The Best of Creative Computing Volume 2 (published 1977)

Page 25 << PREVIOUS >> NEXT Jump to page:
Go to contents Go to thumbnails
This book is also available for the Kindle

Simulated Strategies of Game Playing (Game theory, dominoes-playing program)
by Dr. S. Reisman

graphic of page

In computer play, the aggressive method of play is significantly better than the


by Dr. S. Reisman
IBM Canada, Ltd. Laboratory

Game theory enables one to classify competitive
games according to characteristics of rules of play
of the game. Consequently, the game of chess is
described as a two-person, zero sum game of perfect
information. This classification describes a competitive situation between two
players in which the
total game situation is open to observation to both
players. Both players have opposite interests in the
outcome and one player's win is the other's loss.

in addition, the game can be terminated ln a finite
number of moves. Games of perfect information
differ from games of imperfect information by the
fact that, in the latter, there is no best strategy.

However, in the former, sometimes called strictly
determined games, the player with the best strategy
will win regardless of his opponent's play.

The game of Draw and Match Dominoes is
classified as a two-person, zero sum of Imperfect
information and according to game theory there is
no best strategy of play which can be employed.

It was hypothesized while this might in fact be
true, techniques of simulating cognitive processes
might be used to determine if better strategies do
exist. Consequently, player protocols were gathered
from opponents while they played a simplified
version of Draw and Match Dominoes. An analysls
of the protocols indicated that human players use a
combination of a number of components of play to
form their playing strategy. These components are
described as: (1) the defensive component; (2) the
aggressive component; and, (3) the statistical

The defensive component is characterized by a
player's being more apt to make assumptions about
his opponent's game situation and as a result attempting to block his every
move. The aggressive
component is different in that the player using it
makes no assumptions about his opponent's situation and instead makes his move
only on the basis
of his own known situation with the objective of
playing his longest chain of tiles. The statistical
component is used rarely, and only as a last means
of decision making if the other two components
are unsatisfactory. It is characterized by the pIayer's
counting the various tiles already played and making
decisions as to the likelihood of matches being
drawn from the bank.

In an effort to determine the validity of this
classification system an interactive Dominoes-playing
program was written in the list processing language
IPL-V." The program was altered so that the strategy
employed in a game could be varied to combinations of the above components.
Results of the computer play indicated that the classification system
is, in fact, an operational one.

In order to determine if there are optimal strategies of play, the interactive
program was altered
to allow the play of the game to be between two
computer programs rather than between a human
and a computer, as in the original version. In this
way, one program using one type of strategy could
be played against a program of another strategy.

The programs were each loaded onto a different
interactive terminal and the output of one terminal's
program was used as input to the terminal' with the
second player-program.

In this attempt to determine a better strategy,
one program was set to use only the defensive
component, and the other, only the aggressive component. The results of a number
of games played
in this manner indicate that the aggressive component of play is significantly
better than the defensive component. An analysis of the games played
indicated the reasons for this. The strictly defensive
player makes assumptions concerning his opponent's
situation while ignoring his own game situation and
the harm he may be doing to himself by blindly
attacking his opponent.

The typical human player does not rely on only
one component of play, but both makes assumptions
about his opponent and considers his own situation.

For this reason, a better strategy would probably
consist of a combination of these components in
a particular game situation. Although the search
for a better strategy of play in the game of Dominoes
is not of earth-shaking importance, the potential
spinoff of the techniques used and results obtained
may be of value in other situations of a competitive

'For a complete description see: Dominoes-A Computer Simulation of Cognitive
Processes, Simulation
and Games, Vol. 3, No. 2, pp. 155-164.

Page 25 << PREVIOUS >> NEXT Jump to page:
Go to contents Go to thumbnails
This book is also available for the Kindle