Comments/Ratings for a Single Item

OK, so a Pawn seems worth 9.1% excess score in Apothecary1, and 11.3% in Apothecary2. That is less than I see in normal or Capablanca Chess (where it is some 15%), but that makes sense in these larger games, where much more can happen before you are down to an end-game where the material advantage becomes decisive.Note that the statistical error in the score percentage will be something like 45%/sqrt(1000) ~ 1.5%, so that the difference between Apothecary1 and Apothecary2 Pawn-odds score is not really significant. In fact it is quite likely that these are the same, as both games start with approcximately the same amount of material, so close to 10%.

That means the preliminary result I got for Griffins vs Aancas, which was ~65% (15%excess score) in about 200 games corresponds to1.5 Pawn. That would make the G-A difference about 0.75 Pawn. Because the 2G-2A difference is larger than a Pawn, it might be a good idea to handicap the side with the two Griffins by a Pawn. Then the Griffins should still win, but only by about 55%.

We should keep open the possibility that Pawns are pretty 'light' in a game with so much material, i.e. that a minor is worth much more than 3 Pawns, perhaps even 6. (Even most orthodox Chess programs set the Pawn base value close to a quarter of a minor, and the rule minor = 3 Pawns really only holds for a good passer in the end-game.) What helped me very much in Capablanca Chess is to run N + P  vs R (deletion) and 2N vs R+P. These two results allow you to place the R value in the range {N+P, 2N-P} while comparing the difference of these two results with the Pawn-odds score tells you how many P the 2N-P and N+P are apart. Together that defines both the N and the R value in terms of P, without ever having to delete more than a single Pawn, and without ever getting scores larger than the Pawn-odds score. In Capablanca Chess, at least. Perhaps on this deep board 2N-R would already be near equal. (Although I really doubt that extra ranks behind the majority of the pieces in the start position would matter so much.)

I think it is normal for the pawn in apothecary 2 to worth a tiny bit more than in apothecary 1 as the minor pieces there are weaker.

Also there will be a Queens vs Griffins experiment, coming up next after griffins vs aancas.

About R-P vs N and R+P vs 2N, keep in mind that knights aren't the same nor the same with the classic knights so they have to be measured first. Moreover I'd rather put an aanca/archbishop -pawn(s) at the upper bound of a rook. It makes more sense to me as it involves the natural progression of pieces.

Thank you, H.G.

H.G.,

If you don't mind me asking. From where the 45% comes, I don't get it!

You mean in the expression for the statistical error? In the absence of draws it would have been 50%, because in a single game you would always be 0.5 point away from the average, which is 50% of the total score. With draws this gets a bit lower, because you can also be exactly on the average. But for equal wins / losses / drawsit is still about 40%. Here you have less draws than wins or losses, so I just guessed a value somewhere in between, without calculating. It doesn't really matter much whether it would be 43% or 47%...

Ok, I understand, thanks!

H.G.,

Preliminary results in apothecary 1 show after 130-ish games 65% points for griffins in their fight against aancas, nothing strange here.

But, in apothecary 2 I have in also 130-ish games only 52% for marshalls against archbishops. Could this be correct. I don't see it! What do you think? I can't find a gross error yet, but it certaintly seems so!

It doesn't strike me as strange. In Capablanca Chess I use Q=950, RN=900, BN=875. So that is only 25 centi-Pawn difference between RN and BN. With two of each that would cause an advantage of 0.5 Pawn, and you just determined that a Pawn corresponds to10%. So you would expect 55%. But the error in 130 games is 45%/sqrt(130) = 4%. So 52% is well within one standard deviation from the expected result. The Archbishops might have been a bit lucky.

Bad news,

I haven't used the proper piece values, in all four experiments. So I restarted them.

The worse was a peculiar  small rook just a few centipawns above the minors. That's noise inducing. I actually seen a rook-champion exchange sack I found particulary weird.

So I'm redoing everything for the sake of consistence. I'm still new and learning, so guys please excuse my blunder!

