I don't need to correct you regarding my calculation of e.g. a WAD. At least I added in 2Ps worth of cooperativity, as you put it in different words. The explanation you gave that included reference to N moves/parts is a bit over my head, as I'm still not that familiar with a lot of CV terminology (and being a bit lazy, I've tried to keep it that way for some time now). I would note that I estimate half a knight's value as (N-P)/2 since (as I would much prefer to end things with) as I see it a halfN plus a halfN plus pawn = full N, but only to appearances this is in line with my Q=R+B+P analogy. My estimate of the value a quarter of a N is, perhaps at first glance, based on a dissimilar calculation, however, and it's an illustration of a quandry of mine which I had much preferred not to write about, until your pointed query. I value quarterN as (N-P)/4, i.e. on 8x8 it is (3.5-1)/4=0.625 (i.e. also my value for an A there), so it's significantly less than 1 for that board size (which seems contrary to what your reasoning expected from the beginning, if I get the gist of it all the same).

I'd creatively noted that a full N equals N-P+P=((N-P)/4)x4)+(P/4)x4=3.5, i.e. I'm clearly not using the Q=R+B+P analogy in this case, since otherwise the value I'd get for a quarterN (or its equivalent, an A) would clearly (even to me) be way too small (i.e it would be (N-3P)/4, or 0.125 - note if we used eighths of a N, it would then be (N-7P)/8, which would produce a negative value!). Instead, by using a different way of thinking when estimating fractions of a piece type's total movements (including for that of a halfN), I get a value for a quarterN (or A) I can live with for now (i.e. 0.625), and an A is a piece of relatively low value regardless, as you observed. So, now having yet another tentative estimate method, perhaps an even more imperfect one (which I figure is better than not having it, unless I go questing for different way(s) to get values of CV piece type fractions, and with such apparently giving more accuracy, which may take ages hunting down or concocting a satisfactory number of them), for such a thing as a 'compound' of 4 quarterNs, which in effect is the same as having a N, I'd make the 'compound', of 4 quarterNs (no matter if some move differently), work out to equal a Ns value, by using 'compound' (or N)=4quarterNs+(P/4)x4=3.5.

One fly in the ointment seems to be that I value AD=A+D+P, where I've already put the value of D=A=quarterN. Fortunately for me, so far I can console myself with the thought that none of these piece types move (even almost) the same way as each other. Unfortunately, I discovered that a quarterN + quarterN compound's value would still seem rightly to work out greater than a halfN's value, unless I immediately treat that whole compound as simply known to be identical to a halfN (that having a value I'd work out instead, as I happen to have done already for 8x8); I am to say the least a little unhappy about using such an apparently fishy way to try to patch things up, unless in my toolbox there's another trick, or alternative method to choose from, in such a case, that I have forgotten - I don't always have such written down somewhere. Life is far from perfect for me, and all this looks horribly suspect (i.e. inconsistent, unsound), but so far the CV piece values I've come up with haven't looked too far off in my own eyes, and at least no one has put their finger on my quandry that I mention here, until now.

On the other hand, if a N (or a piece of about the same range and number of targets) were somehow (fully once) colourbound then such would be worth N/2 in my eyes (it's also less than what I got for a halfN above, i.e. (N-P)/2, which makes sense to me). In the case of a AD (which does have 8 targets, and is colourbound), it's also a compound of (known) pieces, so for that I choose to simplify my life and just use A+D+P to get it's value. Nevertheless, I'm very much still feeling my way, regarding such formulae, and guidelines on what to use them for (e.g. in the case of B vs. N I've tried, not quite conclusively, to finely weigh them against each other on my own, in terms of their having an equal number of roughly equally important assets and liabilities, as I see them, and my somehow applying a x0.5 numerical colourbound penalty against a B could complicate things, though I could try to do so one day if I could quantify all the other vital factors to my satisfaction, too). At times I look at piece types that seem similar, when estimating the value of a type that is new to me, to check if they have known values that are relatively close to what I get for the new piece type.

