Comments/Ratings for a Single Item

The numbers written here are not considered promotion.

A Pawn will almost always be promoted to a Queen, so the value of the Queen to which it is promoted will increase by more than this number. The value of the Pawn will increase also.

Why would the value of a piece increase because some other piece can promote to it? That makes no sense at all.

I do not the reason until now. I will think about this problem.

Well, the value one should attach to a piece should reflect how useful you expect the piece to be in the future, if you manage to keep it rather than have it captured. So it should be irrelevant how you obtained the piece, as this is already in the past.

Maybe you mean how promotion ability affects piece values before they are promoted!

BTW I think that piece may be upgraded in value if it’s extended by another one which deletes all flaws of first piece. If that’s right, Bishop+Knight pair costs 6 (it can reach all the board as knight leaps and half of board by diagonal motion), Archbishop costs 7 (it can reach the whole board by any of its parts, but his color-switching “ingredient” isn’t distance ranger), and opposite-colored Bishops’ pair costs 8 (it can reach all the board diagonally, its cost increases on free or very non-crowded board, and 2 bishops near in row are like 2-squares big piece which can’t be reached by enemy king and is better than Rook and Archbishop).

Also cost increases on larger or smaller board sizes – example is Knight (which is OP on boards about 6x6 and smaller), or Magician from my Horizons (which is better on boards about 10x10 and larger; as well as Giraffe, Antilope or my Policeman from Stone Garden (thx to editors!)).

Sorry for my graphomania;). (Costs are measured in pawns where Queen costs 9)

So please watch at least one of my submissions (exc. for Random Piece Fight), I will be glad!

But it is all wrong. With Q=9 the true values (on 8x8) are B=3, B-pair = 6.5, Archbishop=8.25.

I am now thinking about the difference about meaning of VALUE, COST and PRICE so on.

The figures of value may correspond to the figures of cost that considered about CORRECTION.

'Value' is an intrinsic property of a piece in a given context, reflecting how much its presence contributes to winning the game. 'Cost' is a synonym for 'price', and these are arbitrary quantities that could be specified in rules that allow you to buy pieces from a budget to select your army. They imply the possibility to trade the pieces against some 'currency' that exists outside the board.

It has a possibility that COST is more intrinsic property than VALUE.

My material costs' calculation corresponds to correctness of mathematical quantities.

My calculation can adapt to various pieces.

I have already confirmed that the calculation is corresponding the quantities of pieces' cost on square board and on hexagonal board.

That would be improper use of English, where 'cost' refers to what you have to sacrifice in order to acquire something.

With Q=9 the true values (on 8x8) are B=3, B-pair = 6.5, Archbishop=8.25.

If Bishop is just 3, why the Queen is 9 if it's 8?! why Archbishop is 8.25 if it's 6 (according to B=3)?

I consider that there are chessmen with more permanent value (such as Rook or Silver) and with more floating value. (Each piece's value floats depening on board's situation, but some of their values don't exit certain natural number's area).

But a lot of them are worth two numbers and are closer to one in one position, and to other in another situation. There are some factors which are affecting: board's size, number of pieces on the board, abilities which piece has, and amount of squares which are available.

Number of pieces on the board can be sufficient (remember of Janggi Cannon & other hoppers).

Bishop is maneuverable ranger but it has one huge flaw - colorboundness, by this lone B=3. All things which dissolve it will increase bishop's value (slightly, but yes, methods are said in a comment above). In this system, value of Queen is considered as 9 because it's compound of Rook (5) with Bishop without its flaw, additionally giving the non-royal King's motion to Queen. It's synergy. (Archbishop is also strong but it's reachable by King and can't hold a straght line; Chancellor can hold a line, I consider that C≈8, but it's closer to 9 than Centaur, so less size of the board increases its price, all BN, RN and KN compounds).

About Knight. That morning I've come to my favourite pychess.org and played 3 games of Burmese Chess (Sittuyin), so I've understood that in first part of game (with crowded board) it's good to trade your Silver for opponent's Knight, because last has more mobility and forking ability. But in an endgame (on very non-crowded board), it's better to have Silver against Knight (with another weak pieces of course), because Knight + Ferz has less checkmating ability than Silver + Ferz; so Kinght's forking ability isn't useful if rooks are already traded. (So in variation of Thai Chess, called Makpong, where King can't move out of check but can capture checking piece, situation is more clear with advantage of Knight).

