According to my current thinking, after years of investigation,
**Mobility**, **Forwardness**, **Distance**,
**Colorboundness**, and **Capture** seem to be the five main
factors in determining the value of a piece.

**Promotion** is another factor, but is only relevant to Pawns.
( *Out of the pieces I have discussed here so far*, only
Pawns can promote to something stronger. In the wider world, other
pieces may have their values affected by promotion. )

For example, the Wazir is less valuable than the Ferz, even though the mobility calculation would have it be the other way around, ( and even though the Ferz sees only squares of one color ).

One way to verify this is to play a game of Chess where one side has 8 Wazirs instead of Pawns, and the other side has 8 Ferzes; the difference in value between ONE Ferz and ONE Wazir is very small, but this test multiplies the difference by 8.

( In this test, because there are 4 Ferzes on each color square, their colorboundness is minimized. )

In the process of conducting this test by hand, it becomes obvious that the main reason why the Ferz is stronger is that the Ferz has two different moves that advance towards the opponent, while the Wazir has but one.

Except for the Pawn, all the ordinary chess pieces have symmetrical
moves. *(Imagine the difference in value between a piece that moves
either as a Knight or forwards as a Bishop, and the value of a piece
that moves either as a Knight or rearwards as a Bishop!)* This
symmetry greatly simplifies the calculation of forwardness, because
one can simply say that "more directions of movement" is a good
thing.

( **Forwardness** must be the main reason why the Queen is worth more
than the sum of the values of Rook and Bishop. More directions of
movement, more forking power. )

**Forwardness**, you might notice, mixes three things; one is the
number of directions a piece can move, the second is the distance of
the moves, and the third is the directions of the moves. Obviously
it is better to go forward than backwards; I now can provide some
numbers.

**Colorboundness** comes in many degrees; the Bishop can see only half
the squares on the board, the Dabbaba can see only a quarter of the
squares, and the Alfil can see only one-eighth of them. It is
intuitively obvious that Colorboundness must have a negative effect
on the value of a piece, but how to quantify it?

**Capture** is a topic to be introduced much later. It is really
more important than mobility, but for all the pieces on our list so
far, **Capture** is equal to **Mobility**. In the standard
game of Chess, only Pawns have different rules for moving and
capturing, but imagine the difference in value between a piece that
moves like a Knight but captures like a Queen, and one that moves
like a Queen and captures like a Knight!

Center Quotient is an experimental idea.

If we could assign reasonable values to **Mobility**,
**Forwardness**, **Distance**, and **Colorboundness**, then
and only then could we choose a "Magic Number" for the probability
that a square is empty, used in the mobility calculation, and be
able to hope that the results would have some validity.

Next Section