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Thanks, Kevin.

I think the initial knightwa value was too hi (4 pawns). So using a smaller value could help the observed practical problems. I'm not sure how to implement your suggestions in the computer program but I think some of them are considered in an indirect way.

Thinking now (once again in a non-empirical way) about adding a non-capturing wazir component to a given piece in order to make a compound piece of the two, it might heavily depend on what piece is being added to in this way, in my humble opinion. If a non-capturing wazir component is added to a bishop to make a new compound piece (call it a 'bishopwa'), then the bishop loses its handicap of being colour-bound, which I'd guess is worth more than adding a pawn to the bishop's value (I don't know if this is close to a refutation of Dr. Muller's rule of thumb, but it might be a notable exception to it).

The observed problem in practice with the knightwa being hounded by enemy bishops or knights might be reduced in an endgame, where the knightwa might show any special advantages it has more often... but how to get past the opening and middlegame successfully for the knightwa side? That I haven't fully figured out a plausible strategy for. If I did, I'd feel more comfortable with the relatively high value I'm getting for a knightwa, using my primitive methods, which I'm having some doubts about right now (such as, if a Q=B+R+P in value, what is wrong with having knightwa=N+non-capturing wazir+P in value, rather than just knightwa=N+non-capturing wazir in value? Or at least an answer that's something in between these estimates?).

What I can suggest so far as an opening/middlegame strategy for the knightwa side in a chosen setup is to trade his bishops for some of the other side's minor pieces, perhaps at the earliest opportunity that arises, if any. After that, he might generously(?) (if necessary) give up just one of his knightwas for a remaining enemy minor piece, following which there'll be even less ways to harass his surviving knightwa, and he can hope it turns out to be a surprisingly valuable piece as the game further unfolds. Also, it seems a good idea not to allow the side with the extra pawn in the chosen setup to, at little cost, get to a pawn structure where he can eventually force the undoubling of his extra pawn, again at little cost.

No worry, Kevin!

Pardon me Aurelian, my mistake. I somehow thought that you were using a full wazir component in your compound piece (knightwa), i.e. with it having capturing ability when moving like a wazir.

@ Kevin

Why a knightwa should worth 6 pawns as the wazir is a just move power? and it practice is rarely used. As a just move power it never menaces anything directly. According to H.G. Muller's rule of thumb the "wa" power should worth 0.33 of the full wazir which is 1.5*0.33=0.5, so that means a mere 3.5 pawns for the knightwa. It seems in practice it worth even less as the knightwa often gets chased by enemy knights and bishops.

@Greg

There were 100 games played at 30 seconds/move as described earlier. In some games I hand started the first 5-9 ply. But anyway the game doesn't seem to repeat infinitely even without opening book or hand starting of the games, although the first 5-6 ply are the same. I don't know why is that, if you could maybe enlightened me on that one.

@HG Muller

HG, Could you repeat tests with Fairy Max? I have my hands full at the time, otherwise I'll do it myself later.

I've edited my previous comment in this thread somewhat substantially.

Greg Strong wrote:  "I find it hard to believe that the knight enhancement is worth less than half a pawn..."

My own primative way of estimating the value of Aurelian's enhanced knight (i.e. a 'knightwa') would be to add the value of a knight (on an 8x8 board) to the value of a wazir, plus a pawn, to get my estimate for such a compound piece. On an 8x8 board I'd say a knight is worth 3.5 and a wazir is worth about half a king's fighting value (thought to be 4 pawns, by chess theoreticians) minus half a pawn, i.e. I think a wazir worth about (4-1)/2 or 1.5 (since a king's fighting value [or equivalently, a man's value] itself is worth a wazir + a ferz + 1 pawn, in my way of estimating, noting a wazir and a ferz are worth about the same numerically in pawns in spite of the ferz' handicap of being colour-bound, IMHO, since we're dealing with such small values). Thus Aurelian's enhanced knight (i.e. 'knightwa') I'd put tentatively at 3.5 + 1.5 +1 , or 6 pawns. Quite a difference in value assigned to the enhanced knight. Perhaps the true value of the enhanced knight is somewhere in between?

P.S.: My own estimate for a N and Man compound piece (known by at least some as a Centaur, i.e. which has both wazir AND ferz movement capability, besides a N's) on an 8x8 board would be N+Man+P = 3.5 + 4 + 1 = 8.5, which may or may not be fully in line with Dr. Muller's previously expressed (on CVP, I seem to recall) opinion to the effect that a Centaur is quite a strong piece.

