Physicist used interaction graphs to show how pieces attack and defend to analyze 20,000 top matches:
The game of chess has long been central to computer science and AI-related research, most notably in IBM's Deep Blue in the 1990s and, more recently, AlphaZero. But the game is about more than algorithms, according to Marc Barthelemy, a physicist at the Paris-Saclay University in France, with layers of depth arising from the psychological complexity conferred by player strategies.
Now, Barthelmey has taken things one step further by publishing a new paper in the journal Physical Review E that treats chess as a complex system, producing a handy metric that can help predict the proverbial "tipping points" in chess matches.
In his paper, Barthelemy cites Richard Reti, an early 20th-century chess master who gave a series of lectures in the 1920s on developing a scientific understanding of chess. It was an ambitious program involving collecting empirical data, constructing typologies, and devising laws based on those typologies, but Reti's insights fell by the wayside as advances in computer science came to dominate the field. That's understandable. "With its simple rules yet vast strategic depth, chess provides an ideal platform for developing and testing algorithms in AI, machine learning, and decision theory," Barthelemy writes.
Barthelemy's own expertise is in the application of statistical physics to complex systems, as well as the emerging science of cities. He realized that the history of the scientific study of chess had overlooked certain key features, most notably how certain moves at key moments can drastically alter the game; the matches effectively undergo a kind of phase transition. The rise of online chess platforms means there are now very large datasets ripe for statistical analysis, and researchers have made use of that, studying power-law distributions, for example, as well as response time distribution in rapid chess and long-range memory effects in game sequences.
For his analysis, Barthelemy chose to represent chess as a decision tree in which each "branch" leads to a win, loss, or draw. Players face the challenge of finding the best move amid all this complexity, particularly midgame, in order to steer gameplay into favorable branches. That's where those crucial tipping points come into play. Such positions are inherently unstable, which is why even a small mistake can have a dramatic influence on a match's trajectory.
A case of combinatorial complexity
Barthelemy has re-imagined a chess match as a network of forces in which pieces act as the network's nodes, and the ways they interact represent the edges, using an interaction graph to capture how different pieces attack and defend one another. The most important chess pieces are those that interact with many other pieces in a given match, which he calculated by measuring how frequently a node lies on the shortest path between all the node pairs in the network (its "betweenness centrality").
He also calculated so-called "fragility scores," which indicate how easy it is to remove those critical chess pieces from the board. And he was able to apply this analysis to more than 20,000 actual chess matches played by the world's top players over the last 200 years.
Barthelemy found that his metric could indeed identify tipping points in specific matches. Furthermore, when he averaged his analysis over a large number of games, an unexpected universal pattern emerged. "We observe a surprising universality: the average fragility score is the same for all players and for all openings," Barthelemy writes. And in famous chess matches, "the maximum fragility often coincides with pivotal moments, characterized by brilliant moves that decisively shift the balance of the game."
Specifically, fragility scores start to increase about eight moves before the critical tipping point position occurs and stay high for some 15 moves after that. "These results suggest that positional fragility follows a common trajectory, with tension peaking in the middle game and dissipating toward the endgame," he writes. "This analysis highlights the complex dynamics of chess, where the interaction between attack and defense shapes the game's overall structure."
Physical Review E, 2025. DOI: 10.1103/PhysRevE.00.004300 (About DOIs).
(Score: 2, Interesting) by khallow on Thursday January 30, @04:33AM (5 children)
(Score: 1) by khallow on Thursday January 30, @04:34AM
(Score: -1, Spam) by dustintoretto on Thursday January 30, @06:02AM
Chess is fascinating not only for its strategic depth but also for how it continues to be a platform for AI and scientific research. The analysis of crucial tipping points in matches reveals how a single move can drastically change outcomes. Similarly, just as chess players need a secure and reliable platform for online gaming, traders on platforms like Bybit can benefit from enhanced security and privacy. Using a reliable VPN for Bybit [downloadandroidvpn.info] ensures safe trading and protects sensitive information from cyber threats. Thanks for sharing this insightful perspective on chess complexity!
(Score: 2) by DannyB on Thursday January 30, @04:20PM
Let's call that game: Mating and Reproduction!
Satin worshipers are obsessed with high thread counts because they have so many daemons.
(Score: 3, Interesting) by ikanreed on Thursday January 30, @05:33PM (1 child)
No harm in trying, but it wouldn't be fun.
Part of what makes games fun is the same thing that makes stories fun. There's rising action as uncertainty and complexity sets in. You feel tension and a sense of being tested rising, then you feel relief when you pass a critical moment and a sense of relief as you see the outcome before you.
It's easy to see why games that are never fragile suck. Monopoly is a game of slowly watch one player inexorably gain a bigger and bigger lead. No one enjoys that but the winner. But games that try to remain constantly fragile? Those suck too. It'd be like if mario kart handed out blue shells to whoever was not in first all the time. It can be a good way to cover up skill differences, for a more "all-inclusive" game, but it wouldn't have that sense of rising action and resolution that makes chess a millennia-long classic.