In the case of a WAD (or Champion), I still give some consideration to the page of Omega Chess Strategy's piece value of 4 (on 10x10+4 cells), as that game has been played for some time now, and I'm guessing people have established that estimate through many played games - though possibly largely between relatively low-rated people (if they were chess players). It's also convenient for me to accept (at least for a while) that that value is about what I get for a value, too. The alternative is to start re-working or trashing some or all of my primative methods, leading to a lot more work and perhaps the result that I have to refrain from giving even tentative estimates for things, at least for a long time, which is no fun (otherwise, I often can satisfy anyone who wants just any quick and dirty estimate, before a 'more scientific' valuation might become available). As an aside, I once saw someone opine somewhere on the internet that an A was likely worth less than a pawn, unlike the wiki for an A, so when in doubt I again chose to believe something that agreed more with my own methods' results to date, although that time I was even less sure of assuming that that person had done any sort of significant research than in the case of a Champion in Omega Chess.

I recall you once indirectly indicated to me you wrote at least one CV-related wiki entry. I wouldn't be surprised if you've written all or nearly all of them. One thing I don't understand about wikipedia entries in general is why the names of writer(s) of them are not attached (or at least not prominently displayed, if they are there to be found). I think that would be right regardless of the topic, and in your case it would certainly bring you at least some recognition, for any who noticed that you've written many CV wiki entries, especially if you were ever allowed to note in places results of your own research, and that it was yours, in regard to computer studies/formulae (though I seem to recall that extensively quoting independent research goes against established wiki regulations in itself).

Long ago I posted (perhaps via an edit) a summary of my some of biggest doubts re: computer studies, of which I think there were 3. One that was major was the strength of the engines involved (or of the humans, in the case of Kaufman) possibly being too low to establish the probable truth - best play with e.g. B vs. N only comes from consistently high level test games, otherwise it seemed to me it's a bit like having kids play kids and then taking down the results of very imperfect play with imperfect plans used. A second doubt (relatively minor, perhaps) was about the calculation of the margin of error used for such studies, which I thought might be bigger and bigger the larger the value of the piece type being tested (i.e. a B's margin might actually be considerably less than the margin for an amazon, and, e.g., a Ps margin [if such is/can be attempted to be measured] might be smaller than a Bs margin, in each case assuming the same number of test games were used when testing the value of each piece type). I think the third doubt (also relatively minor) was the idea that maybe the margin of error in general should be as much as double than assumed, since it's theoretically possible the materially inferior side might win more games in a random set of them (unlikely, but possible, especially if the engines are relatively weak). However, these last two doubts may just show that I don't get the statistical methods or math in general - but I still feel the whole field of computer studies (or even of concocting piece evaluation formulae based on its results) is immensely complex and relatively unproven, and somehow subtle wrong assumptions or reasoning might creep in, even for experienced mathemeticians. Aside from all that, the composition of the armies for a variant's setup (or possibly even the exact positioning of the pieces in that) can throw something of a wrench into the value estimations, and then there's opening, middlegame and endgame phase piece valuations, which aren't necessarily in agreement, though I know you're aware of all that - the possible issue is that there may be a theoretical need to examine all these cases with computer studies, too.

In my last post I more or less neglected to mention that a Man's (or K's fighting) value is another that is problematical for me, on 8x8 at the least. One way for people to test piece values for themselves is simply to play a variant involving a piece type with an assumed value that the player bases his calculations on. Doing so gives an insecure feeling though, and I'm often reluctant to have piece imbalances in regard to the position on the board or in my calculations, when possible. Moreso when the piece types are powerful, like in the case of swapping an amazon for a collection of pieces of clearly smaller value. In the Modern Shatranj variant, in my games I've been able to somewhat better appreciate the value of a Man on 8x8, relative to 'other' minor pieces, and it's not been often that it clearly seems to be by far the best piece type to own, compared to a N or Modern Elephant. Often in the middlegame or early endgame stages, the types all seem to 'feel' as if about of equal value, in my numerous games (on Game Courier) so far. However, in one endgame that I won, a Man I had proved superior when pitted against a N, as I was able to launch a mating attack at the end for one thing. The final position may give an impression, even if one does not wish to play over the entire game:

https://www.chessvariants.com/play/pbm/play.php?game=Modern+Shatranj&log=panther-cvgameroom-2018-112-744

Another thing I've gotten a bit of a feel for through actual play is the comparative value of a N to a Modern Elephant (e.g. in my 10x8 Hannibal Chess variant), and in the opening phase, at least, a ferfil (aka Modern Elephant) seems at least as influential as a N - contrary to my valuing a ferfil somewhat less than a N on 10x8 (or on several other board sizes).