Complexity physics finds crucial tipping points in chess games | Hacker News Reader

Complexity physics finds crucial tipping points in chess games

arstechnica.com

73 pointspseudolus32 comments

This sounds like an extremely convoluted way of demonstrating a very basic fact, that the authors of the study probably knew beforehand. And that's when a player's position has many weaknesses (or a high 'fragility score') they're probably going to be losing soon. And determining how quickly many pieces can attack a given point versus defend it is, more or less, exactly how you determine if that point is weak. Publish or perish reigns supreme.

A lot of science feels like it's becoming much closer to art where you splash a canvas with a few splotches, and then spend an hour describing how it's an insightful representation of the isolation of the modern world and the struggle against depersonalization. At least there you get to then sell it for a few hundred thousand dollars, rather than just live to renew your contract.

One thing chess engines are still bad at is determining which positions are difficult for humans to play. If there is a sequence of moves where Black has to make the right choice every time from several plausible alternatives to reach a drawn endgame, but White has plenty of margin for error at every turn to keep that situation, the computer will happily evaluate this as "0.0" - a draw.

Solving this would allow handicapped computers to play interesting games against humans, and it would also be hugely useful for strong players preparing opening surprises, but no one seems to have figured it out.

Note that this isn't a simple graph theory question of looking for how narrow a path through the graph is: the word "plausible" is very important above, and a narrow path where most moves can quickly be eliminated is one of the easier things for humans to calculate.

Anyway, I was hoping this was a step towards solving that, but they don't seem to have even tried to apply it there.

For sure, but I think this is really quite difficult even with the wildest of hand-waving. Take, for instance, take the R+B v R ending. The weaker side has literally two pieces, including the king, to move. There are many well studied drawing plans, and in most positions literally any move would lead to a draw (short of absurd things like hanging your rook).

Yet this ending is extremely difficult to the point that GMs lose it with some regularity. That stat about 40% of the possible positions being forced wins is useless, because it includes mostly very weird positions that nobody would voluntarily walk into. The overwhelming majority of times this ending is entered into, as well as normal moves from such, are all textbook draws.

> I think this is really quite difficult even with the wildest of hand-waving

It's difficult for computers! But humans can do it. An 1800 armed with computer analysis (so he knows the right moves) can say with some confidence "this position looks difficult for a grandmaster".

I think an 1800 with computer analysis would never say R+B v R looks difficult for a GM without external knowledge of the fact that it is.

It's hard to isolate the external knowledge. If R+B v R came up once every 50 games, every GM and probably every 2000 would know it inside out.

There isn't a GM that hasn't studied RBvB, and most have also played numerous games with it.

But it's just very difficult to execute properly. Let a 2000 go study it for weeks - he'd still lose it against strong play.

People often see chess as just a game of knowledge, but in practice it's much more like a skill in that for a strong player they'll generally see the right move(s) in a position near instantly. The time spent is then just comparing and double checking stuff.

This is why you might see in e.g. a press conference some journalist ask why the player didn't play 34. Ne5, and they'll think for a few seconds, go ooooo wow as they rapidly work out the [invariably computer generated] idea, and then respond that they simply didn't consider it.

This is how players like Magnus are so strong and why the time control doesn't really matter - his intuition just tends to quickly lead him to better ideas than for other players.

> But it's just very difficult to execute properly. Let a 2000 go study it for weeks - he'd still lose it against strong play

I don't agree. People lose this one because they haven't looked at it recently.

I would be willing to take this as a bet. Train with the computer for weeks, and then I get to defend the endgame against a computer or a tricky human. (I'm a bit stronger than 2000 but I could find someone else).

Consider my side of the bet eating crow with a side that, if you're right, then you'll have mastered arguably the single most important basic ending.

I'd strongly recommend checking out an endgame manual or a youtube video on the proper way(s) to draw it. It's going to take a lot longer than weeks if you just try to learn it through experience.

For further incentivization I can practically guarantee you will also gain rating points if you succeed here - it really requires substantial 'feel' for how rook and bishop can work together (as well as certain stalemate tricks and more), and that's applicable far outside just this ending - same how learning to mate with B+N really improves your feel for how those pieces can collaborate.