P.P.S.: Fwiw, Ralph Betza once gave the value of a N and wazir compound piece (i.e. Aurelian's enhanced knight) as worth about a rook (which I think is 5.5 pawns, on an 8x8 board): http://www.chessvariants.com/piececlopedia.dir/ideal-and-practical-values.html

I find it hard to believe that the knight enhancement is worth less than half a pawn.  How many games were played and how did you prevent it from playing the same game over and over?

I've finished the same experiment with reversed colours:

white enhanced knight wins    40    
black extra pawn wins            54
draws                                     6

That means a 57% victory for black. So the color difference is not that important. 

I have made experiments using chessV to play Enep (the online available variant I think is still bugged). The extra pawn side has played white, the enhanced knight side has played black in the usual setup. Time control was 30secs/move. The results are:

white extra pawn wins           50
black enhanced knight wins   35
draws                                   15

That means a 59% ratio win for white. According to HG Muller's rule of thumb the knight enhancement should worth 0.5 pawns. According to HG Muller with Fairy Max pawn odds give 68%. In the enep experiment, assuming linearity and same level of play for fairymax and ChessV, we get half a pawn for the 2 enhanced knights, 0.25 pawns per knight. When seeing that my first instinct was to cast aside HG's rule of thumb. Second thinking though I posed the extra half point not on the weak knightwa but on better center control for the extra pawn side. Could that worth half a pawn?

Any thoughts on this HG?

What about you Greg?

Now I'm in the process of making the same experiment with colors reversed.

I don't believe the relative importance of captures andnon-captures for the piece value has much to do with the ratio empty squares - occupied squares. Both have a factor 2, but in opposite directions: there are only half as much capture targets, yet the captures are twice as important. Furthermore, tests of end-game values, on a much emptier board, usually give very similar conclusions as for opening values, for 'normal' pieces. (Pieces where the moves depend on 'spectator pieces', such as Pao / Vao,or lame leapers are exceptions.) I guess that even when there is ot much to capture, capture moves represent much of the value of the piece, as they can be used to cast a mate net around the enemy King.

The value of a piece in Chess is much dominated by its end-game value anyway, as sooner or later the board will get empty. This would be very different in games with drops, such as Shogi or Crazyhouse. There the pieces tend to relocate by drops much more than by board moves, so that differences in (non-capture) mobility are much less important.

Most of my piecevalue determinations were done on 8x8 or 10x8 boards, and even from that it seemed the size of the board can have a significant effect on the value of sliders versus leapers. E.g.on 8x8 a lone Bishop or Knight are approximately equal, but on 10x8 the Bishop was half a Pawn stronger. (Wide boards favor diagonal sliders, as the chance that both their forward moves hit the enemy gets larger.In Cylinder Chess the difference etween Bishop and Rook is even smaller than on 10x8.) The latest version of Fairy-Max can handle boards up to 14x12, but I have not used that in systematic piece-value testing yet.

H.G. and Greg,

This Enep page has been out for a while, have you noticed my last comments? How would you conclude a view on Enep?

Thanks!

HG,

I see it is you who has written fairy-max, now I feel silly for not documenting myself enough! I'll try to get it, but I don't know how I can top your research. I care about larger board variants, but I think if the ratio of enemy pieces vs empty squares is the same then your research into different moves and captures holds!

Greg,

Could you guide me through the process of adding Enep to the old ChessV, with your help I think I can recompile myself!

  Based on 3.8 knightwa (or any other knight enhancement) value that should be a balanced game.  Is an very akward game, though.  I admit the original to be a failure at least from the point of view of balance but Enep has it's flavour from the point of view of having advantages from two different worlds- the world of pawns, and the world of short range leapers. I guess I have to work on the concept as is quite promising.

HG,

I was thinking that the 1/2 ratio of power of movement vs power of capture is equal to the 1/2 ratio of enemy pieces vs empty squares. Is that a coincidence? If not the power of movement should increase in importance and I don't think that is true.

I think captures are the important thing in the game as captures could change the material balance. So, I was thinking rather than captures and movement to think in terms of captures and future captures (i.e. captures in 2 moves, captures in 3 moves, etc.). As the board empties capturing in two moves increases via the increased power of movement and decreases via decreased number of targets so it seems to be a better model, giving the fact that for example in my Enep knightwas are fairly constant through the game. This line of thinking is reasonable I think for pieces like pao and vao in Eurasian chess. There is a catch with those specific pieces as the power of capture is related to the number of pieces, too.

I usually measure piece values by playing games where I pit the 'piece under test' against several combinations of material of known value, expected to be nearly equal, in an otherways complete opening position. I then have the same engine (with the same idea of the piece values) play both sides. The remaining difference can then be derived from the result of a match of a few hundred games, by comparing it to the effect of deleting a Pawn. This takes ordersof magnitude fewer games than when you play computers with different ideas about the piece values against each other from symmetric positions.

