Robotics Reference
In-Depth Information
included, at various times, Michael Bowling, Neil Burch, Aaron Davison,
Rob Holte, Dennis Papp, Lourdes Pena, Terence Schauenberg and Du-
ane Szafron. The version of Poker they programmed is Texas Hold'em,
which has long supplanted Five-Card Draw Poker in popularity. This is
the form of the game played in the annual World Series of Poker, where
anyone with $10,000 in stake money may enter and the first prize has
risen steadily over the years, now typically exceeding $5 million. Texas
hold'em has also become a popular spectator sport on TV.
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There are different betting structures for the game. At the World Se-
ries in Las Vegas they play “no limit”, which means just that. The player
whose turn it is to bet may wager up to his entire remaining bankroll.
The University of Alberta group based their research on the “limit raise”
betting structure, where the amount of betting is strictly controlled on
each round.
The Alberta group's first Poker program, developed between 1997
and 2000, was called Loki. It incorporated their first attempt at op-
ponent modelling and the Monte Carlo sampling technique described
in the earlier section on Bridge, and was tested on the IRC Poker site.
Loki's progeny, called Poki, incorporated an improved opponent mod-
elling system and various other improvements. Both programs played at
the strength of average casino players but neither was world class.
Measuring the Strength of a Hand.
Some versions of the University of
Alberta program employ an evaluation function to measure the strength
of the program's two-card hand (the hole cards) in relation to the other
hands, even though the other two-card hands are unknown.
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This mea-
sure is based not only on the program's two cards and the communal
cards dealt thus far, but also on other factors such as the number of play-
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In Texas Hold'em each player is dealt two cards (his
hole
cards) and there will eventually be five
communal cards dealt face up on the table. After the two cards are dealt to each player there follows
the first round of betting. Then comes the
flop
—three communal cards are dealt face up, followed
by the second round of betting. Next there is another communal card, called the
turn
, also dealt
face up, followed by another round of betting. And for those players still in the pot after all this
betting there is a fifth and final communal card, called the
river
, also dealt face up, followed by the
final round of betting. All the players who are still in the pot then show their two hidden cards and
whoever has the best five-card Poker hand from the seven cards (using any combination of his two
hole cards and the five communal cards) is the winner of the pot. If there is a tie, the pot is split
equally.
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This evaluation is calculated by looking at all possible future outcomes (the remaining com-
munal cards that have yet to appear) and computing the percentage of times the program's hand
will improve (called the positive potential) and the percentage of times the program's hand will fall
behind those of its opponents (called the negative potential).
