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Queens VS Marshalls has finished again with what I consider a bit of exagerated results.

Queens wins:129

Marshall wins:54

draws:17

Queens points:137.5

Marshall points:62.5

H.G.,

Could the last 2 experiments have fallen into a slightly nonlinear zone?

Pawn (maybe 2 pawns) deletion for the queens side is in the cue now. But for now I've started apothecary 2 minor pieces games. I decided against reducing material so I kept most pieces (except the ones under test).

Now Camels vs Zebras and Elephants vs Knights is on!

So, now we are on minor pieces contests. In apothecary 2 camels vs zebras has started. This is set up by replacing in the initial setup the camel with a zebra for a player and vice-versa for the other. Zebras vs Elephants is next. This will be set up by replacing an elephant with a zebra an deleting the other elephant and for the other player just deleting the zebra. No other pieces are deleted for the sake of consistence. In apothecary 2, where the initial setup has 2 of each minor pieces (say bishops vs elephants) one player gets deleted one set of minors where the other gets deleted the other set of minors. This is also what always happens in apothecary 1.

Results for camels vs zebras and elephants vs knights coming soon.

Elephnats vs Knights:

Elephants wins:97

Draws:30

Knights wins:73

Elephant Points:112

Knights Points:88

My initial guess of 30 centipawns for the difference between an elephant and a knight was surprisingly close!

Camels VS Zebras

Camels wins:96

draws:22

Zebras wins:82

Camel Points:107

Zebras Points:93

Elephants Vs Zebras

Elephants wins :106

draws :39

Zebras wins :55

Elephants points:125.5

Zebras points:74.5

Bishops VS Knights

Bishops wins :102

draws  :27

Knights wins :71

Bishops Points:115.5

Knights Points:84.5

Just to be clear: this Bishops vs Knights was for the version of the Knight that was enhanced by 4 extra non-captures (Betza NmH), and not the Omega-like NmZ? I guess you are seeing the effect of the Bishop pair here; for a plain Knight in Capablanca Chess I found N = 3, B = 3.5 for alone Bishop, but a bonus of 0.5 for having a Bishop pair. (Interestingly enough that bonus disappeared almost exactly when the Bishops were started on the same shade.) So the BB-NN difference there would have been 1.5 Pawn. I am surprised that is stillseems larger than a Pawn here; I would have expected the Knight enhancement to have more effect. But perhaps the Knight suffers from the deeper board after all. (Although this is exactly what I would have thought the enhancement would be able to prevent.)

Yes, it was that knight, the one with the four threeper enhancements. The fact here is that the knights enhancement is almost useless as a knight can go (3,3) in 2 moves anyway (NmG in Betza notation). And also it's too long. The point of this enhancement was not to have the same enhancement like in omega chess but I guess that one was the most interesting enhancement. Bishop pair matters of course. But this is the proper exmperiment I think as it is close to the real game (where you start with bishops on oposite colors). I think the elephant (who won versus the knight) would be closer to the bishop. I doubt any rock-paper scisors effects are in place in those 2 games. The elephant enhacement has a double role, it is long (not long enough to jump over board) and is unbounding.

Thanks for your help, H.G.

Apothecary 2 Bishops VS Elephants has finished;

Bishops wins:93

Elephant wins:75

draws: 32

Bishops points:109

Elephant points:91

Apothecary 2 experiment Knights VS Camels has finished

Knights wins:84

Camels wins :80

Draws:36

Knights Points:102

Camels Points:98

Apothecary 1 experiment bishops vs knights has finished.

Bishops wins:76

Knights wins:101

draws :23

Bishops Points:87.5

Knights Points :112.5

Apothecary 2 Knights VS Zebras has finished;

Knights wins:90

Zebras wins:72

Draws:38

Knights Points:109

Zebras Points:91

A dramatic difference between the mG-enhanced and the mZ-enhanced Knight! The latter seems significantly stronger than a Bishop. (Even when the latter operates as a pair.) Of course the context is different as well, but not that different.

