p.v One might expect that PIONEER [the name of the software program created
by Botvinnik's team to implement his ideas] would have made substantial advances - unfortunately it has not. There are reasons:
the difficulty of the problem, the disenchantment of the mathematicians (because of the delays and drawing out of the work), and
principally the insufficiency and sometimes complete lack of machine time... our group of mathematicians works at the Institute
for Electroenergy
p.16 As soon as the search tree is truncated, the exact goal of the game
loses all meaning. It is necessary to introduce an inexact goal in the truncated tree; else the game becomes aimless and cannot
be strong. The goal of an inexact game permits the formation of a deep and narrow [analysis] tree... To attempt to
solve an inexact problem without having formulated the goal of the corresponding inexact game is to waste time. This
goal is the basis of a strong algorithm for the solution of an inexact problem, and the basis for development of a deep and
narrow tree... 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.
p.38 The positional estimate should not be a general-purpose affair; it should be specific to each given
situation. A general-purpose estimate might, for instance, be applicable to 67% of the positions encountered, and wrong in
33%; the current position might fall in the latter group. We must give Capablanca due recognition in this respect; in a polemic
[polemic: A controversial argument, especially one refuting or attacking a specific opinion or doctrine] with Znosko-Borovsky,
author of The Theory of the Middle Game in Chess, Capablanca pointed out that the basis for a positional
estimate is the control of fields [apparently, this is an uncited reference to Capablanca's book A Primer
of Chess, p.115, 116, 117 - JLJ]. 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 We shall show later that the positional estimate allows us to solve the question of priorities... Thus
the positional estimate, with the development of the sheaf of trajectories, should be produced at every node in the search
tree . We may assert that the squares under control define the usable mobility and maneuverability of the
pieces. Better maneuverability of pieces often also determines the positional superiority.
p.39 It was assumed that the control of squares involves only those pieces that lie at a distance
of one move from the controlled square (and a blockading piece must lie on the square itself).
p.39 To sum up: The positional estimate is computed at every node of the search tree. The procedure is substantially
more complex than the procedure for computing a material score. All sheaves of trajectories included in the play but not yet
used (in whole or in part) are taken into account in computing the positional value.
p.39 The positional estimate at a given square in a trajectory is computed only up to, but excluding, the
first square at which it ceases to be positive, and this determines the movement of a piece along its trajectory... we see
that we may get a first approximation on those trajectories on which the pieces have not yet had time to move.
Thus the basic factor in the positional estimate is proportional to the ratio Kw / Kb, where Kw and Kb
are the numbers of squares controlled by White and Black, respectively.
p.64 [Botvinnik describes the capabilities of two computers playing a 1977
demonstration game] KAISSA used a computer with a speed of 3 [million] operations per second, CHESS 4.6 had a speed
of 12 [million] operations per second. KAISSA could calculate variations to a depth of 5 plies; CHESS 4.6 could go to 6...
In the end [game], KAISSA extended the length of a variation to nine plies and CHESS 4.6 went to twelve.
p.67 Since 1964, when the author began to seek support for his algorithm, there have been many critical
remarks; these are worth reviewing. It has been said that this is all fantasy: it conflicts with the accepted canons; it demands
more resources than does a full-width search; it would require decades for development.. and so on.
p.105-106 [section written by Tsfasman and Stilman] The concept of the positional estimate plays an important
role in chess programs... The positional estimate proposed by Botvinnik is based on the control of squares in trajectories...
We must first define the nonfrozen trajectories of the pieces... Then for each trajectory... we develop a list of pieces lying
one move away and compute the outcome of the optimal exchange on the given square. The square is traversable if the result
of the exchange is advantageous to the side possessing the trajectory. If the given square is traversable and belongs,
say, to White, Kw is increased by 1... This unravelling of all non-frozen trajectories in the included fields is a
time-consuming process.
