Robotics Reference
In-Depth Information
each card it could play, and then picks the card which leads to the highest
average number of tricks.
As the play of a deal proceeds, certain information is revealed that
increases the accuracy with which the players can estimate which cards
lie in which hands and how many cards of a particular suit are held in
each of the hidden hands. As more information is revealed, so a program
can improve the accuracy of its probability estimates. For example, a
program might estimate that the opponent on its left has a twenty per-
cent probability of holding three or more cards in the heart suit, a thirty
percent probability of the opponent holding two hearts, a twenty-five
percent probability of him holding only one heart and a twenty-five per-
cent probability of him holding no hearts at all. If, on the first occasion
that Hearts are led, this particular opponent plays a card of a different
suit, indicating that he holds no Hearts at all, then these probabilities are
immediately adjusted to zero percent, zero percent, zero percent and one
hundred percent in order to take this new information into account.
After a while Ginsberg found the Monte Carlo process too limiting,
partly because it was unable to discover certain types of play that are
used to elicit information about the locations of cards in the opponents'
hands. Instead he developed a technique that literally solves the Bridge
hand, guaranteeing optimal play.
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How Computers Bid in Bridge
In “The Million Pound Bridge Program” I advocated the use of a com-
puter designed bidding system called COBRA. The system's author,
To r b j orn Lindelof, explains the development of his system thus:
COBRA was developed with the aid of main frame computers, us-
ing a technique for studying the trick-winning ability of various
cards and combinations of cards, as a function of a number of sug-
gested properties of the whole hand. This study eventually formed
the basis for a highly successful hand evaluation method, around
which it was comparatively easy to build a complete bidding sys-
tem. COBRA has few really innovative features, except that it per-
forms at a level of skill which is unusual, even among international
masters.
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It is not possible, of course, for a Bridge program to play perfectly without knowing for certain
where all the unseen cards lie. Optimal play, based on its knowledge of the opponents' bidding,
maximizes the program's performance on the play of a hand.