Well, for a totally new variant with many new pieces it is usually necessary to do more than one iteration anyway, because your initial guessed piece values were off too much. I still expect the extra ranks behind the pieces to have little effect on piece values, so that the Capablanca-Chess values would seem a reasonable first guess. These are Q=950, C=900, A=875, R=500, B=370 (350, really, but 40 extra for a Bishop pair, but Fairy-Max is too crude to make a difference between first and second Bishop, so I just take the average), N=300, P=80.

As you pointed out the Apothecary Knight has extra moves, however, and an educated guess would be 360 for a Knight with 4 extra non-captures, and 430 for one with 8 extra non-captures. Enhanced Camels and Zebras would be similar, but I really have no idea whether they would be worse or better than the enhanced Knight. Normally long strides are worth less, because the go off-board more easily, and make for very awkward manoeuvring. But it is mostly non-captures you need for manoeuvring, and distant captures might actually be more effective than close ones.

Champion and Wizard I would guess as 480 and 640 just based on the number of squares they attack. Although I have no idea how color binding affects the Wizard.

Note that the programmed values are not extremely critical. If two pieces are close, it often does not matter for the result which one you value higher. So rather than doing everything again (perhaps with the values of other pieces still wrong), I would first try some other tests to make sure all pieces have been given reasonable values. E.g. test if a Wizard is bettwre or weaker than a Bishop pair,and whether a Champion is weaker or stronger than a Rook. And how two Apothecary Knights fair against a Bishop pair.

So you were saying H.G. that is better to do more iterations with 100 games for example and then get to the fine tunning part!

And you also said 2 weeks ago something about taking the pawn to an absolute value of 60 or somewhere near.

And you forgot to mention the modern elephant.

Ok, Here in Romania is late at night, but tommorow is a reduced materials endgames day test, like knights vs bishops and so on!

The Elephant is also a piece with 8 normal targets and 4 non-capture targets,so it would also be around 360. If you play a pair of (Knight / Elephant / Zebra / Camel) against a pair of others to determine which is stronger, it is better not to set them exactly equal, but arbitrarily make one 10 points better than the other. This ensures that at one of the players will always think it better to avoid trading them. If they are exactly equal, the initial imbalance gets traded away very easily, and it becomes difficult to see any effect of it.

It should not matter toomuch if you set P to 80 or 60. The idea to use 60 was in the contect of scaling down other piece values too, to keep the total amount of initial material similar to that of Capablanca Chess (to not discourage Pawn pushing too much.),sodeduct, say, 10-15% from all piece values, like R=450, Q=855...

Note that when I was proposing to test Knights against Bishops I did not mean end-games, but start positions with Knights deleted for one side and Bishops for the other. And indeed doing 100-200 games isprobably good enough to get an impression how to set your piece values for the more precise tests.

H.G.,

I've decided for keeping values computed earlier as good enough for first iteration.

Also, you've said nothing on minors vs few (3-4) pawns. That should also provide info on the values of minor pieces.

Apothecary 1 piece values used in first interation:

pawn:60

knight:190

bishop:200

wizard:181

champion:191

rook:345

aanca:476

griffin:524

queen:571

Apothecary 2 piece values used in the first iteration:

pawn:60

knight:162

bishop:200

elephant:175

camel:153

rook:345

zebra:143

archbishop:476

marshall:524

queen:571

Also I decided to rename the to title variants: Small Apothecary 1 and Small Apothecary 2. The reason for that is that I already sketched 3 12x12 variants, and bigger is to come. The main trouble with those is that I doubt I can find a program that can play them, so I'll have to build my own. In the particular cases of the 12x12 Apothecary variants the problem with regard to Fairy-max is that both armies use promotable berolina and regular pawns and moreover the problem with sjaak 2 is that it uses aancas and griffins. Also the weird promotion rule stands.

