Betza notation
Betza notation is a commonly used notation system, originally developed by Ralph Betza[1]. The version described here is based on the extended notation developed by H.G. Müller[2] for use in XBoard and which allows for a more complete description of special piece moves.
Contents
Basics
Atoms
Betza notation describes Chess pieces by dividing their moves into groups with the same board step, such as all 8 moves of the Knight. By default these moves can be made as capture as well as non-capture. Such a group of symmetry-equivalent moves ('atom') is indicated by a single capital, usually the common abbreviation of the piece that has those moves, and only those moves (see table 1). If a piece can do several unrelated moves, it is described by a concatenation of the descriptions of each group.
| G | Z | C | H | C | Z | G | W = Wazir | (1,0) |
| Z | A | N | D | N | A | Z | F = Ferz | (1,1) |
| C | N | F | W | F | N | C | D = Dabbaba | (2,0) |
| H | D | W | * | W | D | H | N = Knight | (2,1) |
| C | N | F | W | F | N | C | A = Alfil | (2,2) |
| Z | A | N | D | N | A | Z | C = Camel | (3,1) older notation J |
| G | Z | C | H | C | Z | G | Z = Zebra | (3,2) older notation L |
Range
To describe sliders, the letter indicating the atom must be followed by a number, which then indicates the maximum number of times the step described by the atom can be repeated in absence of obstacles. By convention a 0 here means 'without limit'. (Older versions of the notation duplicated the atom name for this. Thus N0 (or NN) describes the Nightrider, repeating Knight steps in the same (but arbitrary) direction. There are some shorthands for common expressions: B, R, Q and K describe the orthodox Chess pieces, which formally should have been written as F0, W0, F0W0 = BR and FW, respectively. This way an Archbishop can be written as BN. (Or NB; the order has no significance.)
Directional modifiers
If a piece does not have all the 8 moves belonging to the atom (or 4 for purely diagonal or orthogonal moves), the subset of it can be indicated by 'directional modifier' prefixes. These are lower-case letters indicating directions or sets of directions: f, b, r, l, v, s, h for forward, backward, right, left, vertical (f+b), sideway (l+r), and half, respectively. Note that the exact meaning of each of these depends on the type of atom; for orthogonal moves f, b, r and l each specify a single move, for diagonal and oblique moves they specify move pairs. To subdivide the pairs, a second directional modifier for the perpendicular direction must again be written in front of the first. So lfN corresponds to the move Ng1-f3, the left-most move of the forward pair. Combinations like 'fh' can only be used on oblique moves, and do the opposite: the 'h' extends the meaning of 'f' to all 4 moves that have a component in that general direction. Directional modifiers that do not combine to a single direction imply that moving in each of the corresponding directions is allowed. E.g. frW can move one step forward, or one step right (but not backward or left). If what was parsed upto now can combine with the next letter, it will. To avoid unwanted combining of adjacent directional modifiers to a single direction, they sometimes need to be doubled, e.g. ffrrN is a Knight with the two forwardmost and rightmost moves.
Table 2: directional modifiers
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K N K N K Outer ring applies to 8-fold movers N and K
N F W F K Inner ring applies to 4-fold movers F and W
K W * W K
N F W F K
K N K N K
half-planes right/left pairs single directions chiral
fh fh fh fh fh lv lv . rv rv lf lf ff rf rf . hl . hr .
fh f . f fh ll . . . rr fl lf f rf fr hr . . . hl
. . * . . . . * . . ll l * r rr . . * . .
bh b . b bh ll . . . rr bl lb b rb br hl . . . hr
bh bh bh bh bh lv lv . rv rv lb lb bb rb rb . hr . hl .
forw/backw pairs diam. pairs/quartets
lh lh . rh rh fs ff . ff fs . v v v .
lh l . r rh fs . . . fs s . v . s
lh . * . rh . . * . . s s * s s
lh l . r rh bs . . . bs s . v . s
lh lh . rh rh bs bb . bb bs . v v v .
