[JLJ note that Katsenelinboigen's grammar is almost (but not
quite) perfect and I have chosen to preserve his quotes and his unique style of writing exactly as in his book, including
his use of underlines.]
iii The fourth question I want to pose deals with chess. Chess,
in spite of its apparent simplicity and fixed rules, does not yield in a greater majority of cases to a direct link
between a given step and the final outcome of the game. It is really tempting to devise an optimization algorithm which would
provide information sufficient to ensure the optimality of a given move. But how should we proceed if such an algorithm which
must, of course, be executable in real time, is not available... Here we must resort to all sort of approximations.
iv The reader may be somewhat confused at this point because the concept of indeterminism is not
totally clear. A few words of consolation - the reader is not the only one without a firm grip on this category. The author
is far from understanding it completely
p.21 As the game progressed and defense became more sophisticated the combinational
style of play declined... [The] Positional style of chess does not eliminate the combinational one with its attempt
to see the entire program of action in advance. [The] Positional style merely prepares the transformation to a combination
when the latter becomes feasible.
p.118 So the game of chess as a problem has been formulated... We are presently faced with a task of designing
and implementing a method or an algorithm for solving this problem. Design of a chess algorithm requires a clear understanding
of the nature of the operator or the executor of this algorithm since this algorithm must be executed in real time.
p.125 The number of possible heuristics may grow with the level of skill. Some recommendations are valid
only for beginners. They are modified as far as more mature players are concerned.
p.133 May be we can try to apply the ideas of exact algorithms to determine approximate values of parameters
used in evaluating the current state of the system. These values should be a good approximation of the weights generated by
the exact algorithms. Of course, it should be remembered that the problem of evaluating the overall position is the cornerstone
of our analysis. Evaluation of position's individual parts or of a single piece remains an important issue as far as varying
their values independently of each other, but it is essential to keep in mind the interrelationships between the parts
and the whole.
p.135 for Euler the mobility of a piece was probably the dominant characteristic in establishing
its material value. Mobility, in turn, is determined by the free space or by the "obstacles" (thus
a knight, although it is less mobile than the bishop, has an advantage over the bishop in being able to jump over the "barriers"
set up by the opponent).
p.139 To sum up we can state the following: the relative values of the pieces are functional in
that they reflect the potential contribution of a given piece to the final goal of the game... a piece has to be
examined within the context of a specific position. This is where positional parameters come in... it is easy to see that
one of the major factors responsible for making the opening values of the pieces different from their overall ones is the
immobility of the pieces in the opening, the fact that some pieces limit the development of others.
p.140-141 other parameters have to be introduced in order to improve upon our unconditional values
in each specific situation. Doing so will enable us to give an overall evaluation of the current position (or some
future position). These additional parameters must reflect interrelations among the pieces... I want to start
our discussion with primary positional parameters, i.e. parameters that cannot be decomposed any further with the tools presently
available. Primary parameters can be grouped together to form aggregate positional parameters such as the strength of the
center, the development of the right or the left flanks, and so on. I shall not touch upon this kind of parameters in the
present work. I only want to note that a lack of research on the methods of aggregating-disaggregating chess positions represents
a gaping hole in the field of computer chess. There is no doubt that good chess players utilize these kinds of procedures
to a great extent.
p.145 Unfortunately, the set of positional parameters currently used by computer programs is still based
on the experience of good players who express it in an intuitive manner. I think that one of the major obstacles to
designing more effective algorithms is a lack of formalized procedures for developing new positional parameters.
p.146-147 M. Botvinnik proposed a totally different approach to positional parameters. Acknowledging the
need to evaluate both material and positional parameters, he notes that: [Solution of Inexact Problems. Moscow: Soviet
Radio, 1979]
Such a method [method by which various averaged out weights of positional parameters are introduced A.K.]
of deriving a positional estimate in chess is wrong. A positional factor that yields a positive result in one situation
may yield a negative result in another. For instance, are doubled pawns good or bad? The answer depends on
the situation. Sometimes doubled pawns are a suitable target for an attack, since one of them cannot support the
other. But sometimes doubled pawns contribute to the control of a square through which important communication lines
(trajectories of pieces) pass, and then the doubling is extremely useful. the same thing may be said of other factors
entering into the positional component of Shannon's prototypical scoring function.
In the chess program under consideration, a quite different decision was made about the positional
component of the scoring function, basing it on the control of those squares making up the
trajectories that enter the MM. The side controlling the larger number of squares has a positional preponderance
(p.29)
Botvinnik elaborates on this point:
Control of fields does not mean control of the whole board, but control of only those fields that
may be used in the impending play. Therefore one must strive for control of the field consisting of those
trajectories in which the pieces can move, but have not moved yet.
At the node in the search tree where we find ourselves at a given moment, we must
unravel all those sheaves of trajectories which have not yet been developed and determine which player has control
of the majority of the fields consisting of the trajectories not yet used in the play. This allows us to forecast the result
of the play -- the result of a search which, in particular, had to be renounced at the terminal nodes of the variations
for lack of resources (p.38)
An interested reader can refer to Botvinnik's book quoted above for a more detailed discussion [the book
however is in Russian J.J.] of the methods of assigning weights to the positional parameters... I refer the reader to G. Adelson-Velskii's
book [Machine Plays the Game, Moscow: Nauka, 1983] which presents a comparative analysis of Botvinnik's approach.
p.155 How then is the game to be played? It must be played positionally. Positional play does
not preclude combinations. On the contrary, it creates predisposition towards a combination... So positional
play makes sense if it eventually leads to a combination.
p.157 [Botvinnik quoted from Computers in Chess: Solving Inexact Search Problems p.16-17] To attempt to
solve an inexact problem without having formulated the goal of the corresponding inexact game is a waste of time... The goal
of a game says what our aim is; only when we know this can we identify courses of action that cannot lead to our target, and
exclude them from the tree. Knowing the goal lets us define the lines along which the search is to occur.
The goal lets us direct the search; the scoring function lets us evaluate and stop a variation.
The goal lets us form a search tree; the scoring function lets us strike a balance.
The scoring function acts together with the goal of an inexact game and is therefore itself inexact.
As distinct from the goal, which must be unique, the scoring function consists of two components: the first component allows
us to evaluate the results obtained with the limits of the truncated tree; the second forecasts the possibility of reaching
the goal beyond those limits.
p.158 According to Botvinnik, M., Solution of Inexact Problems, Moscow: Soviet Radio,
1979, positional value represents a ratio Kw / Kb where Kw
and Kb is the number of squares in the trajectory controlled by white and black respectively.
(p.144).
p.176 "The style is the man himself," says Buffon [b. September 7, 1707 d. April 16, 1788 French naturalist,
mathematician, biologist, cosmologist and author J.J.], and nowhere is the famous phrase (Le style est l'homme meme) more
appropriate than in chess. Many men, many styles; and what is chess style but the intangible expression of the will to win?
[Reinfeld, F., Nimzovich the Hypermodern, Philadelphia, David McKay Co., 1948, p.23]
