When chess AI outplays humans, it doesn't necessarily treat the board the same way. A research team from the Complexity Science Hub and the University of Parma analyzed 1,200 human grandmaster games and 1,200 Stockfish-versus-Leela Chess Zero games move by move, finding that AI tends to preserve interactions between pieces for longer. The paper was accepted by APS Open Science on July 17, 2026. Rather than focusing on win rates or the accuracy of best moves, the study examines when complex positions get resolved.
What the team measured was not the psychological tension a player feels. Instead, they converted attacks, defenses, and control of empty squares into a network and quantified how complex those connections were. Humans temporarily reach peaks higher than AI, but then exchange pieces quickly afterward. AI, even after passing its peak, continues playing while holding onto overall board complexity for longer.
Turning the 64 Squares Into a Network of Interactions
The team built a network of up to 64 nodes from each half-move position. Nodes represent pieces or empty squares on the board, connected as "attacks" if an opponent's piece can be captured on the next move, as "defense" if a capture could be recaptured, and as "control" if a player occupies a square the opponent could move to. By capturing the whole board regardless of whose turn it is, the method simultaneously counts unresolved relationships remaining for both White and Black.
For the "strategic tension" value, they used the spectral radius — the largest eigenvalue of the network's adjacency matrix. The value rises higher in positions where many pieces and squares are densely connected, such that moving one piece could trigger a chain reaction in distant parts of the board. The paper also introduces a "tension load" metric, summing values up through 150 half-moves, to compare how much complexity was sustained throughout a game.
However, this metric does not directly count the total number of legal moves or the size of the search tree. It also doesn't measure whether a good move was chosen or whether a player subjectively found the position difficult. It tracks the tangle of attack, defense, and control relationships remaining on the board through a network metric the authors defined themselves.
Humans Peak High, AI Sustains Long
The average trajectory was similar between human and AI games up through the opening. As pieces develop and contact increases, strategic tension rises, reaching a high level in the middlegame. From there, as piece exchanges progress, the network shrinks and tension declines. The difference showed up not in the height of the peak but in how it declined afterward.
Top human players followed deeply studied opening theory up to around move 40, momentarily reaching higher tension than the AI. But once they moved past theory into independent calculation, they exchanged pieces and simplified the position quickly. Stockfish and Leela Chess Zero, in contrast, even with lower peaks than humans, sustained high tension across more moves. Researcher Vito D. P. Servedio explained that while humans reduce complexity quickly, AI is able to sustain it.
Other quantities on the board support the same pattern. AI games retained more pieces on average through the endgame, along with more interaction links and closed paths. The balance between attacking and defending links was also more even than in human games. Human games, meanwhile, featured more captures, and tension per remaining piece was higher than AI's throughout the game. In other words, humans concentrate complexity onto fewer pieces, while AI sustains distributed relationships across more pieces for longer.
The AI games used for comparison were drawn from official Top Chess Engine Championship (TCEC) tournaments from 2019 to 2024. The human grandmaster games came from PGN Mentor game records. Since time controls and starting conditions weren't fully matched between the two, the team also ran additional skill-matched comparisons and random-move benchmarks. Even so, this remains a comparison of observational data, not a laboratory test with all conditions controlled between humans and AI.
Random Moves Put the Correlation With Strength to the Test
The tendency to sustain complexity longer grew stronger along with human playing strength and time controls. In rapid and blitz games collected from Lichess across a wide range of skill levels, a linear regression between Elo and tension load produced R² = 0.970 and 0.975, respectively, with each data point representing an average of 1,200 games. Even among top humans, cumulative tension was higher in classical games than in shorter time controls.
On the AI side, the team created self-play games with Stockfish's search depth fixed, to examine the relationship with computational effort. They gave the engine the first 12 half-moves randomly selected from top human games, then had one side play at depth D or D+1 and the other at D or D-1. Across 120 games per depth level, deeper search was associated with higher tension load, with a regression of R² = 0.497, p = 0.023. For humans, time and skill were linked to the range over which complex relationships could be sustained; for Stockfish, it was search depth.
However, high tension cannot simply be taken as a sign of high-quality play. In 300 random games where legal moves were chosen uniformly at random, tension remained higher than in both human and AI games well past the middlegame. This happened because pieces were exchanged without purpose, letting chance interactions accumulate on the board. Even though the AI and random games captured pieces at similar frequencies, their tension curves over time differed.
So what this study captured is not a simple linear relationship where "more complex means stronger." A distinction needs to be made between moves that increase relationships chaotically and moves that sustain many interactions while maintaining purpose. The correlation with skill or search depth is meaningful only when comparing within strategic play aimed at winning, at minimum.
Even a One-Pawn Advantage Doesn't Guarantee the Outcome
When all games in the main comparison were evaluated using Stockfish at depth 20, the proportion of the side holding an advantage of 100 centipawns — roughly one pawn's worth — at move 40 that went on to win was about 71% for human games and about 59% for AI games. Even when the evaluation clearly favors one side, the favored side fails to win in roughly 30% to 40% of remaining cases. This shows that a single positional evaluation cannot be treated as a settled outcome.
Once an advantage emerges, both humans and AI move toward exchanging pieces and simplifying the position. However, AI transitions into that position while retaining more pieces and interactions than humans do. Sustaining complexity is not itself the goal; the difference lies in how much of the attacking and defending relationships can be carried along while moving toward an advantageous position. The network metric used here is one yardstick for measuring that difference.
When extending this to real-world AI, the scope of the measurement must be respected. Chess is a perfect-information game where the rules and board are fully visible, but diplomacy, financial markets, and military planning involve hidden information and exogenous shocks. The paper itself cautions against direct extrapolation, and the data here does not demonstrate that AI would gain an advantage in negotiation or conflict, nor that it would create danger. Additionally, the explanation that humans simplify positions due to cognitive load is an interpretation drawn from game records, not something confirmed through eye-tracking, verbal reports, or stress responses that would establish causation.
Future verification needs to confirm whether the same time-course pattern appears with engine designs other than Stockfish and Leela Chess Zero, and whether the difference persists when human and AI skill levels are matched. Furthermore, the metric needs to be applied separately to Go, shogi, and imperfect-information games to measure how sustaining complexity relates to performance and safety in each case. The authors have published their analysis code and data for the main figures except Figure 5 on GitHub. Reproducing the figures involving Elo and search depth in Figure 5 exactly would require data beyond what's in the public repository. If the results are reproduced with other engine designs, it would move the explanation for why AI chooses better moves than humans forward — from simply having more computational power to which relationships it can keep unresolved, and for how long.