifecycle. Here, we analyze four large-scale datasets that capture the temporal and structural patterns of innovation abandonment across scientific, technological, commercial, and pharmacological domains. The paper makes three primary contributions. First, across these diverse domains, we uncover one simple pattern of preferential abandonment, whereby the probability for individuals or organizations to abandon an innovation increases with time and correlates with the number of network neighbors who have abandoned the innovation. Second, we find that the presence of preferential abandonment fundamentally alters the way in which the underlying ecosystem breaks down, inducing a novel structural collapse in networked systems commonly perceived as robust against abandonments. Third, we derive an analytical framework to systematically understand the impact of preferential abandonment on network dynamics, pinpointing specific conditions where it may accelerate, decelerate, or have an identical effect compared to random abandonment, depending on the network topology. Together, these results deepen our quantitative understanding of the abandonment of innovation within networked social systems, with implications for the robustness and functioning of innovation communities. Overall, they demonstrate that the dynamics of innovation abandonment follow simple yet reproducible patterns, suggesting that the uncovered preferential abandonment may be a generic property of the innovation lifecycle.

physics.soc-ph↗

arXiv2026

When higher-order interactions matter: reducibility, parsimony, and microscopic organization

The current debate on higher-order interactions raises a fundamental question: when can systems organized through group interactions be faithfully represented within a graph-based formalism? Recent results show that graph descriptions can reproduce higher-order dynamics exactly or preserve selected macroscopic observables. Yet reducibility does not necessarily imply simplification, as information removed from the interaction structure may reappear as complexity in the effective dynamics, while structural features such as nestedness, heterogeneity, and cross-order correlations may be obscured by the reduction. We argue that formal representability alone is insufficient as a criterion for model choice. Both "simpler" and "equivalent" are question-dependent notions: parsimony must be assessed for the complete structure-dynamics model, and adequacy must be defined relative to the observables, scales, and regimes required by the scientific question. A reduced model may therefore be fully adequate for locating a phase transition or identifying a universality class while being inadequate for reproducing microscopic trajectories, transient dynamics, or structure-function relations. When group structure carries relevant microscopic information, higher-order representations may remain the most direct, interpretable, and parsimonious description, as well as the natural framework for understanding how microscopic organization gives rise to macroscopic behavior and functionality.

physics.soc-ph↗

arXiv2026

Emotions as intrinsic colored noise in biological systems

The idea that emotions in biological systems are analogous to intrinsic colored noise is advanced and justified. A model describing the dynamics of operation of biological networks under the influence of colored noise is suggested. The agents of a biological network can be represented either by biological species, such as humans and animals, or by neurons of the brain, or by the nodes of a neural network. Operational actions, or decisions, in a biological noisy network are based not only on the evaluation of utility of alternatives, but also on the agents emotions. The model is probabilistic, with the choice of alternatives characterized by the related probabilities. At the initial step, the agents make decisions individually and then start exchanging information with each other and imitating the actions of other agents, thus forming a biological network of interacting agents. Numerical simulations are accomplished for a heterogeneous society consisting of three groups of agents, one group possessing long-range memory, the other group, short-range memory, and the third group of super-rational agents acting strictly on the basis of utility, being deprived of emotions. Dynamics of opinions in different groups can be smooth, oscillatory, or chaotic. Altogether, eight types of operation are found, depending on the dynamics of group decisions. Under strong imitation effect, there appears chaotic motion in the evolution of decision choice. It is shown how the Ellsberg paradox can be resolved and how the exchange of information influences the dynamics of this paradox.

physics.soc-ph↗