But I'm not sure you appreciate what you're getting into here. R v R+B makes B+N look like child's play.

Do let me know if you're seriously going to try this. I'd honestly just like to know how it goes, and can just hit you up in a couple of weeks in some rando thread. It'd be pretty awesome if you succeed!

> the single most important basic ending

This just isn't right. According to de la Villa (whose book is a great trainer on this endgame among others) this balance comes up 1 time in 5000, compared to RPPvR or PPvP which each occurred more than 10x as often. Ok, some of those are trivial, but there are many more half-points to be had by studying those.

I have studied this endgame before to the point where I was confident in holding it (mostly based on the selected defences given by de la Villa, which I reckon cover almost all positions), but I confess I didn't practice it against a tablebase. I also lost this the one time I had it over the board.

1 in 5000 seems very off. A quick search has it occurring in 1.7% of all games which sounds about right. [1] If he indeed said 1 in 5000, it might have been from a database with lots of quite low rated games.

There are two reasons I think it's one of (calling it the most was a bit of hyperbole) the most important basic endings.

One is that it's not only relatively frequent but also an endgame that just constantly sees the 'wrong' result.

The second point though is what I already mentioned - it really teaches you a lot about how a bishop and rook can play together. If you can genuinely internalize that ending, your play with these pieces, in all phases of the game, would just naturally improve. Again it's similar to the way that the B+N ending can help improve your play with those pieces.

I mean sure it's useful to know that R and f+h pawns v R is only a [difficult] draw, but that knowledge is not very useful outside of that exact scenario.

[1] - https://thechessworld.com/articles/endgame/chess-statistics-...

That link is the lowest quality article I've ever seen, but if it means anything, it seems to mean Rook and Bishop vs Rook, but both sides also have any number of pawns. Pure RB v R does not come up one game in 60 at any level, that's ridiculous. Has there ever been one in a World Championship match? Out of 1000+ games I can't think of any.

I've had R+F+h vs R several times, and the evaluation of it being important to another endgame countless more.

In looking at my old reference database (~300,000 good quality and relatively contemporary games at/before 2020) R+B v R with pawns on either side showed up 5.6% of the time. The exact ending with 0 pawns showed up 0.15% of the time. That's probably understating it since it's more likely to occur against relatively evenly matched players.

It's also going to depend on the style of the players. Caruana, for instance, had it at least 10 times including 4 wins (starting from theoretically drawn positions) against 2666 rated Guseinov, 2765 rated Radjabov, 2557 rated Gareyev, and even one kind of against 2809 rated Aronian. The one against Aronian needs an asterisk because they were playing with both sides having 1 pawn (in a still theoretically drawn position) and eventually Aronian voluntarily transposed into a completely lost RB v R ending.

So 1.6% is very much in the realm of possibility depending on the specifics of the dataset. 1 in 5000 is difficult to imagine by any composition. It might have been a typo in his notes and he meant 1 in 500? That probably is underestimating it, but it's at least an order of magnitude closer to the right ballpark.

"Knowing" something is different from formalizing it into a mathematical model. Almost all papers are about relatively minor findings at best.

Publish and perish is real though. As are hype and bad popularization of research.

The insight of this article is less in describing the dynamics of chess games than in the fact that you can apply the methodology of network analysis, percolation, phase transitions etc. to recover them.

This is interesting because both chess and complexity science have a long but unrelated history. So it’s a bit harsh to call this out for “Publish or Perish”.

I agree the takeaway of the article is mostly garbage: middlegames are complex and hold pivotal moments. But the real value is quantifying the "pivotal-ness" of each piece, which could have real world uses. How about a chess tutor that can instantly highlight the linchpin of any position? This is how grandmasters see the board and I imagine just flashcarding complex positions with a heatmap of pivotal pieces could be illuminating.

