The basic idea is taken from the game of Different Augmented Knights, whose basic idea was in turn taken from research into the values of chess pieces; and that basic idea is that there are a number of weak pieces which, as standalone pieces, are not equivalent in value but which, when their powers are added to other pieces to form combination pieces, result in augmented pieces of equivalent value.
The basic pieces, to which powers may be added, are the familiar Rook, Knight, Bishop, and Queen, plus the Fibnif and the Chancellor (or the Rook plus Fibnif, which is equivalent).
The Fibnif and the Chancellor are alternates for the Queen and Knight. The King and the Pawns are not changed from their usual powers.
The weak pieces, which augment the basic pieces, are the Alfil, Wazir, Ferz, Dabaaba, Narrow Half-Knight, and Crab.
In order to play the game, each player selects an army, and the game then begins, following the usual rules of FIDE Chess with two special rules added.
The first special rule is that when a Pawn promotes it may promote to any piece that was in the game at the beginning. The second special rule is that when choosing pieces no augmenter should be used twice by the same player; that is, if you have chosen Rook plus Ferz as your Rook, you may not choose Knight plus Ferz as your Knight.
The above are the general rules. Specific discussion of the basic pieces and the augmenters will follow, after some general observations about the game.
Some augmenters cannot be chosen with some basic pieces, for example you cannot choose Rook plus Wazir, because that is the same as making no choice at all. Rook plus Dabaaba is not completely worthless, but it is clearly a weak choice. Bishop plus Dabaaba is a slightly weak choice because it is assumed that the Bishop would gain more from being able to move to squares of a different color, with Bishop plus Wazir, or Bishop plus Crab, or Bishop plus Narrow Half-Knight.
It is possible for both players to select the same army, though it may be unlikely. More likely, both players might have (for example) the same Knight but different Rooks; there is an obvious set of alternate rules of the game which would forbid two players to use the same piece, but that makes the rules more complex and so I decided to allow it.
Assuming that the enemy King can be driven to the edge of the board, and then to a chosen corner, all the Augmented Bishops (except the BD) and all the Augmented Knights except the NW (Knight plus Wazir) can force checkmate in an endgame with K plus one piece versus King. Therefore the NW and BD may suffer from an endgame disadvantage and are less likely to be chosen. (Can you confine the enemy King in the endgame K + BfbN versus K? The answer is not known; but if the answer is "no", this paragraph is moot.)
There is a game called Super Chess where all the pieces are augmented, and gain the move of the King. I believe that this makes movement too amorphous and flexible, and that Augmented Chess will produce much more interesting games.
It might have been possible to provide more basic pieces and more augmenters, but I thought it better to keep it simple, and to stick to basics and augmenters whose intrinsic values are well known and well matched.
This game could have been described years ago, but I was tied up in the more important and difficult task of designing different armies that have the same strength as the FIDE army.
W: The Wazir moves like a Rook, but only one square.
As an augmenter, the W adds more mobility to the combined piece than any other augmenter does. This strength is balanced by its lack of range and its awkwardness in blocked positions.
F: The Ferz moves like a Bishop, but only one square.
The F is second in added mobility, and its diagonal move is flexible, and the fact that two of its moves are forwards is good; however, it is short and does not shine in blocked positions.
D: The Dabaaba jumps two squares in the direction a Rook would move. It can leap over obstacles.
As an augmenter, the D provides quick development plus some ability to sneak past Pawn chains or to deliver a smothered mate.
A: The Alfil leaps two squares diagonally, over obstacles as needed.
As an augmenter, the D provides quick development plus excellent ability to sneak past Pawn chains in blocked positions. It can deliver a smothered mate, and because it has two forward moves it has better forking power than the D.
Crab: the Crab moves to half the squares a Knight can go to; forwards narrow and rearwards wide.
As an augmenter, it has the advantages of a Knight; but of course it goes to only half the squares a Knight can go to, which keeps it from being too powerful.
Narrow Half-Knight: the fbN moves to half the squares a Knight can, narrowly forward and narrowly to the rear. For example, from e4 it can go to d6 or f6 or f2 or d2, but not to c3 or c5 or g3 or g5.
The fbN is not very different from the Crab.
The Fibnif moves as Ferz plus Narrow Half-Knight, and as such it is itself composed of two of the augmenters. It is chosen as an alternate form of Knight because experience has shown it to be a very exact equivalent of the Knight in value. (No two different pieces can ever be exactly the same in value, but differences below a certain degree have no practical impact. The Knight and Fibnif are unusually close in value, and there is no way to say which one is better than the other.)
The Chancellor is Rook plus Knight, just as the Queen is Rook plus Bishop. My opinion is that the Chancellor is fully equivalent in value to the Queen, although some other people believe it is worth slightly less, perhaps even as much as half a Pawn less. Such controversies make for interesting games. Because only two of the augmenters are useful with the Queen, the Chancellor was added; but notice that only the Ferz and Alfil are useful augmenters for the Chancellor.
The unnamed is Rook plus Fibnif, very logical because the game allows two kinds of Knight. The only augmenter useful with the unnamed is the Alfil. (There are thus five possible types of Augmented Queen in the game, Q + Crab, Q + fbN, RN + F, RN + A, and RfbNF + A.)
The four types of Augmented Rook are untested, but their equivalence is assumed: RF, RA, RfbN, RffNsbN.
Of the four types of Augmented Bishop, only one is still colorbound, and therefore the BD is less likely to be chosen. The remaining three are BW, BfbN, and BffNsbN.
There are five types of Augmented Queen, arising from the three basic types of Queen allowed: RBffNsbN, RBfbN, RNF, RNA, RfbNFA.
The rule forbidding more than one use of the same augmenter means that there are fewer than 560 possible armies the players can choose. I have not worked out the exact number, but I know that it is large enough to prevent players from spending their lives memorizing opening lines.