Command Area Speed Targets
CAST is a method for valuing chess piece types used in a given CV.
A java implementation of CAST can be found here.
Introduction
CAST arose out of my frustration with using the SMIRF approach combined with my liking for playing with numbers. Whereas SMIRF uses per square figures CAST uses per board numbers and is therefore easier to apply with less room for error.
It is still a work-in-progress, with the latest addition being the Command element; and soon there may be a Range element - when I shall have to change the acronym! (C-STAR?)
Examples
Before getting into the detail here are 3 examples of valuing Pawn, Knight, Bishop, Rook, Archbishop, Chancellor, Queen and King on various sized boards.
Note: Over the 3 tables the 19 comparisons (CAST*100/SMIRF) have a mean of 99.95 with a s.d. of 4.84
The Calculation
A piece's total points value (TPV) is given by
TPV = AP - B + (TP + SP) x C
where
- AP represents the Area Points
- B the Blocking Value
- TP the Target Points
- SP the Speed Points
- C the Coverage Factor
taking each parameter in turn
Area Points (AP)
This is a measure of the total target area covered by a piece. Any enemy piece within the target area is potentially in danger of being captured. The final value is derived by determining its maximum and minimum and then applying appropriate weights.
AP = (Wmax x APmax) + (Wmin x APmin)
The maximum target area is derived by placing the piece in the center of an empty board and counting the squares attacked. The minimum target area repeats the process but with the piece placed on a corner square.
The weights allow for the pattern of per-square AP values across the whole board as they diminish from the center outwards.
Target Points (TP)
This measures the number of enemy pieces within the target area that can be threatened with capture at the same time. For standard pieces where moves finish with the first capture, this equates to the number of directions in which a piece may move. The calculation follows that of the Area Points, thus
TP = (Wmax x TPmax) + (Wmin x TPmin)
In this article the 8x8 piece values have been cited errornously from the SMIRF's 10x8 section. They should be corrected. Because of those being part of a PNG picture I cannot do that myself. Thus I would like to encourage the author to review his contribution.
Thank you for pointing out my error. I have corrected the image and updated the comparison calculations.
Those who have had a closer look to the SMIRF method deriving the average piece exchange values will have noticed, that there is its third component "mobility value". Currently I am convinced, that this part is not simply a constant but instead depending on the percentage (as I prosume) of empty squares at the board. I will try to derive a calculatable relation between both. As a consequence it seems that especially sliding pieces have an increasing of their values while the board is becoming more and more empty during a game.
Yes, I think that beside the board's size and shape, and a piece's move distance and pattern, the density of pieces should have a bearing on a piece's value. Another aspect of density is the effect it has on valuing pieces like the chinese cannon which need a screen in order to effect a capture, although I must admit that I am currently unclear how best to derive the values of such assisted pieces.
Have also a look at Derek Nalls "Symmetry Perfect" page [http://www.symmetryperfect.com/shots/] and his PDF article on "Universal Calculation Of Piece Values". (Maybe it could be a good idea to invite him to join.) Whereas the SMIRF attempt aims to be very elementary, Nalls' approach tends to be rather complex. Overmore there is another paper on piece values written by Ed Trice (GothicChess) [http://www.gothicchess.com/piece_values.html].
Thanks for the info, Reinhard. Interestingly, both Mr. Nalls and Mr. Trice seem to believe very strongly in the "one best chess game" philosophy; and they've each chosen different games. I suspect most of us here are of the "many different awesome chess variants" school. Probably none of us agree on what, if any, games are the very best. We won't agree on pieces, or types of pieces. So I propose a very broad interpretation of pieces and what a good chess variant is in general. I think that would fit the spirit of this wiki. We'd want a lot of contributers and a whole bunch more comments. Just to show I'm not shy, I'll throw my 2 cents in.
I would add a factor for "Attack Fraction" - the number of squares a piece attacks vs distance and squares at that distance. The beginnings of this are posted under Design Principles.
I'd also add a factor for "blockability". A slider is blocked by 1 piece. A leaper can jump over 1 piece, so needs 2 to be blocked. There are some pieces that jump twice, and may change directions during movement. A "Block Fraction", similar to the attack fraction, can be developed.
I'm not suggesting these factors, or any others, be added to SMIRF or the gothic chess engine, or anything like that. I am saying that the numbers on this site, to be of maximum use, must consider a wide range of piece and game types. I'm looking forward to seeing what people put up. Graeme Neatham is posting some interesting stuff here. It'd be nice to have a central page for all this stuff, even if we have to truck all over outside to see it all. How much of the relevant stuff can someone put on one page?
Enjoy,
Joe
People are different, Joe, so am I. If you would spend some time in looking at my always unfinished program SMIRF, you would find it to be a multivariant approach. The bad payload of that is, that it is far from the center of interest of most chess programming people (which are nonetheless only few). Most chess fans regard the traditional 8x8 chess game to be the only one valid, the incarnation of a perfectly designed game. But millions of people playing that game, gathering experiences through centuries, actually putting those into huge data bases and by that are transforming this fine game from a save harbour of creativity into a dead and boring graveyard of endless reproducings.
