[ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]
Comments/Ratings for a Single Item
H. G. Muller wrote on Wed, Sep 26, 2012 09:28 AM UTC:OK, after fixing some bugs, and some testing mistakes, I have the first valid results. To begin with, I made one change in the engine: the factor two discount on a Pawnless (but otherwise unsuspect) lead is not applied when the opponent has a bare King. When you have mating potential (mating minor, more than a minor ahead and no 'defective pair' or a color-bound piece, or 3 pieces) there is no reason to shy away from the end-game. Mating potential is mating potential... This solves problems in KRPKB, here the advantage can be very high if the Pawn is on 7th rank (and counts for ~2.5, so you are at +4.5), where the Bishop covers the promotion square, so you cannot make progress other than forcing the BxP trade, to convert to KRK. But with a 'Pawnless penalty' that would only be +2.5, so the engine refuses to do it unless the KRK mate is already within the horizon. (Which it usually isn't at the fast games I do, so this easily won game ends in a 50-move draw...) With this change Pair-o-Max beat the old Fairy-Max by 53.67% in 409 games (here the statistical error is 2%), so I don't have to worry that it has lost strength because the implemented changes slow it down too much (>90% confidence). The more accurate scoring of the Bishop pair and recognition of drawishness more than make up for it. The 3.67% excess score corresponds to a superiority of 25 Elo. With this version of Pair-o-Max I ran a Commoners vs Knights match, replacing 2 Knights by 2 Commoners for one side in the FIDE setup. In half the games I then swapped B and C of the Commoner side, to provide more game variety. The Commoners player alternately had black and white, to elimiate the white advantage, and in half the games black was given the first move, also to drive up game variety. After 393 games the Commoners are leading by 52.3%. This is just a bit larger than the standard deviation, so barely significant. But, hen taken at face value, the 2.3% excess corresponds to 16 centi-Pawn. And because that is for a pair, it implies the Commoner is 8cP (+/- 7cP) stronger than a Knight. This is consistent with the value of 333 I programmed for C (where N=325). In an earlier run I had programmed C at 300, i.e. below N, but when this run also had the Commoners winning (even more!), I changed the value to mae it consistent, and redid the run. As usual, this did not have a dramatic effect on the average score. The test now runs on to increase the precision. I will start a second test in parallel (now new-vs-old version is decided), for Commoners vs Bishops.
The increased knowledge of mating potential has raised the apparent value of Commoner, then?
H. G. Muller wrote on Thu, Sep 27, 2012 09:06 AM UTC:> The increased knowledge of mating potential has raised the apparent value of Commoner, then? It seems so. To be frank, I am not entirely sure if the previous value determination was for 8x8 or 10x8 board. I did a lot of 10x8 measurements for Great Shatranj, where Commoner is one of the pieces. I also remember having done some tests with divergent K+N combinations, though, and that was most certainly on 8x8. But I remember I also found then that 3 of the 4 combinations were equal, and only mNcK was 50cP stronger. [Edit] I looked it up, and the conclusion then was that Commoner was 30cP weaker than Knight. So in that case good handling of the mating potential does seem to have a significant effect. Perhaps I should redo these tests with various aspects of the new knowledge disabled, to see what helps most. [End Edit] The Knights vs Commoners match is now at 777 games, and the lead of the Commoners has dropped to 6 points. Which is an excess of only 0.4%. Against a standard deviation of 1.4%, so totally insignificant. After 338 games the B-pair vs Commoners is at 57.4%. The excess of 7.4% (+/- 2.2%) is exactly half of the 15% Pawn-odds score I remember from the previous version of Fairy-Max. This also points to exact equality of Knight and Commoner, as B-pair is also worth 50cP more than Knights. (Kaufman values, confirmed by my tests with the old version. Which in this case should not matter much, as neither B nor N have mating potential, and drawing tricks based on KNNK are excedingly rare (plus that Fairy-Max is not likely to be able to win KBNK either, not knowing in which corner to drive the bare King)). Next I will probably do B-pair vs Commoners + Pawn, to check if the sore eactly reverses. (Doing an implicit determination of the effect of Pawn odds at the same time as more Bishops vs Commoners comparison.)
You might also consider repeating your experiment of adding mating potential to a bishop. Another consideration: does the value of mating potential depend significantly on how many other pieces already have it? If you replaced rooks on both sides with a similarly-valued but non-mating piece, does the value of commoners relative to knights go up? If you replaced the bishops on both sides with a similarly-valued piece with mating potential, does it go down? I think Betza suggested once that it was important for a side to have a piece with mating potential, but not so important how many pieces had it.