Facility score may IMHO be understood as some statistical measure of tactical involvement. It has really nothing to do with the established and important concept of weakness in chess, which looks at significant static features of a position. For example in the position from figure 1, white's pawns on the queen side are all weak, especially c4. Also the black squares around the white king are weak. After 1...exd4 these weaknesses are pronounced sharply. Considering fragility score, I see nothing that points towards these weaknesses. a4 and b6 are not attacked, hence ignored. c4 is attacked once and defended once, but there is no trajectory over it. Weak squares are not considered. If we look at the knight D4, it's BC score may tell us, that after taking it with a pawn, which can be done in two different ways, the bishop e3 is hanging, hence we gain a tempo, which is significant, also f3 is weaker (noise) and bishop e6 is not under pressure any longer. Hardly something which convinces to identify the key moment, but may be useful in a statistical sense. Nevertheless it appears to be an oversold complexity measure.

It's really difficult to pick my least favourite part of this article. Could be this;

"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..."

At least AI systems can write slop fairly well. Why do I hate this so much? It just feels lazy, underdone, superficial, vaguely nonsensical. The magic of chess has little or nothing todo with the "psychological complexity conferred by player strategies". It has much more to do with aesthetic beauty, and many a great writer has illuminated that. It's utterly unsurprising that you can model the game as nodes interacting in a network graph (I mean essentially that's what it is), and even more unsurprising that the complexity of the interactions is higher in the tense and complicated positions that do indeed often decide the fate of individual games. Note, games not matches. If you can't get even the most basic domain terminology correct, you don't deserve anyone's attention.

I'll probably calm down in an hour or two.

https://arxiv.org/abs/2410.02333

Okay, but will this research help me get above 700 ELO rapid on chess.com?

No, but

  1) don't hang pieces

  2) notice when your opponent hangs pieces

  3) win endgames where you're up material

should be enough to get you to 1500.

As a ~900 Elo player, I feel like point #3 is doing the heavy lifting here—kinda reminds me of that "rest of the owl" meme (not that you're wrong, of course!) :-P

When you're up material? Assuming your opponent is in a tier to leave pieces hanging, we should be talking more than a pawn here, and following the first two rules should hold/build that advantage.

At least, as someone not even 900, closing an endgame when I'm already winning sounds like the easier part. But it's hard to believe that's all it takes to get to 1500, it is not my impression that 1300+ players are losing to big "whoops" moments.

I would agree the "don't blunder" and "punish opponents blunders" are harder than endgame knowledge. However, knowing the basics of endgames is actually important to closing out games. Specifically, knowing KQvK, KRvK, and the "ladder technique" is important.

Without any tactics "take free pieces" probably only gets you to around 1200 (chess.com), but if it includes knight and pawn forks, skewers, pins, and discovered attacks it can get you to 1500. Playing perfectly every game is hard though. I would recommend having more chess knowledge than just those 3 rules before you really try for 1500.

Maybe it's just me, but in an endgame where (for example) it's just kings and a bunch of pawns, even a two pawn advantage is easy for me to lose—I pick the wrong pawn island to support with my king, and I've already lost. Knowing good heuristics in these sorts of situations is something that takes active study IME—"don't blunder pieces" is not sufficient, at least for me.

Not hanging pieces is definitely the hard one!

practice tactics..don't study openings..

Learning basic variations of even one opening for white and for black can be extremely useful. There's not much tactics in first moves, but knowing how to set up a solid position will help a lot. Just learn basic stuff, no need to go into the weeds too much. Also the names of the openings are pretty cool

A huge one is also to assume your opponent will make the best move. Don't just make one move threats hoping your opponent will miss them.

This seems like it should be somewhat more advanced, because players at a low level often will miss one move threats. But it is basically the first principle from which nearly all other good habits directly derive. Why develop all your pieces, not bring your queen out early, etc. Why do all those things when you know your opponent will often just miss something anyhow if you start pecking him with one move threats?

It's because if your opponent does not miss those threats, then you've likely just made your own position even weaker. And as a corollary a one-move threat which improves your position is perfectly fine of course, but in that case you're not hoping your opponent misses it. I mean you probably are, but you expect him to see it. But it doesn't matter - because your position has improved regardless.

4) Develop your pieces first. 5) Castle. 6) Don't move the queen prematurely. 7) Analyze all your games.

At our ELO, games tip back and forth like a metronome, almost move to move. Confuses the AI - never can tell who the winner is!

Stop playing rapid until you're well above 700. Play classical so you can think about each move long enough to not hang pieces.

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