Miguel Ballicora wrote:BTW, This may be unrelated, but when I look at Fruit 1.0, it looked to me that Fabien was using a similar mental approach, with a higher edge and corner penalty. Just using the whole 2D-table unrolled, and the bonuses looked more disorganized, but they were there (diagonals were present, bonus for 6th rank for knight were explicit, but he later expressed them neatly with a vector etc.). I think that Fruit 2.1 and 1.0 were conceptually very related.
Due to my method of regenerating the "wave" nature of
KnightRank as 2 less than
(r-(2<<(r^6)))&7, I found your "SixthRank" parameter to be quite odd when I saw it, but that's just a side comment. I think the PSTs are
conceptually related (and indeed, aren't most PSTs [maybe they fall into 2 or 3 "equivalence classes" of similarity], particularly those from the same author?), though quite different in their instrumentation [and as you say, Fruit 1.0 is more "disorganized" -- FL told me that he deliberately tried to reduce the "dimensionality" of the question, so as to tune it easier]. Of course, with Rybka 1.0 Beta we only have the end result of PST, so we can't compare methods directly.
Here is a guess as to how likely the Fruit/Rybka match for "centralisation ramping parameters" should be "at random" -- it uses lots of assumptions, but I think most are reasonable. What are the common elements of the Fruit/Rybka PST? I think it is fair to eliminate KingOpening, as though the file array is the same, the rank differs. Similarly with PawnOpening (the difference in "bonus squares"), and I don't think the fact that Rybka uses nontrivial PawnEndgame PST is anything to speak of. Similarly, I think QueenOpening can be eliminated, as Fruit 2.1 has a parameter that is 0, thus obscuring the picture. With RookEndgame PST being zero, this leaves 7 PSTs, involving 5 pieces. I think the
-2,-1,0,1 of RookOpening
is reasonable to keep, as there at least is a direct comparison (no matter how perfunctory). One can try to extract "partial information" from the some of the above, but I will not.
So the next step is to choose a "mainstream" ramping array. I think there are at least 3 reasonable ones (my glance at ~50 open-source programs suggests a greater number, but I won't dispute), of which both chose
-3,-1,0,1. As you say, the 5 or 7 choices of when to use this are not independent. One can argue that the "times to vary" from the mainstream array consist of either 7-choose-3 (2N and 1R array), or 5-choose-2 (vary for N and R). This is at least a 1 in 10 chance that the "varying" from the mainstream occurs at the same places -- it seems rather unclear to me whether one could argue that it is "natural" that N/R "should" vary from the others, particularly as any "extra" centralisation impact (for N) could be obtained in a similar way by (say) doubling everything. Then there is the choice of "varying" element. If there were 3 reasonable arrays to begin, there is a 1 in 2 chance for each variance to match (I think these are reasonably independent). This gives a total of 3 x 10 x 2 x 2, or about 1 in 120 for the "centralisation" structural match in Fruit/Rybka.
One can additionally adduce the KnightRank, where (say) it might be logical for it to be more "mainstream", such as
-3,-1,0,1,2,2,1,0, but I think the argument suffices w/o this.
This is an imperfect mathematical model of the situation, but I think it gives a ballpark estimate. If nothing else, it shows that VR had "something to answer" about the situation, and more specifically than just a vague "took lots of things" comment, or an assertion that this was merely "common chess knowledge" or the like.
Disingenuous comment to wonder why it took so long, because you could have filed a protest 5 years ago if you wanted to. Until the letter you signed, there was NO formal protest filed with the ICGA. Do they just investigate out of the blue? Don't think so. For the other cases, there was plenty of suspicion and protest were filed quickly.