H. G. Muller wrote on Thu, Sep 27, 2012 06:33 PM UTC:Interesting suggestions. I will keep them in mind. Similar in value to Rook, (+/- 25cP) but non-mating are Nightrider and the color-bound BD. Unfortunately Nightrider is a bit troublesome in Fairy-Max, because it allows mutual perpetual check, which in Fairy-Max leads to infinite recursion. BD produces the problem that it is a second color-bound type,if I also keep the Bishops, so that the possibility for color-bound hetero-pairs will exist. The current drawishness code does not test for that. It might be important to add it, because at some point I will certainly want to test BD to measure its pair bonus. 12-move leapers are usually close to Rook in value. Perhaps the NW would do it; as a pure alternator it does not have mating potential. Bishop-valued with mating potential could be a fWFA, or perhaps sWFA. I stopped the Commoners-nights match at 910 games, with 1.3% advantage for the Commoner pair. That is about 1 STD, so not really significant. The B-pair beat the Commoners in 480 games by 56.5%
How does the inclusion of Nightriders lead to a mutual perpetual check? Betza also believed the crooked bishop to be worth about a rook, but that's also colorbound, so I suppose it would have the same problem as BD. The "aanca" (W>B bent rider) might also be close enough to be an intersting test, if you want a long-range non-colorbound piece. It's almost certainly noticeably stronger than a rook, but should still be closer to rook than queen. Of course, those both assume your engine can handle nonlinear riders, which may not be the case...
H. G. Muller wrote on Sat, Sep 29, 2012 08:30 AM UTC:> How does the inclusion of Nightriders lead to a mutual perpetual check? Sooner or later the engine encounters this motif in its search tree (h=Nightrider): h . . h . . . . . k . . . . . . . K . . . R R . Both kings can then move left-right, discovering checks on the opponent with their Nightriders and Rooks. As checkks are extended in Fairy-Max (i.e. it always searches all evasions when in check), it extends to infinit depth. Fairy-Max can be configured to do Crooked Bishops, but not Aanca. But I could always change the code, of course. Yet is seems best to try WN first. If both sides play with this piece in stead of R, it is not that important how strong it is. New results: Commoners + Pawn vs B-pair (584 games) 58% So the B-pair had an advantage of 7.5% against 2 Commoners, but when short a Pawn they see that advantage reverse to -8%. That means they ae pretty much halfway (and a Pawn is apparently worth 15.5%). This is actually the same as Knights do against the B-pair. So the Commoners come out pretty consistently now as exactly equal in value to Knight. I also tried to test end-game value, by setting up positions like 1m4k1/ppp2ppp/8/8/8/8/PPP2PPP/1N4K1 w - - with various permutations of k, m and n. This was won by the Commoner in 932 games by 58.9%. (~56% of he games are draws there.) I have no idea yet how much an extra Pawn would be worth in such a position, though. But even a single Commoner seems to have a significant advantage over a Knight, in such an end-game.
> h . . h . . . . . k . . . . . . . K . . . R R . I'm not sure I follow this diagram, but I think I can now envision an arrangement with the properties you describe. Does the same thing still happen if you have nightriders BUT NOT rooks? I suppose you could substitute queens for the rooks, though that would require a promotion...
H. G. Muller wrote on Sat, Sep 29, 2012 06:43 PM UTC:Indeed, the display of tables is still not fixed, after the overhaul of the site broke it. I would not be surprised if something similar was possible with Bishops and Nightriders, though. The important thing is that the angles between the slider rays are small enough that the Kings can be far enough apart. With Rooks and Bishops the pattern would only work if the Kings were on adjacent ranks, checking each other.
H. G. Muller wrote on Sun, Sep 30, 2012 11:29 AM UTC:I now ran an end-game test of Commoner + 5 Pawns vs Knight + 6 Pawns (same setups as with 6 vs 6 Pawns, but with the c- or f-Pawn deleted for the Commoner (M) side. This ended in a 69.4% victory for the Knights. So N+P have an advantage of 19.4%, while just a Knight has a disadvantage of 8.9%. It seems a Pawn makes a difference of 28% at this late stage of the game, and the Commoner is twice as close to N as it is to N+P. So Commoner(end-game) = Knight + 0.33 Pawn (or ~360cP on the Kaufman scale). So the value of the Commoner rises appreciably compared to that of the Knight when you reach the end-game. Perhaps this is what should be expected from a piece with mating potential. Or perhaps it is just because the Commoner is so much more effective in annihilating Pawns. I am now testing the same end-game setups, replacing the Knight by a Bishop.
