Newsgroups: comp.ai.games
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From: darken@scr.siemens.com (Christian Darken)
Subject: Re: How to teach a computer to bluff?
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Date: Thu, 25 May 1995 15:57:42 GMT
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As pointed out by Bruno Wolff, it is an interesting, and not widely
understood, fact that the question of an optimal bluffing strategy
(and an optimal response- to-bluffing strategy, for that matter) can
be calculated analytically.  See the highly simplified form of poker
in von Neuman and Morganstern's famous book (there is an even nicer
treatment in some editions of Encyc. Britannica under "Game Theory",
1969 for instance).  Draw poker is simplified by restricting the
number of different cards in the deck (say, to two!), the size of the
hand (say, to one!), disallowing discarding, and limiting the number
of rounds of betting (to one or two). To give a flavor of the form of
the solution, for each specific set of information available to the
player (i.e. the player's hand and the visible actions of the
opponent) an optimal distribution for the player's actions is given
(e.g. fold 10% of the time, see the bet 70% of the time, and raise 20%
of the time).  So the decision to bluff is random, but dependent on
the situation.

Trouble is, exact calculation of optimal strategies is intractable for
all but simple (and I do mean simple) games.  I agree with Bruno that
analysis for a game of the type and scale as Stratego is impractical.
Methods for finding tractable approximations is a pet interest of mine
(anybody have any in their pockets?).

The only paper on a full version of poker that I know of is old!
[ Waterman, Art. Intel. 1 (1970), 121-170. ]  The method employed is
basically heuristic, with some parameters of the system trained to
better imitate expert performance.

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Christian J. Darken                  phone: (609)734-6536
Member of Technical Staff            fax:   (609)734-6565
Learning Systems Department          email: darken@scr.siemens.com   

Siemens Corporate Research, 755 College Road East, Princeton, NJ  08540

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Christian J. Darken                  phone: (609)734-6536
Member of Technical Staff            fax:   (609)734-6565
Learning Systems Department          email: darken@scr.siemens.com   
