Re: Would someone be interested in programming....
Posted: Thu Oct 04, 2007 2:30 pm
On the piece evaluation itself:
Knights vs Commoners
As the Commoners were losing quite decisively from the Bishops (by about the same margin as Pawn odds), both with 320cP with 280cP set for the Commoner value, I now tried Commoners vs Knights (both 280cP). The Knights still win this, but only by ~56%.
I also tried playing in a different starting position for the side with Commoners+Bishops, putting the Bishops on b1 and g1, and the Commoners on c1 and f1. (To make sure the Commoners don't appear bad just because they were started in a position from which they could not reach the centrum easily enough.) In the number of games I have so far, this was not significantly different. I also tried a match between two FIDE armies, swapping the opening position of B and N in one of those. With even less games this was practically even (38-36). Knights do not seem to mind starting on the b and g file very much, their lateral manouevrability lets them still reach the center quickly enough even from there (which might be more difficult for the Commoners). Starting them in the corners might be a different story, but I see no reason to try that.
As 56% is about half the Pawn odds advantage, each Commoner seems about 20cP weaker than a Knight, i.e., the opening value in uMax is 260cP. It is still rather surprising to me that the Commoner is weaker than the Knight, as in contrast to the latter, it has mating potential. I will certainly repeat this test sometime with a slower time control, to make sure the apparent superiority of N over M is not due to the fact that uMax simply doesn't know how to handle Commoners well in the end-game, in bullet/blitz games. I can imagine that Commoners, being slow pieces, need deeper search to make sure they don't inadvertently let an opponent's passer escape.
Bishops vs Knights
To see if the relative strength of B vs M and N vs M make sense, I had to know more presicely how much the N-B difference actually is. uMax uses 280cP vs 320cP as a kludge to protect B-pair, which works, but the true value of this difference was never tested. So I had set up a match where one side had 4 Bishops, and the other 4 Knights. When the score reached 6.5-0.5 in favor of the Bishops, I decided to abort that in stead of letting it run all night, as the difference seemed too big. So I started a match where one side had NNNN in stead of NNBB against a normal FIDE army. This ended 196.5-169.5 = 53.6%. This is only 1/4 of Pawn odds, suggesting that there is only a 20cP difference between the opening value of BB and NN, in favor of BB.
This small difference was hard to reconcile with the way the NNNN were whacked by BBBB. So I am now running the latter as a long match after all, to see if the previous 7 games were merely a statistical fluke. If not, there could be something funny with the Bishop pair, though. The B-pair is the best-established example of non-linear piece interaction. So it would not be too weird if the value of a larger number of Bishops is also not simply proportional to their number. After all, with two Bishops on white and two on black, you really have 4 Bishop pairs, not 2. In addition even if BB is better than NN, the advantage might shrink by giving each side two additional Knights: the Bishops will be very vulnerable to swapoff for a Knight, wrecking its B-pair when this occurs even once. With 4N vs 4B it should be possible to manouevre such that the first two Bishops you have to give for Knights are on opposite colors, so that you are always left with an ordinary BB vs NN advantage.
To investigate the value of the B-pair, I will play BBNN vs BBNN, were one side will play from an opening position where B and N swap location on one wing, but not on the other. That side will thus play with two Bishops on the same color. I yet have to start this.
again, Camels vs Knights
The Camels were beaten quite decisively by the Knights, better than Pawn odds. To make sure we are in the linear range of the piece-value vs score relation, I tried to test the N-C value in a more even setting, by giving the Knight-side Pawn odds to compensate for its superior piece makeup. This match (where I led the engines to believe C=200cP) is still running, and after ~150 games the Knights still seem to have the upper hand (hoof? ), but now only by about 6%. This seems to confirm that the N-C difference is more than half a Pawn, and would place the Camel near 220cP.
next
The next thing I will try is probably Nightriders. I can do that almost without any programming, making the exo-piece a slider in stead of a leaper. It is of course enticing to replace the Knights by Nightriders (H), but H is supposed to be a quite strong piece. So it might be better to start by replacing BB for HH. If the Bishops get whacked, I can try replacing the Rooks in stead. Or perhaps R on one wing, and N on the other, if the H value lies around 400cP.
I am not sure how to test Ferz and Wazir, as they are expected to be even weaker than the Camel. Perhaps the most favorable position would be F or W on c1/f1, and B on b1/g1, and give the opponent Pawn odds.
I am actually more curious to the value of a Cannon, which seems a quite intersting piece. But such hopping pieces would require some more programming, so I am not sure when I will get to do that.