So I wrote a book in German on "Fischer Random Chess" or its better new name "Chess960" to argue for a highly creative to be played chess variant, which is nevertheless not far from common chess experience. Moreover 10x8 chess could impregnate chess programming by making it necessary to think over all elementary details of chess and related games, beginning with pieces' gaits and their resulting average values. But even that very basic question is still keeping me busy, especially when I try to reduce it to only few elements. And thus I am not finished with it …
Hi, Reinhard. I agree with you completely on the problem of FIDE. I don't wish to spend a great deal of time memorizing opening lines and traps to be able to hold my own through the first 20 turns of what I think is a small chess variant with a rather limited variety of kinds of pieces.
I'm interested in the lower range of sizes, from 8x8 to 12x12, and in using shortrange leapers preferentially in this size range. I have a CwDA submission at CV waiting to be posted that pits the Fabulous FIDEs against some pieces that move 2 or 3 squares max per turn, and a Grand CwDA variant of it. I'd love to know the values of the shortrange pieces in those games, and I'd love to see how the FIDE sliders and shortrange power pieces' values scale to boards that range in size from 12x16 to 20x30 to 100x100. Graeme wants the same thing, for hex chess. We're looking to explore chess behavior under a much wider range of conditions than we've seen so far, if that's not too immodest a claim.
And it's true that what we've [Graeme and myself] done here is quite large, but there are 2 reasons for that. First, this is a "sandbox", where we can work out ideas in a way that's unsuitable for the CVPages [even though I did it with Fortress Chess - maybe that's why David start… hmmm]. Second, we've both done some little stuff, it's posted at CV; look at Spartan Chess and Lemurian Shatranj for 2 games that show we can do decent, novel "little" variants.
There is a limit to the number of things you can do to have a game that's "very close to chess". Any variant we would deal with here would have 3 parts: Rules, Pieces, and Board. Change one a little, and you've changed the game. Several people have staked out that "very very close" area and are covering it very very well. I enjoy ranging a bit farther afield, but certainly respect the roots of these games, and want the knowledge gained as a solid foundation for games that are a bit farther from the norm.
Clearly, a good knowledge of the basics is necessary for good design range. One can only hope that the spark of creativity necessary for a good game is also there. But the basics will give a game with a spark the playability any game needs to be enjoyable.
So where do we start? Put together a page of the best calculations? Take the average of these calcs? Rate the different methods - how would you rate the top several methods of piece value calculation?
Enjoy,
Joe
Reinhard, Graeme:
I've looked over both your piece value calculations and find them very interesting from a number of aspects. I'd like to look at 2 shortrange analogs of the Archbishop [B/N] and Chancellor [R/N] to start, the Minister [D/W/N] and High Priestess [A/F/N].
This is the basics of Graeme's numbers, I believe.
More later - including Smirf numbers
Joe
Joe, SMIRF's approach should be usable for consistent gaits here. But I have to mention, that it has not been thought to work also on split approaches (like "Quing" and "Keen"), where moving and capturing would act at different distances. May be it thereby is less flexible.
It is a difficult task to think over a rating of those existing different scaling methods. Because it would need a huge amount of appropriate played games and highly experienced players within that variants to valuate pieces "objectively" by comparing those to theoretically derived figures. Currently that seems to be applicatable for traditional chess only. (But I hope for more practise experiences from 10x8 chess based games on Capablanca's extended piece set.) But even in chess the bigger pieces will find the wider value regions.
Derek Nalls currently is doing some experiments with SMIRF, where this program has been compiled twice using our different model results and having some long time matches, to experience a "winning" model. But I have found out, that because my program has internal optimizations which probably are supporting that own model, thus the model rankings from its results might hardly to be claimed as absolutely valid, if the differences (like in this experiment) of the model result values are not that big. Nevertheless this approach seems to be the most promising attempt to test evaluation results of such model concepts. In that sense chess programming could be a tool to verify the workability of new value model concepts.
It would be helpful, if each model designer would write his own chess program to perform comparable experiments. If then happily the ranking results would be consistent, that would be indeed more significant. But I doubt, that this extreme idea could be performed in reality.
A three-fold confluence of ideas -
led me to the think it might be possible to assign values by running "combat trials" using random generation of moves for groups of one type of piece against another.
Put another way, throw say 8 Queens against maybe 8 Knights (perhaps with 16 randomly placed but static Pawns to provide density) on an 8x8 board and see whose left standing. Repeat a few million times and just maybe the averge win ratio might be around 3:1 in favour of the Queens?
Anyway, I was intrigued enough to start designing Java application to test the possibility.
Intriguing idea. Hope you get somewhere.