Ah yes, I miscounted the Wizard. It has 12, not 16 moves. The values seem reasonable for a first iteration. Next thing would be to get the order right of Knight / Elephant / Camel / Zebra, which are all pieces with 8 mc moves and 4 extra m. Or Champion / Wizard an Knight / Bishop in the other.

Perhaps it would be best to use 'synthetic start posititons' for that, with only about half the number of pieces, to magnify the effect and speed up the games. I.e. set op a position where each side has 10 Pawns, a King and two of the 'piece under test', and then give each side two other minors, 2 Rooks+Bishops and one super-piece in various (symmetric) combinations. Initially you would only be interested to know which pair of pieces did better.

I have finished the first iteration for griffins vs aancas for the new set of experiments, results are below. No surprises threre. Now queens vs griffins has started under similar conditions.

Griffins wins:114

Aancas wins:61

Draws:25

Griffins Points:126.5

Aancas Points:73.5

Apothecary 2 Marshalls VS ArchBishops have ended. Now Queens vs Marshalls have started.

Marshalls wins:103

Draws:20

Archbishops wins:77

Marshall points:113

Archbishops points: 87

Sounds reasonable. 56.5% in favor of the Marshalls is about half a Pawn, so a quarter each between them. That is consistent with what I found on 10x8 boards. Griffin - Aanca is about double that, also close to what I found (but on 8x8).

H.G.,

I'm watching some queens vs griffins matches and I remembered what you've said about most of the power of the pieces coming from empty board mobility (Griffin mobility=27/25 Queen mobility). I think we are for an exception here as the griffin has a slightly higher empty board mobility than the queen but in the early game gets hindered much more easily by having only four squares nearby. The queen also has 3 forward direction as opposed to two, for what that worths. From what I'm seeing the queen is roughly half a pawn above the griffin in apothecary 1 (as is above the marshall in apothecary 2, nice to know for different armies maybe). Larger boards will probably provide even more interesting encounters between the 2.

Weakly related: An even weirder case of fluctuations along a game of ratios of pieces, I think is rook vs nightrider. As the NN is clearly superior in the early game the R is superior due to its traits in the late game.

H.G.,

I'd like to confess something, I wanted to be a bit profane on Fairy-Max, as it plays both apothecary games so open. But after trying to play myself against myself on the diagrams (I'm blundering later now) I've noticed that with so many leapers these games are pretty open themselves. So pushing pawns and closing the game may not work. This is a weakness of both apothecary games I have to think about in the future.

Moreover, I'm now in a position to defend apothecary 2 (or small apothecary 2 as is it's real name- but as of now they are the only apothecary games, simple apothecary works) against your criticism that the game is too long (and maybe stale as a result). Introducing the minor pieces enriches the middlegame a lot and even if more often than not the minor pieces get exchanced in the middle game (camels in the endgame are very rare, zebras even more so) the damage to pawn structure and the more weird endgame pieces combinations make up for the increased lenght. It's all an opinion of course.

The eagerness of Fairy-Max to advance its Pawns is controlled by the scaling of the piece values. Large value of the total board content discourages Pawn pushing, and would keep the position more closed. You should realize that Fairy-Max is an extremely simplistic engine, almost completely devoid of any kind of knowledge. Pawn structures are only evaluated in a very crude way. (I.e. pushing a Pawn is in principle encouraged over other moves, but gets a penaly if there is no Pawn 2 squares left or right from the square thePawn comes from, becauseit would then give up control over the squares diagonally in front of it. That is really all it knows (and it backfires with Berolina Paws), except that 6th and 7th rank Pawns get a 64 and 128 value increase. I am not even sure the latter works in Apothecary, with its 3-deep zone. )

As to the Nightrider: even when pitted against Rook with still a lot of Pawns on the board (4 or 5 on each side) the Nightrider seemed to have the advantage. Nightriders used to be a bit problematic for Fairy-Max, because they can cause mutual perpetual checking, and Fairy-Max would crash on positions where that occurs. (I am not sure if the 5.0 version still has that problem.) But with just a single Nightrider there were no problems.