By subjecting large numbers of short-range leapers to such tests, I found that the values of pieces that are not obviously defective (e.g. because they an access oly a small part of the board, or cannot return to squares they once left) primarily depends on the number of moves N they have in the center of an empty board, according to the formula 1.1*(5/8*N + 30)*N centi-Pawn. So there indeed is a non-linearity there, but it is comparatively small.

Then I tested the effect of taking away one or a symmetric pair of moves from the 'ultimate' short-range leaper with 24 moves, which can go to all squares in the surrounding 5x5 area. I had that piece play against a handicapped version of itself, which could make certain jumps only as captures or non-captures, or not at all. According to the formula taking away a single move (N=23 instead of 24) would already lower the value by ~2/3 of a Pawn, so such differences are easy to measure. It turned out that changing a move or pair ofmoves to non-capture only depressed the value twice as much  as changing it to capture only. Also, taking away a forward move hurt twice as much as taking away a backward or sideway move. Apart from that it did not matter very much which move you took away.

@Greg

I was not familiar with sjaakII and fairy max, I'll check on those, too. Thanks for this, too, Greg!

When Steve Evans was working on how to make Zillions-of-Games play Shogi better, his area of focus was on changing the piece values. Instead of releasing his own Shogi ZRF, though, he let me combine our efforts together. So, the Shogi ZRF I put out has various tweakings of the piece values to get it to play better. The point being that knowledge of piece values is important for deciding which moves to make. If a Chess program, for example, evaluated a Queen as worth one point and a Pawn as worth nine, it would usually lose against humans.

@Greg,

The fact that altering internal values of pieces changes the outcome of the game is very funny, have we accidently discovered computer self-confidence? :)

@Greg

Thank you very much for all your help, it is highly apreciated!

I added an extra pawn on purpose, mostly to do something different but also as you say it provides a smaller increment in power, if not for any other reason just because 1/9<1/8.

@HG

I was aware of your rule of thumb, from somewhere on the internet, I don't remember where. I was out to check it and maybe improve it. But actually what I was most interested in, is there a way to derive these coeficients? I see no reason for them to be linear, although linear (the relationship between capturing strength and movement strength) is always the simplest case, and I don't know all your work, but to me it seems fine in 8x8 settings. Not sure about the enhanced knight in enhanced Omega chess, but I think it is a good aproximation there,too.

All in all I'm very interested for the desing purpose of my own large board variants of an way to derive the "rules of thumb". If you have any ideeas on that I'll be highly apreciative!

Ok, with colors reversed, the side with the augmented knights still won at all three time controls.

So I changed the evaluation for the augmented knight to 3.75 and reran.  Still won at 5 and 10 minutes.  At 20 minutes it was a draw by repetition.  So I kicked it off again with an hour a side before leaving for work.  That ended in a draw by repetition too.  This does not necessarily say which evaluation is better (although H.G. is probably right - he's done a lot more work on piece evaluations that I have with his program, FairyMax.)  We're likely to get more draws when we tell the engine that the position is balanced by tweaking values.  To really establish, you'd need to run tests between different engines that are same except that each has a different idea what the augmented knight is worth, and see which performs better.

Regarding balance, also consider the possibility that the extra pawn you added may be worth less than a pawn.  It can't make a double move, and it prevents the pawn behind it from making a double move.  You'd have to move the new pawn twice before the existing d-pawn can make a double move.  And blocking the d-pawn hinders the development of the queen's bishop.

Regarding open vs. closed play - yes, this, or any other evaluation criteria or paramaters can certainly alter results with unpredictable results.  As such, my tests aren't really proof of anything, but are still a useful indicator.  Confidence increases as you run more and more tests with different engines, different openings, different tuning ...

Regarding adding Enep to old ChessV, this should not be very difficult but does require recompiling the source code.  There may be value in doing this as, at present at least, the old version contains a stronger engine then the new version (a complete re-write in C# designed more for universality than playing strength.)  You could also look at adding this to SjaakII and/or FairyMax.  They are programmed with text files, so if they can support Enep there's no recompiling involved.  I think both programs are capable.  Then you can run tests with WinBoard.

Rule of thumb is that captures are about twice as valuable as non-captures. Pieces with 12 non-divergent target squares (i.e both capture andnon-capture) are approximately worth a Rook. Soone would expect that adding 4 non-captures to a Knight increases the value by about 1/3 of the Knight-Rook difference. That brings you indeed very close to 3.8 (N=3.2, R= 5).