Knights vs Commoners
As the Commoners were losing quite decisively from the Bishops (by about the same margin as Pawn odds), both with 320cP with 280cP set for the Commoner value, I now tried Commoners vs Knights (both 280cP). The Knights still win this, but only by ~56%.
I also tried playing in a different starting position for the side with Commoners+Bishops, putting the Bishops on b1 and g1, and the Commoners on c1 and f1. (To make sure the Commoners don't appear bad just because they were started in a position from which they could not reach the centrum easily enough.) In the number of games I have so far, this was not significantly different. I also tried a match between two FIDE armies, swapping the opening position of B and N in one of those. With even less games this was practically even (38-36). Knights do not seem to mind starting on the b and g file very much, their lateral manouevrability lets them still reach the center quickly enough even from there (which might be more difficult for the Commoners). Starting them in the corners might be a different story, but I see no reason to try that.
As 56% is about half the Pawn odds advantage, each Commoner seems about 20cP weaker than a Knight, i.e., the opening value in uMax is 260cP. It is still rather surprising to me that the Commoner is weaker than the Knight, as in contrast to the latter, it has mating potential. I will certainly repeat this test sometime with a slower time control, to make sure the apparent superiority of N over M is not due to the fact that uMax simply doesn't know how to handle Commoners well in the end-game, in bullet/blitz games. I can imagine that Commoners, being slow pieces, need deeper search to make sure they don't inadvertently let an opponent's passer escape.
Bishops vs Knights
To see if the relative strength of B vs M and N vs M make sense, I had to know more presicely how much the N-B difference actually is. uMax uses 280cP vs 320cP as a kludge to protect B-pair, which works, but the true value of this difference was never tested. So I had set up a match where one side had 4 Bishops, and the other 4 Knights. When the score reached 6.5-0.5 in favor of the Bishops, I decided to abort that in stead of letting it run all night, as the difference seemed too big. So I started a match where one side had NNNN in stead of NNBB against a normal FIDE army. This ended 196.5-169.5 = 53.6%. This is only 1/4 of Pawn odds, suggesting that there is only a 20cP difference between the opening value of BB and NN, in favor of BB.
This small difference was hard to reconcile with the way the NNNN were whacked by BBBB. So I am now running the latter as a long match after all, to see if the previous 7 games were merely a statistical fluke. If not, there could be something funny with the Bishop pair, though. The B-pair is the best-established example of non-linear piece interaction. So it would not be too weird if the value of a larger number of Bishops is also not simply proportional to their number. After all, with two Bishops on white and two on black, you really have 4 Bishop pairs, not 2. In addition even if BB is better than NN, the advantage might shrink by giving each side two additional Knights: the Bishops will be very vulnerable to swapoff for a Knight, wrecking its B-pair when this occurs even once. With 4N vs 4B it should be possible to manouevre such that the first two Bishops you have to give for Knights are on opposite colors, so that you are always left with an ordinary BB vs NN advantage.
To investigate the value of the B-pair, I will play BBNN vs BBNN, were one side will play from an opening position where B and N swap location on one wing, but not on the other. That side will thus play with two Bishops on the same color. I yet have to start this.
again, Camels vs Knights
The Camels were beaten quite decisively by the Knights, better than Pawn odds. To make sure we are in the linear range of the piece-value vs score relation, I tried to test the N-C value in a more even setting, by giving the Knight-side Pawn odds to compensate for its superior piece makeup. This match (where I led the engines to believe C=200cP) is still running, and after ~150 games the Knights still seem to have the upper hand (hoof? ), but now only by about 6%. This seems to confirm that the N-C difference is more than half a Pawn, and would place the Camel near 220cP.
next
The next thing I will try is probably Nightriders. I can do that almost without any programming, making the exo-piece a slider in stead of a leaper. It is of course enticing to replace the Knights by Nightriders (H), but H is supposed to be a quite strong piece. So it might be better to start by replacing BB for HH. If the Bishops get whacked, I can try replacing the Rooks in stead. Or perhaps R on one wing, and N on the other, if the H value lies around 400cP.
I am not sure how to test Ferz and Wazir, as they are expected to be even weaker than the Camel. Perhaps the most favorable position would be F or W on c1/f1, and B on b1/g1, and give the opponent Pawn odds.
I am actually more curious to the value of a Cannon, which seems a quite intersting piece. But such hopping pieces would require some more programming, so I am not sure when I will get to do that.