p.65 [Romanovskii, 1990 quoted] A combination is a variation (or even a series of variations) where each
side makes forced moves and which leads to an objective advantage for the active side. [Katsenelinboigen, Concept of Indeterminism,
p.57, 83]
p.67 A combination represents a forced variation involving a sacrifice... [a forced maneuver is a] forced
variation involving no sacrifices. [Katsenelinboigen, Concept of Indeterminism, p.57]
p.241 the game of chess
represents a generalized form of exchange of material and circumstantial weights of the pieces... Circumstantial weight denotes
the true strength of the piece as measured at a given moment of the chess battle; the material weight is the established average
strength of the piece [Katsenelinboigen, Concept of Indeterminism, p.56-57]
p.246-247 In my 1968 book, Algorithm of Play in Chess I wrote:
in my opinion, the game of chess (and probably any other game) is based on a generalized exchange, meaning an exchange which
involves (in the general case) both material and positional (invisible, circumstantial) weights. Unlike the material weights
which reflects the average strength of a piece, circumstantial weights reflects its real strength in a given position. The
question is to how to compute and formulate these circumstantial weights?
In developing a subprogram to govern the exchange of material weights of the pieces at some square
of the board (1978) we took into account the possibility that the pieces in question may be exchanged at more than one square.
We decided to assign a "spot" (mark) based on each exchange; we dubbed the procedure the "lady bug method". By analogy, this
procedure was applied in computing the circumstantial weights.
Previously, the trajectory of a piece was assigned material priority based on the exchange of material
weights (actually, setting priorities distorted the results). We decided to use priority ranking to define the size of the
spot of the piece connected to a given trajectory (based on exchange at a square). As a result, the piece acquires spots which
vary in size. The circumstantial weights of the piece is calculated based on these spots. Material prioritizing was replaced
by circumstantial prioritizing and Pioneer's search algorithm now resembled that of a chess master. [Katsenelinboigen, Concept
of Indeterminism, p.58-59]
p.255 Over the last 25 years I worked on the problem
of an "artificial chess master." I have come to the conclusion that the key component of such an algorithm is positional analysis
incorporated into the weight function. This function allows the master to select high priority moves to be included in the
search, to determine when to terminate the search, and to evaluate positions at the end of the search - in other words to
select a move.
I believe grandmaster approach is based on three
factors:
1. The balance of material available to each player (Dm). This is the most prominent factor and it serves as the starting point as the beginners
embark on their voyage of positional understanding (rather primitive at first).
2. Expectation of material gains (mg*). Here m denotes material,
g - the goal, and * - the guiding light. mg* is the material, the weight of the piece targeted by the opponents pieces. However,
this variable signifies not just material under attack, but material subject to a mounting attack. So, mg* is the material
expected to be captured.
3. Purely positional factor (p): control over certain squares
of the board and traversability of the trajectories leading to an attack of the opponents pieces [Katsenelinboigen, Concept
of Indeterminism, p.59]
p.255 Combinatorial play, a sacrifice so much appreciated by chess fans, is based on the second factor (mg*);
a combination always involves a sacrifice which is more than offset in the end. Emergence of mg* is a precursor of a combination.
Material (m) can be sacrificed if it is less than the material gained as a result of the combination [Katsenelinboigen,
Concept of Indeterminism, p. 60]
p.255 The Italian school of chess (particularly Gioachino Greco) introduced into the chess praxis a combination
as a potent tool of the master's algorithm. The list of the great masters of a combination includes Anderssen, Morphy, Alekhine,
Tal, Fischer, Kasparov.... But Greco was certainly the first! The positional component (p) was introduced into the masters'
algorithm by Philidor, Steinitz, Capablanca, Karpov and perhaps the author of these lines. [Katsenelinboigen, Concept
of Indeterminism, p. 47- 48]