Modality modifiers
If a piece is 'divergent', i.e. it cannot both capture and non-capture with the same move, then a 'move modality' prefix will describe what the move can do (c = capture, m = non-capture). A Shatranj Pawn (which does not have initial double-push or e.p.) thus is fmWfcF.
Advanced modifiers
Jumping
The original Betza notation included a number of special-purpose modifiers, defined in a rather ad-hoc way to indicate certain aspects of common pieces that could not be handled by the basic system. 'Lame leapers' are pieces that can be blocked on squares they cannot move to, and are indicated by modifiers 'j' and 'n', for 'must jump' and 'non-jumping'. By default moves to non-neighboring squares can do both, as they completely ignore the state of other board squares, even those geometrically between their origin and destination. A Xiangqi Elephant would thus be nA, where a Shatranj Alfil is simply A. The weakness of these modifiers is that they are only unambiguously defined on purely diagonal or orthogonal atoms, as in other cases it is not clear what constitutes the path taken to reach the destination.
Hopping
Hoppers are pieces that must move over an occupied square (the 'platform') that they might be able to move to in other situations. Famous examples are the Xiangqi Cannon ('Pao', a Rook which must jump before it can capture), and the Grasshopper (a Queen that can only land on squares directly behind the first obstacle in its path). The modifier 'p' can prefix slider moves, and indicates that these moves can and must jump exactly one obstacle, so that the Cannon can be denoted as mRcpR. The modifier 'g' indicates a slider move that in a similar way can only continue a single step after hitting the obstacle, so that a Grasshopper is gQ. The more general case, where pieces could also change direction ('bifurcators') or stride after hopping the platform, could not be covered in the original Betza system without introducing new ad-hoc modifiers describing each case separately.
Specials
Other ad-hoc modifiers in the original Betza system are 'q' and 'z', for riders that move along curved and zig-zag trajectories. I.e. they take their consecutive steps not in the same direction, but with a fixed angle between them, rotating in the same direction on every new step for 'q', and alternating direction for 'z'. It is a bit ill-defined how exactly the direction changes; one assumes by the minimum amount, which depends on the atom. The prefix 'o' is used to indicate moves on a cylinder board, which would wrap around from the side edges.
Ad-hoc Extensions
En passant
Not in the original Betza system, but very much in the spirit of it, a prefix 'i' can be put on a move that is only allowed for 'virgin' pieces. Similarly, 'e' is a very useful additional move modality next to 'm' and 'c', indicating en-passant captures (which go to that empty square where the previous opponent's move could have been blocked due to an 'n' prefix, had it not been empty, and remove that moved piece as a side effect). These modifiers allow accurate description of Pawns; a FIDE Pawn would be fmWfceFifmnD, which includes both the blockable initial double push ifmnD and the e.p. capture feF on top of the Shatranj Pawn.
Castling
Conventional castling is described with an O atom, where the following number indicates the number of steps the piece having this move takes in the direction of the corner. It implies that the corner piece then has to swing around it, and applies the usual restrictions on virginity of the corner piece, and not moving through check (if the described piece is royal).
Drops
The atom @ indicates a piece can be dropped from the hand. (Never mind how it got there!) Directional modifiers make no sense here, so the corresponding letters are reused to indicate other things. 'f' restricts the drop to board files that do not contain a piece of this type yet. Similarly 's' forbids a drop on squares the same color as where there already is such a piece, and 'b' even forbids the drop if there is already such a piece anywhere on the board. These modifiers can be duplicated to crank up the maximum to two pieces of the same type. A numeric suffix on the @, which normally would indicate a range, indicates the depth of the 'drop zone' measured in ranks, (default 1), starting at the back rank. A 'j' prefix means the back-rank itself is exempted. So in Crazyhouse Pawns would have j@7, the other pieces @8. In Shogi we have P:fWf@8, L:fR@8, N:fN@7, while other pieces would have @9.