Anyway and anyhow, (in wide sense) chess is fun))))))))

A Queen is 9 because piece values are relative quantities, and you need to define a scale by assigning some, otherwise arbitrary value to one reference piece. Often one chooses Q=9 for that. (One could also define Pawn=1, but Pawns are very cooperative pieces, and their value changes very much depending on neighboring friendly and enemy Pawns, so they are not really suitable as standard.)

With that calibration B=N=3 (on 8x8), because a material imbalance where one player has a Bishop and the other a Knight on average give both players equal chance, just like an imbalance of 2N+B vs Q, as has been established by centuries of play.

The Archbishop has value 8.25 because with an imbalance of A+P vs Q it wins more often than not, but with pure A vs Q the Q has about a 3 times larger advantage (in the win vs loss statistics).

Yeah, Queen is about 9, but even little more (especially in endgame), so:

If you became to put practical arguments, N+N+B≈Q, but B+B+N (if B-s are on different colors of cells) isn't, such as Bishops' pair is more than Knights' (but it's not 8 because board isn't fully free, and they can't be safe by standing near each other due to Queen's existence there). Yeah, B=N, but B=N≈3.5 (average price).

So about Archbishop, it's possible to have its value slightly more than 7 as average value.

I want explain other pieces of my calculation.

Wazir=4
Ferz=2
Dabbaba=2
Alfil=2
Threeleaper=4
Camel=4
Zebra=8
Tripper=2
Pawn(Shogi)=1
Gold General=5
Silver General=3
King+Bishop=10
King+Rook=12
Cannon=5


Queen(Q)=16(⇒18)
Pawn(P)=1(⇒2)
Bishop(B)=6
Knight(N)=6
Rook(R)=10

B-pair is half a pawn better than B+N or N+N, so 6.5. I don't see how you would get B=N=3.5; that would make B+N+N=10.5, far stronger than Q (which was set 9 by definition), while in practice they offer equal chances. Archbishop=8.25 on this scale, as I already mentioned (Q - 0.75 Pawn).

The Kaufman scale uses Q=9.5, but it also has B=N=3.25, and B+B=7. Archbishop would be 8.75 then.

Fwiw, Dutch world chess champ Euwe set Q=R+B+P=10 with R=5.5 and B=3.5. Chess players have argued whether N is microscopically less than a single B (usually saying yes). In any case, if N=3.5, 2N+B=10.5 (more than a Q - Euwe argued in an old middlegame book with Kramer that 3 pieces are usually slightly better than a Q).

I had a chess master friend that once told me that when Q is vs. 'other material', it was usually critical whether the 'other material' side had 'stickiness', that is that its pieces stuck together and defended each other effectively.

I am now thinking about differences of cost, price and value.
I can compare these terms to economics language.

Cost is a cost.
Price is a list price.
Value is the proceeds.

So this formula is made up.

[Price]=[Cost]×(1+[Profit Ratio])
[Value]=[Price]×(1-[Discount Ratio])

Value≈Price≥Cost
0≤Profit Ratio≤1
0≤Discount Ratio≤1

These two ratio are a correction changing in various situation.

Profit Ratio

Pawn=100%
Archbishop=37.5%~45.8%
Queen=12.5%~18.75%
Bishop-pairs=8.3%

Fwiw, Dutch world chess champ Euwe set Q=R+B+P=10 with R=5.5 and B=3.5.

Indeed, so he used a different scale. Translated to the Q=9 scale this would amount to R=5.05 and B=3.15. Since he did not seem to make a distinction between first and second Bishop, the number he quotes apparently refers to the average of those, which would be 3.25 when we set B=3 and B-pair-bonus=0.5 in the more advanced system. The main difference thus is the value ascribed to the Pawn. Which is a bit meaningless if it doesn't state what is considered the 'reference Pawn', as a 7th-rank passer is easily worth 5 times as much as an unmoved Rook Pawn (say 2.5 vs 0.5).

One should realize, however, that Euwe's values just reflect his personal feelings. And although these must be reasonably good for a world champion, they were not really based on objective criterea like statistical analysis of thousands of games. So they are unlikely to be more accurate than, say, a quarter Pawn.