Did the values you programmed into Fairy-Max take account of the Knight being more valuable than the Bishop? If not, the tests could exaggerate the difference. There is a paradoxical effect that between pieces that intrinsically are nearly equal, the one that the engine values the most is worth the least. Because the fear that it would be exchanged for the one the engine values lower will inhibit the use of it. So if a Bishop, which in reality is less powerful than the enhanced Knight, would be given a value higher than it, the Knight can wreck its damage with impunity, scaring away the Bishop, where in reality the Bishop should chase the Knight away. This effect pulls values of nearly equivalent pieces closer together, and is no doubt the reason why the Bishop and Knight are so very close in value in orthodox Chess.

The mZ enhanced knight was indeed considered weaker as I expected the enhancement to be long, too. But it seems perfect giving the circumstances. So in the second iteration the NmZ knight will be considered stronger. Also remember the real promotion rule. I wonder how are things on a 12x12. I assume that the mZ would increase in usefulness but overall the bishop will close the gap. On a 10x10 the knight appears to be better despite nothing being said on the omegachess.com. So this could be an interesting discovery. Not much can be said about NmG though, is very little stronger than a N on a 10x10. In apothecary 2 the elephant FAmH is the most interesting minor although weaker than a bishop. The camel LmW does cool things, too.

Apothecary 1 Champions vs Wizards

Champions wins:105

Wizards wins :76

draws:19

Champions Points:114.5

Wizards Points:85.5

Apothecary 2 Bishops VS Camels has finished

Bishops wins:107

Camels wins:67

draws:26

Bishops Points:120

Camels Points:80

Apothecary 1 Bishops VS Wizards has finished

Bishops wins:82

Wizard wins :102

draws:16

Bishops points:90

Wizards points:110

I'm quite excited about the last two result of my 2 small apothecary games using Fairy-Max. It seems a normal B bishop is roughly half a pawn stronger than a apothecary 2 camel LmW but a quarter pawn weaker than a Wizard LF . So the wizards colourboundness doesn't seem to affect that much. The difference between LF and LmW should be 0.5 pawns according the H.G.Muller's rule of thumb (mPower=1/2 cPower) but it it's hard to tell. Here it seems a bit more, but there are several factors not considered in this approximation. The point is that the wizard's colourboundness is not that relevant. That's why I gave the camel and just move wazir power after all, and it doesn't seem to suffice.

So the Wizard is stronger than a Bishop. This is what I would expect of a 12-targets leaper; these are normally (i.e. on 8x8) of Rook class. It puzzled me that the article on Gross Chess rates it even below an orthodox Knight. It is true that this claim is for 12x12, while you are doing 10x10, but surely the Knight should suffer from that even more. In fact the Wizard might benefit from large boards, because the Camel move reaches its full set of targets on a much larger area there. On 8x8 a Camel has all its moves on the four center squares only! On 10x10 this is on 16 squares (still only 16%), and on 12x12 it rises to 36 squares (25%).

Sliders also get more moves on larger boards,and many naive 'calculations' of piece values award this a lot. But in practice it is worth only a little, because:

• The board is rather crowded for most of the game, so the board edge is invisible to a well-developed slider anyway.
• Captures are worth much more than non-captures, and the number of captures a slider can have is determined by the number of directions it moves in. Moving over a larger distance is only helpful because it enhances the probability that you will indeed hit something in that direction, so you can hope it is an enemy. But with a 25% filled board the chances to move unobstructedly further than 4 squares dwindles pretty quickly. So it doesn'treally matter much if you have moves that can do that.

H.G., Well I meant the difference between the F captures of LF by comparison to the wazir just moves (but  unbounding) of the LmW. It is highly weird that the LF is 0.75 pawns stronger than a LmW,although we are talking different games.

I hope Fergus is reading the gross chess assesment as I believe, too, that the wizard is sensibly stronger than a knight. We'll see how it faces the advanced knight NmZ soon.

Color binding does not really seem to hurt a piece, as long as you play it in pairs on opposite square shades. It will involve a pair bonus, though. (At least in the case of Bishops; I never really measured this for other color-bound pieces.) Which means that a single piece would be worth less than half the pair value. To see the Wizards suffer they should be started on the same shade.

I once tested a BbmW, to break the color binding, and a pair of those was just a tiny bit stronger than a pair of regular Bishops. And the gain seemed mostly from increased manoeuvrability, as giving the bmW move to the Knights instead of Bishops hardly made any difference.

Color binding doesn't hurt a piece if there are enough friendly pieces to compensate for the missing squares I guess.