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Spacious Pieces

By Ralph Betza

The Dabbabah is a piece that leaps two squares in the direction a Rook could go, for example it can move from f1 to f3, blithely ignoring any obstruction that might exist on f2 -- it leaps over.

The "lame"[1] Dabbabah can also move from f1 to f3, but only if f2 is empty -- it cannot leap over. Its mobility is reduced by the probability that the square it wants to cross is occupied, and its value presumably suffers the same reduction. (This is exactly what happens when the Rook moves two squares, so the Rook can be seen either as a repetitive one-step move or as a combination of Wazir plus lame (0,2) plus lame (0,3) and so on.)

Using the usual magic number, the lame D is worth roughly two thirds as much as a normal D, or perhaps 0.7 times as much if the wind is from the West.

The Wazir moves one square Rookwise. Of course, there is no such thing as a "lame" Wazir, because a piece that moves only one square crosses no intervening squares to reach its destination. It would be useful if, for the sake of devising new pieces, there were such a thing as a "lame" Wazir.

Did I say there was no such thing? Well, let me introduce you to the Spacious[2] Wazir, which moves one square Rookwise but which cannot move if the square one step further in the desired direction is occupied. Its value is reduced by the probability that the next square is occupied, in exactly the same proportion as the lame Dabbabah.

Indeed, just as the Rook is a Wazir-Rider, that is, it makes a Wazir move and then if the square it landed on was empty it makes another, and so on, so is the Spacious Rook a "Spacious Wazir"-rider; and so we have a whole new class of pieces, from the Spacious Ferz to the Spacious Nightrider, the Spacious Queen, and indeed the Spacious Amazon. In every case, the expected value is 2/3 to 0.7 that of the normal piece.

Another way of looking at the Spacious Rook is that it often moves one square less far than the Rook.

What did you say? Why yes, I am hiding something behind my back. These are the rules about Spacious capture, and about what happens when a Spacious piece wants to move to the edge of the board. I'll explain them now, but first you'd better put down your glass of Refreshing Bubble Fizz, lest you spill it and ruin your keyboard.

In order for a Spacious piece to capture, the square beyond the target must be empty. In order for a Spacious piece to move to the edge of the board, the wraparound square must be empty.

For example, if a Spacious Rook wants to move from e2 to e8, the wraparound square is e1 -- going out the top of the board and coming in the bottom -- and so the move (or capture) is legal if e1 is empty. Notice that the Spacious Rook cannot move through e8 to e1, instead it merely examines e1 when deciding if it can go to e8. A special case is seen when a Spacious Rook goes from e1 to e8 -- by the time it gets there, e1 will be empty, and so it does not block its own move.

The first reason for the wraparound rule is that it makes it much easier to calculate the values of Spacious pieces, but the second reason is that it creates strange and unusual tactics. In the field of chess variants, strange and unusual tactics are a good thing.

The capture rule also creates unusual tactics. Consider a Spacious Rook on e1, facing an enemy Ke8 and Qe7. The Spacious Rook cannot capture; however, if the King moves the Queen can be captured, and the Queen may not move except along the e-file (perhaps to capture the Spacious R), but becomes vulnerable to capture if she does so. This is not quite like having a normal R on e1, nor is it like having a Cannon there.

Another strangeness in the rules is that with a Spacious R on e1 and an enemy piece on e8, the Spacious Rook can go as far as e8 to capture, but cannot reach e7 with a non-capturing move. In other words, the Spacious Rook captures at the same distance as the normal Rook (when not blocked), but often moves one square less than the normal R.

Spacious pieces increase in value as the board empties out. Although the whole-game value of a Spacious Rook may be a mere two-thirds of a normal Rook's, in the opening it is worth much less than the normal Rook and in the late endgame it is worth as much as the normal R (for all practical purposes it is worth as much, the difference in values at that point in the game being so small).

Note that the normal Rook increases in value as the board empties out, but that in Spacious pieces this effect is even more pronounced. As a result, a piece that combines Spacious movement with Cannon movements is likely to be especially well balanced.

My common practice of making up a whole new army with a new type of piece would fail miserably using Spacious pieces, because the army as a whole would lack balance: If a Spacious Queen is worth a mere 0.7 Q in the midgame but is worth a full Q in the ending, there is nothing you can do to make a fair army out of it.

Instead, I offer you Spacious Chess with Different Armies: for example, you can play using the Spacious Nutty Knights versus the Spacious Remarkable Rookies because all pieces are equally affected.

Wraparound Squares

For your convenience, here is the traditional[3] UAD[4] showing how wraparound works. As an example of how to read it, a Bishop coming down the diagonal from b6 to a7 wraps around to h8, but a B coming from b7 to a8 wraps to h1; and a Knight going from c7 to a8 wraps to g1.

e4   f4   g4   h4  | a4   b4   c4   d4
e3   f3   g3   h3  | a3   b3   c3   d3
e2   f2   g2   h2  | a2   b2   c2   d2
e1   f1   g1   h1  | a1   b2   c1   d1
e8   f8   g8   h8  | a8   b8   c8   d8
e7   f7   g7   h7  | a7   b7   c7   d7
e6   f6   g6   h6  | a6   b6   c6   d6
e5   f5   g5   h5  | a5   b5   c5   d5

[1] "Lame jumper" is a traditional technical term.

[2] I call it Spacious because it needs extra space beyond its move. You may call this name specious.

[3] I have seen this diagram often, but don't know where else one might find it on the web.

[4] UAD == Ugly Ascii Diagram

Written by Ralph Betza.
WWW page created: October 26th, 2001.