Dan Heisman has written of a new style of positional evaluation
which is similar to the concepts presented in this paper. 'A change is necessary!' - great opening, Dan. In his own
words, My life 'treatise' - originally written on a typewriter in 1974-75. Now sold out its 3rd edition.
Describes the basis for how each piece gets its value and relates, in a very basic (but not for beginners) way how that relates
to evaluating positions. Describes the basic elements that can be used for non-tactically evaluating a position.
Not as many diagrams or examples as I would like because I didn't have the tools at that time to include them! Very
unique for its time (and even now!).
p.7"A change is necessary! For many years chess players have relied
on a loosely knit, confused set of ways to non-tactically evaluate a chess position. People programming chess on computers
find that quantifying this evaluation in the form of a 'scoring function' results in a difficult algorithm, which is
experiencing poor results. Programs relying heavily on evaluation don't play much better (if at all) than those with just
'brute force,' and very little evaluation. No wonder! But such difficulties may be overcome. The purpose of this introduction
is to lay the foundation for a new evaluation theory"
How does the positional chess player seek to win a chess game?
p.13"the positional player tries to win by increasing positional pressure until the opponent 'breaks
down', allowing a simple tactical denouement [resolution]."
Traditional computer chess programs often give fixed point scores to certain concepts such as development
and penalties for doubled pawns. A positional chess player knows that these concepts deserve a more complex
understanding for accurate evaluation.
p.26"there is no 'better' way of getting a cramped and passive position than by aiming only at development
[Botvinnik, One Hundred Selected Games, p. 144]... When considering a doubled pawn's effect, one must also consider
other factors... [such as] mobility, vulnerability, and flexibility."
There is more to piece mobility than just counting moves. Heisman looks at the potential mobility
of the pieces and suggests that it is one key to unlocking an accurate evaluation of a chess position. Heisman's principle
of global mobility is similar to concepts discussed in this paper.
p.30"Mobility - This is a key part of the theory. One could construct
a reasonable argument that mobility is so important that all other elements can be examined with mobility as a basis. The
concepts considered as part of mobility are therefore the most important and basic of all the elements for understanding positional
evaluation... We will define three types of mobility:
1) Actual mobility - The number of legal moves a piece can make at any given time in a game.
2) Potential mobility - The number of squares to which a piece could move from a given square if
the board was empty.
3) Global mobility - The total number of squares to which a piece could move during a game.
Actual and potential global mobility can be defined:
3A) Actual global mobility is the total number of squares that a piece could legally get
to if it had possession of unlimited tempos in a given position.
3B) Potential global mobility is the total number of squares a piece can move to on an empty board...
An understanding of mobility may rank second only to the understanding of tactics."
What a piece can do in its current position on the board, as well as what it cannot do, contribute
to the material score we assign to it.
p.32"Potential mobility does more to determine the material value of a piece than all other factors
taken together. The standard 'value' of each piece and its respective importance has a high correlation with the average value
of the piece's potential mobility, with the exception of the Knight. This exception is because the Knight's potential and
actual mobility are usually very close in value"
The three types of mobility identified by Heisman form a large portion of his new theory -
and mine.
p.33"The above has established the basic definitions for the three types of mobility. These three
will form the foundation for the new theory, and we will see how the other elements, real and pseudo, correlate with the various
kinds of mobility."
Space is really future piece mobility in disguise. We can see a 'space advantage' but for this to
be real the pieces must be able to trace future mobility in a way that is not constrained by the activity of the enemy pieces.
p.45"So to better understand space, we must once more return to
mobility. What is important to realize is that space depends on mobility; that is, mobility 'defines' space. This means that
no matter how the board looks, the player with more space is really the one with more actual and actual global mobility, despite
what the pawn structure may seem to indicate. For example, in a closed position where White's pawns seem more advanced, if
Black's pieces, through open files or diagonals, can get around the pawn mass in some way, then it is he who may obtain the
space advantage. This is possible because pieces are not legally bound to stay behind the pawns. Indeed, an overambitious
early push of a pawn mass sometimes leaves one's pieces scattered to the defensive at some later time because the opposition
was not effectively reduced in total actual mobility. So, whereas space is an existing and useful term, it does not qualify
as a basic element."
How a piece can be used - offensively, defensively, and the threats that can be used to constrain
the operation of the enemy pieces all contribute to the material value of a piece.
p.70"Pieces have no inherent material value - it is how they can
be used in the future of a given position which determines their worth."
Heisman thinks that we must consider the future capability of the
pieces in order to properly evaluate the chances in a position - and so do I.
p.78"It is one of the main purposes of
this book to show that evaluation of a position (excluding tactics; i.e., who stands 'positionally better') based on statics
[those features which can be determined by just looking at the board, without any knowledge of motion of the pieces, nor any
attempt to analyze moves] alone is insufficient."
Heisman points out that a robust chess analysis theory should work just as well as previous theories,
plus it should be able to handle cases that the old theory did not.
p.99"A new theory should not only be
able to explain current phenomena more exactly than its predecessor, but should also be able to accomplish certain new tasks
that were 'impossible' under the old theory."