Chess players have argued whether N is microscopically less than a single B (usually saying yes).

Kaufman found that this depends on the number Pawns that are still present; there was exact equality with 5 Pawns per player; with fewer the Bishop is better, with more the Knight. Of course there is the common lore that it also depends on having Pawns on both wings (which favors the Bishop) vs on a single wing. And there is the 'good Bishop' vs 'bad Bishop' thing as well.

I had a chess master friend that once told me that when Q is vs. 'other material', it was usually critical whether the 'other material' side had 'stickiness', that is that its pieces stuck together and defended each other effectively.

This is very true. A Queen on a sparsely populated board becomes very dangerous, because it can switch the direction of distant attacks quite easily (unlike Chancellor, Archbishop, Griffon, ...) So unprotected pieces get easily forked, and subsequently lost. OTOH, if all pieces can protect each other the Queen can be completely powerless, even unable to defend its own Pawns against and the numerical majority of the lighter pieces.

So we should keep in mind that piece values just reflect the average performance of a piece, and that the actual performance for some imbalances might have a far greater variation than for other imbalances.

So we should keep in mind that piece values just reflect the average performance of a piece, and that the actual performance for some imbalances might have a far greater variation than for other imbalances.

So if it's that, why do you use = symbol when I and Hirosi Kano use ≈ ?!

B+N+N≈Q and B+N+N=Q isn't same.

Why I count A≈7 (if accurately, 7.44) Archbishop has a less color-switching ability than Centaur or Chancellor.

One should realize, however, that Euwe's values just reflect his personal feelings.

It's right)))) so I also don't use (rude for me) computer analysis.

So if it's that, why do you use = symbol when I and Hirosi Kano use ≈ ?!

Well, foremost because the latter symbol is not on my keyboard. :-) But empirical piece values are like measurements in physics; they are never precise, there is always a margin of error. So equality in the mathematical sense never exists, the meaning of '=' here always is "equal to within the precision of the measurement". There also exists the problem that the entire concept of piece values that can be added to get the strength of the army is only an approximation. Q loses to R+B more often than not in Capablanca Chess when all Chancellors and Archbishops are still on the board, while without the latter two, Q usually beats R+B (as in orthodox Chess). So presence of other material affects the value, even when nothing else is known from the position than the material that is present. (Which of course was already known from the Bishop as well, that it gets much better if the complementary Bishop is present.)

But this has nothing to do with the variation being large or small; in statistics average and variation are independent quantitities, an a set of wildly varying values can still have a very precise average. It just means you have to realize that a piece value is an average, with all limitations that follow from that. As the proverb goes: "A statician waded trough a river that was on average 1m deep. He drowned!".

This is why chess players employ the 'rule of thumb' that a simple advantage is better than an equal complex advantage. With Q vs R+B (part of a pair) you can have exactly the same advantage (piece-value-wise) as with R+B+P vs R+B. But the latter imbalance (a plain P ahead) gives a much more predictable outcome than Q vs R+B, which the Q player might very well lose. As far as the average is concerned 50% win + 50% draw is the same result as 75% win + 25% loss.

Why I count A≈7 (if accurately, 7.44) Archbishop has a less color-switching ability than Centaur or Chancellor.

Well, it is also possible to 'count' Q=1 and P=3. But if you use that as a guide for which pieces to trade for which other, you won't win many games. Likewise with 'counting' A=7.44. You will voluntarily trade into badly lost positions, just because you though that A was worth less than Rook + Knight, while in practice the Rook and Knight you are left with then lose most of the time. What you can imagine and what would really work are entirely different things.

BTW can you check Faceoff or Kinzoku (Neodobutsu)? Please. I have so much ideas (about 20!) and only few are realized.

About Archbishop I meant only pure endgame (K+A vs K), because Bishop is maneuverable.

Well, K+A vs K is a generally won end-game, and piece values have no meaning there. A win is a win, whether you achieve it with Archbishop, Rook, or Queen. That doesn't mean A=R=Q in a context with many pieces. Any piece can be the difference between a win and a draw in a late end-game. E.g. King +  Ferz + Bishop on opposit shade is a win vs bare King, and losing the Ferz is just as bad as losing the Queen in K+Q vs K, as both lead to a draw.