H. G. Muller wrote on Mon, Oct 1, 2012 05:28 PM UTC:Result for the Commoner vs Bishop end-game: 6 Pawns each: 61.7% (+/-0.9%) in favor of Commoner (879 games) Commoner + 5 vs Bishop + 6: 63.4% (+/- 1.35%) in favor of B + P (729 games) Again, the extra Pawn swings the result by about 25%. The Commoner seems nearly 0.5 Pawn stronger than a Bishop. The statistical error is ~6 cP. So against a Commoner a Bishop seems less successful than a Knight in the end-game. This could be because it has more difficulty winning games when it creates an advantage, due to its color binding: two Pawns are easy to stop by King + Commoner. if they just position themselves in front of the Pawns on a color the Bishop cannot reach. This is unbreakable defense even when the attacker calls both its King and its Bishop to the aid, because a King cannot approach a Commoner either. (And there is no zugzwang, as you can do moves with the King / Commoner in front of the Pawn that has no King support. So the defense is even easier than with unlike Bishops, because there you have to worry that the Bishop might not be able to stop a Pawn supported by its King, so the defending King has to keep opposing the attacking one. Which it can usually do, as the Bishop can control squares in front of both Pawns. A Knight can also not stop K+P, but if your King aids it in the defense, there is nothing stopping the other Pawn, as the Knight usually is too far away. So a defending Knight cannot easily exploit the color-binding weakness of the Bishop, but a defending Bishop or Commoner can. This is another case where the unapproachability of a Commoner makes it a very strong defender. (The other is in KQKM, which is draw if King and Commoner can protect each other before the Queen snipes off the Commoner through a fork.)
Here's an idea how to switch on the can-mate property without changing the moves of a given piece:
Can-mate Knight: Moves and captures as a normal FIDE Knight; but when the endgame KN vs. lone K is reached, it gives immediate check (and checkmate, if the lone King cannot capture it).
Switching off the can-mate property is not so easy. Just defining a Cannot-mate Rook as normal Rook, but when the endgame KR vs. lone K is reached, it it automatically a draw, unless the last capture gives checkmate -- seems to work, but in practice the stronger side will be keen to keep a pawn or two on the board and perform the mate with the full Rook before it is too late.
I wondered about that possibility, but I was concerned about endgames where there are a couple of pawns stuck somewhere such that they couldn't interfere with a normal mating strategy but where a weak piece that has been artificially designated "can-mate" cannot capture them safely, and therefore the game is technically not a KXK endgame.
Here's the position for mutual perpetual check with bishops and nightriders. You need two bishops on the same field colour (or a queen and a bishop); a position with bishops on different colour does not exist because the kings come too close to each other. Bishop's team: Ba2, Bb1; K b3/c2 Nightrider's team: NN f8, NN h6; K e6/f5 ... it just fits on an 8x8 board.
15 comments displayed
Permalink to the exact comments currently displayed.
I made some enhancements to Fairy-Max, to make it pay attention to lack of mating potential and pair bonuses. This was relatively easy, because it already contained code to keep a count of the total number of pieces (for the baring rule in Shatranj) as well as of each piece type (for Spartan Chess' King counts). So I now added a list of pair bonuses to the piece info, and each time when after capture there is an odd number of that piece type, I add the pair bonus for that piece type to the score. I let it initialize the pair bonus to 1/8 of the piece value if the piece is 'obviously color bound', which for B (325cP) would give 40 cP, which is about right. No idea how this would work for other pieces, but this can be tested now. Interesting candidates would be the Clobberer pieces BD and FAD, which are worth about a Rook, and Adjutant (BDD), which is worth about 7 (IIRC). Recognizing lack of mating potential is a bit trickier. I did not have a very fast algorithm for that, it must loop over piece types to see what each side has. But as a fast filter I can use the Pawn count of the side that is ahead: if it is 2 or larger there is no need to worry about lack of mating potential in your pieces. The way I evaluate 'drawish' endings is like this: 1) If the leading side has no Pawns, its advantage is divided by 2. 2) If he has one Pawn, and the opponent has Pieces, (non-Pawns!), we assume the weakest piece is traded for the Pawn. 3) If the strong side has no Pawns and not more than 2 Pieces, and the weak side not more than one piece, we recognize some cases that are dead draws, and divide the advantage by a further 2 (if a Pawn has to be traded away first) or 4 (if the strong side is already Pawnless). The recognized cases are: 3a) Less than 350cP advantage in Piece material, and no minors with mating potential. This catches cases like 2 minors vs 1, R vs minor, R+minor vs R, Q+minor vs Q, but not Q+minor vs RN or RN+minor vs BN 3b) The strong side has only one piece, and it is color bound (seen by the pair bonus). This catches a lone BD or Adjutant vs weak stuff, which can easily have an advantage 350. 3c) A 'defective pair', like two Knights. I encode this by giving such a piece type an insignificantly small negative pair bonus, specified explicitly in the piece description file. (Mating potential in a minor is likewise encoded by an insignificantly small positive pair bonus for the piece.) So advantages in drawish endings are divided by 2, 4 or 8, so the leading side will try to avoid them. E.g. KNNK would normally be 2*325 = +750; the factor 8 trims this to 94, i.e. less than a Pawn, so the program would prefer KPK. KNK would score only +47. I am now running some tests of thei new program ('Pair-o-Max') against the old Fairy-Max, to see if this extra knowledge would make it indeed play stronger.