(Score: 1) by khallow on Monday February 03, @05:24AM
A space civilization game I've played a few times, Stellaris has a staged game with three stages of conflict. In the first stage, you're just butting heads with your neighbors. Then there's what I think they call "mid-stage crises". Basically, some larger threat that requires either a lot of power to fend off, or coordination with other empires: for example, one of the advanced societies "awakes" and starts interfering/invading or one of the barbarian factions (basically a collection of bloodthirsty nasties who normally merc out to nearby civs) unites under a great khan. These have the power to wreck anyone near them, but typically, if it's on the other side of the galaxy, then you don't have to worry about it.
Then there's the endgame crisis which is typically a galaxy spanning threat that can obliterate a large part of the map. As each stage evolves, you have plenty of opportunity for fragility and getting wiped out.
(Score: 3, Funny) by Anonymous Coward on Thursday January 30, @07:29AM
Like that time I parked my Queen diagonally in front of an opposing pawn. I totally would have won if not for that small mistake.
(Score: 4, Interesting) by VLM on Thursday January 30, @02:28PM (2 children)
I tried to read the official paper but its (subscription required) so nope. And reading a journalist/AI/AI-journalist interpretation of the academic paper.
My first guess is they calculated some kind of thermodynamic entropy to determine the "complicatedness" of each turn of the game. Which sounds tricky, but couldn't another measure of complexity be the size of a compressed file representing the board state?
I don't have an infinite amount of spare time, but it would be humorous to get a great pile of chess game data, ranging from noob computer players to human players to human competitive players and look at graphs of compressed size of each turn of the game board; I imagine the graphs would be distinctive in some way. Sounds like a homework assignment for a data science class. Is data science still a thing or did it dry up and blow away in the wind with IoT and all the other buzzwords?
(Score: 2) by Freeman on Thursday January 30, @02:43PM (1 child)
There is a stupid amount of chess data out there. For many years, it's been tracked online and before that (even recently) there have been books published about it. As in, games played, moves made, printed in a book. The problem is having enough free time / spare money to do so.
Joshua 1:9 "Be strong and of a good courage; be not afraid, neither be thou dismayed: for the Lord thy God is with thee"
(Score: 4, Interesting) by bzipitidoo on Thursday January 30, @04:45PM
Yeah, stupid amount of data is right. Computers and networking have made an insane difference in the sheer quantity of chess data, not by playing the game, but simply by setting up and recording games whether the players are human or computer. I started playing chess in the 1970s, in a summer chess camp between my 2nd and 3rd grade school years. None of those games were recorded. In the 1980s, I joined a chess club and played in tournaments. A tournament was typically 3 games on one weekend day, or 5 games spread over both days of the weekend. We recorded moves by handwriting them on paper. Tournaments close enough to reach happened 1 or 2 times per month. A 2 hour drive was not uncommon. Speed chess, in which a game lasts no more than 10 minutes, was not recorded, as writing down the moves would have taken a crippling amount of time. From 1985 to 1990, I played roughly 100 tournament games.
Now, with chess websites such as lichess.org, the computer records every move of every game. Since joining lichess a couple of years ago, I have played a bit more than 10,000 speed chess games, and these are all recorded, and stored. No more waiting for a tournament, just hop online and get a game within seconds of asking. It's faster even than casual speed chess at the clubhouse. With physical pieces, the few seconds it takes just to set up the pieces becomes significant, taking away time that could go to game play. You also have to punch the clock. Online, you just move, and the computer handles the clock for you. The Internet is crucial, too, enabling players to join a game without having to spend time traveling.
As to "tipping points", and "fragility", yes. The simple point system of assigning 1 to a pawn, up to 9 for the queen, is pretty good at predicting the outcome. Absent a winning attack involving dramatic sacrifices, once you're 3 points down you may as well quit. The game has passed the tipping point so that the only chance of turning things around is to hope the other player makes a massive blunder. Computer players have gifted us with a few more exceptions to this general rule. There are games in which the side with more material has that material shut out early in the game, blocked behind weaker pieces, unable to participate and so is actually losing.
(Score: 2) by YeaWhatevs on Friday January 31, @05:17AM (1 child)
You can stop right there. I don't need to hear yet another physicist who think they are a mathmatician try to convince me that another field is explained by physics. Just last week a physicist was trying to tell me how physicists see the universality of all things, and that's why all of AI it turns out can be explained by physics. Oh boy.
(Score: 0) by Anonymous Coward on Friday January 31, @11:04AM
> I don't need to hear yet another physicist who think they
> are a mathematician try to convince me that another field
> is explained by physics.
When physicists get old...
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