Packing Density Formula

You may find "Game Changer" interesting:

www.amazon.com/Game-Changer-AlphaZeros-Groundbreaking-Strategies-ebook/dp/B07N6G7X5V

I'm about halfway through. Somewhere in the first half of the book, there are charts about king mobility for various chess engines. One of AlphaZero's strategies is limiting where the opposing king can move. It's interesting.

@ericmsd

I did not know there is a book about AlphaZero. So far I only read their papers and followed it on youtube.
Thank you for the recommendation.

Your questions are exactly what this is about.
I do not intend to calculate one number that tells the player what to do, thats what chess engines are about.
Rather I am creating a set of guide line parameters/principles. The player should not (need) calculate these numbers themselves.
But in my App the player can see these parameters based on many high level chess games and that sparks these questions you have formulated.

If they work, then the App can help you with your chess improvements and tell you on what aspekts of the game you need to work on.

I highly recommend Game Changer. You can find PGN versions of most of the games online so you can follow along yourself without manually entering moves. There's a study here on Lichess, as well as a collection on chessgames.com.

Sounds interesting! Are you following Maia? maiachess.com/

They're building on the AlphaZero/Leela programs to try to find more human-like moves at various ELO levels.

@ericmsd yes I follow them, its a really cool project. I hope they make it easier for developers to run their models with javascript.

I'm still sort-of confused by the point of all this. Ideas like "packing density" and "expansion factor" may be relevant in engine design, but that's because traditional engines typically use concrete but club-swingingly simple position evaluation combined with extremely deep and comprehensive calculation. As far as I can tell, these sorts of metrics are trying to produce a marginally more sophisticated approach to positional evaluation, but they still seem a long way below the sort of intuitive awareness that even a fairly mediocre human player would have.

@RamblinDave
The Expansion Factor, is something that slowly increases for the winning side in engine play.
Let me explain the point why I calculate it.
1) We have a value (expansion factor) that increases on average when winning.
2) We know what this value means. Is it greater than 1 then white has more space, is it smaller than 1 then black has more space.
This means I can analyse your games, calculate how much the expansion factor contributes to your wins/draws/loses.
I can compare the analysis with other players from different ELO groups.

I can then tell you something like:
After the opening at about move 14. you might want to make sure to keep your space advantage.

All you need to do is play games with my App, or Import your games. Then when you play against the engine it will coach you at the right moment. No need to calculate anything. You have your own understanding of space and you can use that.

I hope that gives you a better picture. Of course its not only expansion, also other parameters, that also can be combined.

@RamblinDave Have you ever played Go?

The concept is somewhat similar, and there are ties to chess, albeit somewhat indirect.

#17
Go is about winning space, chess is about checkmating the king.

It woudl nonsense trying to imitate engine style of evaluation . Computer is good at calculting obscure packing densities. though I doubt any top engine using them.

WEe definately would improve our game by memorizing stockfish piecevalue on each squeare. if we coudl remember and woudl time recall add all features together. Not really do able.

so we stuck seeing the positiion and just knowing which one is better. And slowly by study and play get better at. Not by imitating computer style of move selection

Go and chess are very different. For starters no one has yet managed to build evaluation function manually that plays more than very weak amateur level. I have somettime have hard time understanding in chess why someone is better. I can easily show go situation where i would hate have white pieces while a pro give climple and think white shoudl win. Just length of the game and very non verbalizable connection between opening and result is totally on different level.