EXPANDED CHESS FOR THE NEW MILLENNIUM
Value of Expanded Chess Pieces
Table 1A and Table 1B present the results of the weighting/rating system
evaluation for Expanded Chess. The tables provide the values for each piece
in Expanded Chess for 9 different square game board sizes from 8x8 to
16x16. The results are normalized only once with the lowest value piece (the
Pawn) taking a value of 1.00. There is no attempt to directly compare the
strength of any particular piece at one board size with the same piece at
another board size. In simple terms, the value of an Empress on an 8x8 board
is 12.31 and is 22.97 on a 16x16 board. However, it does not mean that the
22.97/12.31 = approx. 1.9 times as powerful on a 16x16 board as on an 8x8
board. It simply means that am Empress is 12.31 times the value of a Pawn on
an 8x8 board and 22.97 times the value of a Pawn on a 16x16 board. Some
final comments on Tables 5-3A and 5-3B. Note the values of the traditional
players i.e. the Queen, King, Castle, Bishop and Pawn. Since the
methodology was mathematical, note that it was not possible to get a perfect
balance where all the pieces matched the traditionally assigned values. The
values were determined as follows:
The floated value of the King is 3.15 on an 8x8 board.
If one were to quibble at the most theoretical level, it can be argued that the
only way for the Bishop and the Castle to be identical in value to the Queen
is to have them both occupy exactly the same square at the same time. Since
this is not possible in a real game, the value in the chart actually represents
an idealized maximum limit, assuming the Bishop and the Castle are
occupying the same single square.
When relating the rating of a piece to its row & column index (6 6 to 1 1),
pieces with the lower “X” indices generally have lower values the pieces in
the upper “X” indices. Values also increase as the “Y” index increases within
a sub-classification i.e. either the first three pieces or the second three pieces
within in a row. However, the first piece in the second sub-classification
might or might not be of greater value than the last piece in the first sub-
classification. This is because each sub-classification represents a different
set of expanded moves. For example, the Castle exceeds the value of the
Cathedral for most board sizes.
One final observation is that as the game board gets larger, the spread in
value between the Pawn and the Empress increases. This is to be expected
since the range and coverage keeps increasing with increasing board size for
pieces with unlimited coverage and range such as the Empress. The Pawn is
a piece with fixed range and coverage and as the board size increases, its
relative influence decreases. Therefore, the net result is a relative increase
in the value of the Empress as the size of the board increases and this also
occurs for any other pieces with unlimited moves.
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|EXPANDED CHESS is a new series of Chess games with larger game boards, more pieces and new pieces.
EXPANDED CHESS provides an alternative type of Chess, where computers have not yet overwhelmed humans
and the book for the game is not yet written.