# Comments/Ratings for a Single Item

Piece (S) (m+M) Double Average Pawn 1. --- ------ Knight 3. 10 10.500 Bishop 3. 20 17.500 Rook 5. 28 28.000 Queen 9. 48 45.500 Guard 4. 11 13.125

The table above includes a 'Guard', moving like a nonroyal King. Joe Joyce is quite fond of it, even I have been known to use this piece. The (S) column gives one popular set of standard piece values. The (m+M) column is based on a simple pencil and paper calculation, adding the minimum number of possible moves for the given piece (from a corner square) to the MAXIMUM of possible moves (from a central square). The Knight, for example, has 2 moves minimum and 8 moves MAXIMUM, giving a total of 10 moves. Other people, with more determination, have precisely calculated a grand total of 336 possible moves from all 64 squares on the board , giving an average value of 5.250 possible moves. Dividing 336 by 32 puts 10.500 in the 'Double Average' column, which is surprisingly close to the previous column. From time to time, I play around with piece values on a cubic playing field with 216 cells, content to use an (m+M) column as my source of raw numbers.

What, if any, sense can we make of these numbers? The last two columns measure piece mobility on an empty board, so they indicate the general strength of each piece in the endgame - which I have found the (S) column well suited to. Note that **N + B = R** in the Double Average column. No great mystery here, the Knight has 60% of the mobility of the Bishop, while the Rook has 160%. Holding the Bishop at 3 points, this column suggests 4.8 points for the Rook, not an unreasonable choice - some writers assign as little as 4.5 points to the Rook. But nobody values the Knight at 1.8 points! To arrive at the 'standard' values, one must make arbitrary changes in the raw numbers, forcing them towards a desired conclusion. 'Knight-moves' need to be counted as more valuable than the moves made by other pieces, perhaps by a 5:3 ratio. The penalty I am inclined to give the Bishop for being colorbound (therefore limited to half the board) needs to be cancelled out by a matching bonus for the fact that every Bishop move either attacks or retreats. The Rook, with its boring sideways moves, usually attacks only a single enemy piece - also it will have only a single line of retreat after capturing that piece. I love Rooks, but am forced to admit that they are superior to Bishops only because they have many move possible moves, on average. The 3D Rook moves up and down along one axis and sideways along two different axes, making it even more 'boring' than the 2D Rook. I am presently re-thinking the entire subject of piece values for 3D chess.

Here is an idea I had one day: recently Joe Joyce and I have been using the **Elephant** piece, which can move like a Ferz or an Alfil. Let the **Grand Rook** move like a Rook or an Elephant and let the **Chancellor** move like a Rook or a Knight. These two pieces, each adding eight shortrange moves to the Rook, should be nearly identical in value on most boards. But I consider a Grand Rook to be worth around half a Pawn less than a Queen on the 8x8 board - contradicting several statements by Ralph Betza (**gnohmon**) that the Chancellor and Queen are equal in value. This procedure is an art, not a science, and is even more difficult when working with different boards and new pieces. See my Rose Chess XII for a collection of interesting pieces, inspired by the writings of Ralph Betza, plus some theory of their values on a 12x12 board.

H.G.Muller has written here '**It is funny that a pair of the F+D, which is the (color-bound) conjugate of the King, is worth nearly a Knight (when paired), while a non-royal King is worth significantly less than a Knight (nearly half a Pawn less). But of course a Ferz is also worth more than a Wazir, zo maybe this is to be expected.**'

Ralph Betza has written here '**Surprisingly enough, a Commoner (a piece that moves like a King but doesn't have to worry about check) is very weak in the opening, reasonably good in the middlegame, and wins outright against a Knight or Bishop in the endgame. (There are no Commoners in FIDE chess, but the value of the Commoner is some guide to the value of the King).**'

*'... Play the High Priestess and Minister on SMIRF or ...'*

SMIRF still is not able to use other non conventional piece types despite of Chancellor (Centaur) or Archbishop (Archangel). You have to use other fine programs. Nevertheless the SMIRF value theory is able to calculate estimated piece exchange values.

Currently I am about to learn the basics of how to write a more mature SMIRF and GUI for the Mac OS X operating system. Thus it will need a serious amount of time and I hope not to lose motivation on this. Still I have some difficulties to understand some details of Cocoa programming using Xcode, because there are only few good books on that topic here in German language. We will see if this project will become ready ever.

exchange... gentlemen, an interesting midpoint. I was going to note

that some of the Muller numbers are quite similar to others' numbers.

For example, the values of the minister and priestess fell between 6

and 7 by both HG and Reinhard's methods. Yet other numbers are quite

far apart, like the commoner values. This, of course, presents 2

problems, one to explain the differences, and the other to explain the

similarities. Derek, could you give us a verbal explanation of what you

did and found?

Reinhard, my apologies for some sloppy phraseology. You've posted your

theory for all to see. You have provided numbers both times we've

spoken on this. In fact, you have been kind enough to correct my

mistakes in using your theory as well as providing the 2 sets of numbers.

[I will have to find some time to upgrade the wiki on this. Excellent.]

Thank you; I could ask for very little more. [Heh, maybe a tutorial on

that 3rd factor; Graeme had to correct my mistakes too.] I wish you the

very best with your new endeavor.

Ji is right, the number of squares attacked may be a first

approximation, but the pattern of movement is a key modifier. I put

together a chart a while ago after discussing the concept of

approachability with David Paulowich. The numbers in the chart are

accurate; the notes following contain observations, ideas, statements

that may be less so. Fortunately, the numbers in themselves are rather

suggestive, one way to look at power and vulnerability. They present a

two-dimensional view of pieces, a sort of looking down from above view

in chart form.

http://chessvariants.wikidot.com/attack-fraction

The chart clearly could be expanded, should anyone be interested. [The

archbishop, chancellor, amazon should be added soon, for example; any

volunteers? :-) ] But can it be used for anything? Colorboundness, and

turns to get across board, both side to side and between opposite

corners, are factors that must have some effect. [Board size and

edge effect are 2 more, this time mutually interactive factors. How

much will they be explored? Working at constant board size sort of

moots that question.] What do your theories, gentlemen who are carrying

on or following this conversation, have to say about these things?

Please note this conversation is spread over 3 topics:

this Piece Values thread,

Aberg's Variant game comments

Grand Shatranj game comments

**The infeasibility of using different armies to calculate piece values**

To Derek Nalls and H.G.M.:

Nearly everyone - so I think - will agree, that inside a CRC piece set the value of an Archbishop is greater than the sum of the values of Knight and Bishop, and even greater than two Knight values. Nevertheless, if you have following different armies playing against each other:

[FEN 'nnnn1knnnn/pppppppppp/10/10/10/10/PPPPPPPPPP/A1A2K1A1A w - - 0 1']

then you will get a big surprise, because those 'weaker' Knights will be going to win.

There are a lot of new and unsolved problems, when trying to calculating piece values inside of different armies, including the playability of a special piece type, e.g. regarding the chances to cover it by any other weaker one.

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