@thefrickouttaherelol said in #5:
> I think the Bishop and Knight don't have a fixed "point value" but that the "point value" of those pieces is based on the advantage you have depending on the above. I hope that makes sense. Great article.
These values for all pieces but the king are all relative to each other, first, and mean as an average over all possible legal positions. Although I wonder the exact history and arguments about those relative counts since they have been used.
In Murray boo,k about the history of chess there is a mention of some piece getting a change of mobility definition because its "naked" board "power" or mobility compared to other pieces was not enough surface area, and given its reality analogue (chess being the analogy) real life attributes, it should have more area... Did i dream reading that anecdote. Perhaps i misread the words.
My more abstract guess as to what they might represent as rules of thumb of exchange arithmetic, that they be an average might be more testable and perhaps even more valuable. Whatever the real original reason, based on the isolated mobility say with placement at center of board. for each piece.
but maybe that very way of attributing power (in an abstract board as we learn very early each of us anyway), would lead to also an average relative count of the chess dynamic relative importance given all legal positions to continue toward terminal positions.
anyone could make a better fact based rational on them. If accepting that they are average relative importance toward some terminal goal odds, then clearly one is left with debating the positions features and sub-dynamics of the continuations from there to terminal end-points as modulating factors from these mobilitiy based (in abstract of otherboardly features) values (relative, again, no absolute, that the pawn be valued one is rather arbitrary, and i guess i was not thinking of them).
I don't know when promotion came into history, and I should admit that I find it difficult to argue in abstract their relative value based on mobility over all possible legal positions.. (we know there are ending positions when they get really hot real fast).
@dboing said in #11:
> ...
Yeah all good thoughts. I mean in my opinion piece point values are really just rules of thumb. They're averages. They really don't indicate much in and of themselves beyond being of statistical value.
If all your pawns are on the wrong colors then a bishop isn't going to help you that much, but it would take a little work (even these days, I feel) to have an AI that could properly gauge the point values of every piece based on the board configuration. Maybe that's already done, but I wonder if it's being done well?
Anyways, I wish stuff like this was talked about more. Chess seems like a game that you could "solve" on the surface but the really interesting stuff - dynamic point values, open vs closed games, strategy and tactics based on tempos - only come into play later on and not much of it is formalized. It's just stuff people learn and write about but everyone seems to have different ideas about things.
I'm a huge fan of tactics where gaining a tempo even when making a sacrifice offers a massive advantage. It goes to show how important tempo is.
Likewise, I find it super interesting how in the early opening (when there's enough pieces on the board that it's "crowded") you can sometimes waste tempos outright and still come out ahead. Hence the ability of top-level players such as Magnus Carlsen to play Bongclouds or cycle knights back and forth between the same squares multiple times and still win against GMs.
Chess is interesting... Also kind of weird :)
Carlsen might be doing this as a statement of confidence. that given the depth of the continuation, his blundering chances cumulated would still be low enough for a win in spite of the board disadvantage.
but yes. it might also be testing hypotheses of the board.. I was wondering about that knight cycle opening.. does the initial standart position one-side, being far from barycenter of opponent material (like the opponent own pawn barrier is not likely going to give way to the rooks by themselves)... how far can the opponent advance closer and maintain a self-defending network of interactions, (in other words not overextend a part of its whole mass, chess mobilities included) that would not be exploitable by the cryptic un committing other side material placement. having lost the time, does it delay beyond repair, by virtue of the 2 backrank being a poor initial defensive structure.. how much does knowing the committed opponent structures outweight the delay in changing own pieces activities on rest of board..
Carlsen may not have proven anything about the board, but may have suggested some questions.. an exagerated version.. but the fog about continuiation from any position, during the whole depth of a game and about opponent differential abilities, makes it hard to attribute his wins to the board properties.
But yet chess is bigger than some might think. I believe that.
Thank you for this very interesting guide: I found very useful the rule of thumb of exchanging queens when you have B+R vs N+R or, on the contrary, keeping them when you hake N+Q vs B+Q.
However, I didn't understand the last rule of thub: "When you have the knight, play on the opposing color of the Bishop you don’t have. When you have the Bishop, then play on the color of the Bishop your opponent doesn’t have."
The second part is clear to me but not the first one: if I have the knight, does it mean that I have one bishop left and I need to play on its color (or -in the words of the article- the opposing color of the bishop (I) don’t have)? Or do you assume that I have just the knight but no bishops? In this case which is the color?
The dream n vs b endgame looks to be a draw if black to move.
@cavalier-spaniel said in #7:
>
Interesting proposition.
What set of positions or games is that based from? an average still. I am skeptical of the 1 value for pawn. It might be a given of the conversion.
LC0 (A0 too) internal measure has to be converted to assign material values, so it would have been done on some given database of positions (or games, and positions with given depths within).
I looked at the medium article, but it seems to have extracted a figure from somewhere else. I would be curious about the method.
I always thought the knight and the bishop had the same value ._.
Nice blog!
@I_Love_Queens said in #18:
> Nice blog!
Everyone says that!!!