For his analysis, Bartllimi chose to represent chess as a decision -making tree in which every “branch” leads to victory, loss or tie. Players face the challenge of finding the best movement among all this complexity, especially in the middle of the game, in order to direct toys to the favorite branches. Here comes the role of decisive turning points. Such situations are unstable by nature, which is why even a simple mistake can have a major impact on the course of the match.
A state of consensual complexity
An example of a position taken by Mehedlishvili-Van Forrest.
Mark Bartelimi, 2025
A graph of reaction that shows the white knight as the main piece in the previous position.
Mark Bartelimi, 2025
A graph of reaction that shows the white knight as the main piece in the previous position.
Mark Bartelimi, 2025
An example of a position taken by Mehedlishvili-Van Forrest.
Mark Bartelimi, 2025
A graph of reaction that shows the white knight as the main piece in the previous position.
Mark Bartelimi, 2025
Bartllimi re -photographed the chess match as a network of powers in which the cut works as a network contract, and represents the ways in which the edges interact, using a graph to interact to capture how to attack different pieces and defend each other. The most important chess pieces are those that interact with many other pieces in a specific match, which according to it by measuring the number of times the knot is located on the shortest path between all the pairs of the contract in the network (“Al -Bilah Central”).
He also calculated the so -called “fragility degrees”, which indicates the ease of removing the important chess pieces from the plate. He managed to apply this analysis to more than 20 thousand actual chess games played by the best players in the world over the past 200 years.
Bartllimi found that its scale can already determine the turning points in specific matches. Moreover, when he calculated his average analysis on a large number of games, an unexpected global style appeared. “We have noticed an amazing comprehensiveness: the average degree of fragility is the same for all players and for all openings,” Bartllimi writes. In the famous chess matches, “the maximum fragility often coincides with articulated moments, characterized by great movements that change the game balance decisively.”
Specifically, the fragility degrees begin to increase by about eight moves before the point of the critical turning point remains and remains high for about 15 movements after that. “These results indicate that the fragility of the concentration follows a joint path, as tension reaches its peak in the middle of the game and dissipates towards the end of the game,” he wrote. “This analysis highlights the complex dynamics of chess, as the interaction between the attack and the general structure of the game constitutes.”
Physical Audio, 2025. Doi: 10.1103/physreve.00.004300 (About digital identity definitions).