Robotics Reference
In-Depth Information
intelligence to the program where none was present. After losing a 1,000-
hand match, one experienced player commented “The bot has me figured
out now”, suggesting that the program had developed an accurate oppo-
nent model for him, when in fact the version of Poki he was playing
against did no opponent modelling at all.
Eventually Billings and his colleagues decided they needed a test ses-
sion for their program in a long match against a world-class player, partly
because the matches it had played hitherto were not long enough for the
results to be statistically reliable and partly because they wanted to learn
from the comments of a top player. They had a volunteer in Gautam
Rao, who is recognized as one of the best players in the world and is
exceptional at two-player Hold'em. Like many top-flight players, he has
a dynamic ultra-aggressive style of betting. Rao played more than 7,000
hands over the course of several days in January 2003 against a version of
the program called PSOpti.
Rao was able to utilize his knowledge that the program did not do
any opponent modelling, allowing him to systematically probe for weak-
nesses in the program's strategy without any fear of being punished for
playing in a methodical and highly predictable manner. Although he
won the match, Rao's victory was not by a wide enough margin to be
statistically conclusive, and he was impressed: “You have a very strong
program. Once you add opponent modelling to it, it will kill everyone.”
Creating a Model of the Opponent. In most strategy games there is usu-
ally little to be gained by modifying one's own decision making in order
to address any stylistic quirks or known strategies employed by the oppo-
nent. The former World Chess Champion Bobby Fischer was very clear
on this issue: “I don't believe in psychology, I believe in good moves.”
In contrast, not only does opponent modelling have enormous value in
Poker, it will often be the distinguishing factor between players at differ-
ent skill levels. The ability by a player to modify his decisions based on
an accurate model of his opponents, may have a greater impact than any
other factor on his success.
Creating a model of an opponent at the Poker table necessitates mak-
ing appropriate inferences from certain observations and then applying
them in practice. Unpredictable play makes it difficult for one's oppo-
nents to form an accurate model of one's own strategy, so not only must
a strong Poker program be sensitive to changes in strategy by each oppo-
nent, it should also vary its own playing strategy over time, attempting
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