Ideal Values and Practical Values (part 2):

Atomic Pieces and Subatomic Movements

By Ralph Betza

I have said they were the atoms of Chess, but in fact they can be further divided.

The Ferz, for example, can move in four directions and can capture in four directions; and it is possible that a piece could be composed that would use just a few of the eight movements that make up a Ferz. Indeed, such a piece exists, and Philidor said it was the soul of Chess.

If a combination of any two atoms gives a new piece whose ideal value is the same as the ideal value of the Knight, then wouldn't you expect that the combination of sixteen movements would create a new piece with Knightly ideals?

In fact, I think it does create such a piece. However, there are several reasons why such pieces may have practical values much lower than their ideal values. For example, a piece with sixteen different non-capturing movements will be nearly worthless (see my article about the Black Ghost), while a piece with sixteen captures but which cannot move without capturing is less bad, but not nearly worth a Knight in practice; also, pieces that have many non-capturing movements can sometimes suffer from being blocked by enemy pieces, pieces with many more forward movements than rearward are too strong (because you start the game with foe in front; Hans Bodlaender has pointed out that much of this advantage dissipates in the endgame, but I feel that by then the excessive forwardness should have won the game) and pieces with too many retreats are too weak.

Even if the forward and rearward movements and captures are balanced, so that the piece has a practical value equivalent to its real value, many possible pieces are too much of a hodgepodge to be interesting. For example, a piece that moves Northwest as a narrow Knight, captures Northwest as a wide Knight, moves and captures Northeast as an Alfil, moves South in retreat as W or D, captures Southeast as a Ferz, and captures Southwest as a Ferz, may have the practical value of half a Knight, but who would want to have such a piece in their game?

Unless, of course, the game was based on having such awful pieces; for example Subatomic Chaos Chess, in which you make a legal move and then randomize one piece, be it friend or foe, but not K or P (otherwise K versus K might be a win for a randomly-chosen player).

"Randomize" means you throw the dice to choose 16 subatomic movements for a N, or for a rider such as R, Q, or B, you randomly choose the right number of moves or captures in the directions W, F, and N. (The Queen could become a Nightrider.) You can't randomize the piece your opponent just randed. You must randomize if you can, no penalty if you cannot, and if randomizing an enemy piece puts you in check, you lose. Basically, the rules of Avalanche Chess are applied.

Randomizing the moves by hand could be tedious. With a computer moderator, this might be an interesting game.

Thousands of new pieces can be created by combining the subatomic movements, and even if most of them are bad in some way, the remaining small portion must contain dozens, even hundreds, of possible new pieces that would be useful in Chess variants. I cannot make such a statement without choosing an example, so consider the left-handed Commoner, right-handed Waffle: it moves and captures as a W in all directions, to the left as F and to the right as A. You would start the game with one sinister and one dexter of this charming new piece whose practical value is very probably close to the Knight's.

Of course, the Rook, Bishop, and Nightrider can also be decomposed in similar fashion, and used to form combination pieces whose ideal values can be described simply by adding up the appropriate fractions of the known values of these pieces. A Knight that can also move left and capture right as a Bishop should be worth a Rook; a piece moving and capturing West or South as Rook, but NNW, NNE, ENE, and ESE as Nightrider should also be worth a Rook; and both pieces should be fairly easy to learn to use.

Now I have divided the ideals into their smallest possible parts. Next article, I will run with the great unsolved mystery of piece values.

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