COMPUTER GAMING SYSTEM
First Claim
1. In a computer gaming system, a method for generating card playing strategies for a game of cards comprising at least one round of betting comprising the steps of:
- determining possible action sequences for a round of said game for each player of said game;
determining possible outcomes for said round of said game resulting from said action sequences;
assigning variables representing dividing points between intervals of a card hand strength hierarchy for each player, each of said intervals corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a particular action sequence;
constructing an expression for an expected return to a player for said game using said variables;
deriving expressions for said variables that maximize said expected return;
evaluating said expressions to obtain values for said variables;
identifying endpoints of said intervals of said card hand strength hierarchies of said players using said values.
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Accused Products
Abstract
The present invention comprises an intelligent gaming system that includes a game engine, simulation engine, and, in certain embodiments, a static evaluator. Embodiments of the invention include an intelligent, poker playing slot machine that allows a user to play poker for money against one or more intelligent, simulated opponents. In one embodiment, the invention generates card playing strategies by analyzing the expected return to players of a game. In one embodiment, a multi-dimensional model is used to represent possible strategies that may be used by each player participating in a card game. Each axis (dimension) of the model represents a distribution of a player'"'"'s possible hands. Points along a player'"'"'s distribution axis divide each axis into a number of segments. Each segment has associated with it an action sequence to be undertaken by the player with hands that fall within the segment. The dividing points delineate dividing points between different action sequences. The model is divided into separate portions each corresponding to an outcome determined by the action sequences and hand strengths for each player applicable to the portion. An expected return expression is generated by multiplying the outcome for each portion by the size of the portion, and adding together the resulting products. The location of the dividing points that result in the maximum expected return is determined by taking partial derivatives of the expected return function with respect to each variable, and setting them equal to zero. The result is a set of simultaneous equations that are solved to obtain values for each dividing point. The values for the optimized dividing points define optimized card playing strategies.
207 Citations
33 Claims
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1. In a computer gaming system, a method for generating card playing strategies for a game of cards comprising at least one round of betting comprising the steps of:
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determining possible action sequences for a round of said game for each player of said game;
determining possible outcomes for said round of said game resulting from said action sequences;
assigning variables representing dividing points between intervals of a card hand strength hierarchy for each player, each of said intervals corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a particular action sequence;
constructing an expression for an expected return to a player for said game using said variables;
deriving expressions for said variables that maximize said expected return;
evaluating said expressions to obtain values for said variables;
identifying endpoints of said intervals of said card hand strength hierarchies of said players using said values. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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9. A method for generating card playing strategies for a game of cards comprising at least one round of betting comprising the steps of:
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determining possible action sequences for a round of said game for each player of said game;
determining possible outcomes for said round of said game resulting from said action sequences;
assigning variables representing dividing points between intervals of a card hand strength hierarchy for each player, each of said intervals corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a particular action sequence;
constructing an expression for an expected return to a player for said game using said variables;
generating a plurality of simultaneous equations by taking a partial derivative of said expected return expression with respect to each of said variables and setting said expected return expression equal to zero;
solving said simultaneous equations to obtain values for said variables;
identifying endpoints of said intervals of said card hand strength hierarchies of said players using said values. - View Dependent Claims (10, 11, 12, 13, 14, 17, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30)
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15. In a computer gaming system, a method for generating a virtual hand for a card game having a hand strength ranking corresponding to a value of a action sequence triggering variable representing a dividing point between first and second intervals of a card hand strength hierarchy for a player, said first interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a first action sequence, said second interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a second action sequence, wherein said hand strength hierarchy of said player comprises a first hand in said first interval having a hand strength immediately below said value of said variable and a second hand in said second interval having a hand strength immediately above said value of said variable, said method comprising the steps of:
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determining a ratio between (i) a difference between said hand strength of said second hand and said value of said variable and (ii) a difference between said hand strength of said second hand and said hand strength of said first hand;
undertaking said second action sequence with a fraction of said first hands equal to said ratio.
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16. In a computer gaming system, a method for generating a virtual hand for a card game having a hand strength ranking corresponding to a value of a action sequence triggering variable representing a dividing point between first and second intervals of a card hand strength hierarchy for a player, said first interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a first action sequence, said second interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a second action sequence, wherein said hand strength hierarchy of said player comprises a first hand in said first interval having a hand strength immediately below said value of said variable and a second hand in said second interval having a hand strength immediately above said value of said variable, said method comprising the steps of:
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determining a first ratio between (i) a difference between said value of said variable and said hand strength of said first hand and (ii) a difference between said hand strength of said second hand and said hand strength of said first hand;
undertaking said first action sequence with a fraction of second hands equal to said first ratio.
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18. An article of manufacture comprising:
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a computer usable medium having computer readable program code embodied therein for generating card playing strategies for a game of cards, the computer readable program code in said article of manufacture comprising;
computer readable program code configured to cause said computer to manipulate a plurality of variables representing dividing points between intervals of a card hand strength hierarchy for each player of said game, each of said intervals corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a particular action sequence;
computer readable program code configured to cause said computer to construct an expression for an expected return to a player for a round of said game using said variables;
computer readable program code configured to cause said computer to derive expressions for said variables that maximize said expected return;
computer readable program code configured to cause said computer to evaluate said expressions to obtain values for said variables.
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26. An article of manufacture comprising:
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a computer usable medium having computer readable program code embodied therein for generating card playing strategies for a game of cards, the computer readable program code in said article of manufacture comprising;
computer readable program code configured to cause said computer to manipulate a plurality of variables representing dividing points between intervals of a card hand strength hierarchy for each player of said game, each of said intervals corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a particular action sequence;
computer readable program code configured to cause said computer to construct an expression for an expected return to a player for a round of said game using said variables comprising computer readable program code configured to cause said computer to determine products of an expected return for each of a plurality of outcomes of said round of said game and a probability of the occurrence of said outcome;
computer readable program code configured to cause said computer to derive expressions for said variables that maximize said expected return comprising computer readable program code configured to cause said computer to generate a plurality of simultaneous equations by taking a partial derivative of said expected return expression with respect to each of said variables and setting said expected return expression equal to zero;
computer readable program code configured to cause said computer to evaluate said expressions to obtain values for said variables comprising computer readable program code configured to cause said computer to solve said simultaneous equations to obtain values for said variables.
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31. An article of manufacture comprising:
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a computer usable medium having computer readable program code embodied therein for generating a virtual hand for a card game having a hand strength ranking corresponding to a value of a action sequence triggering variable representing a dividing point between first and second intervals of a card hand strength hierarchy for a player, said first interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a first action sequence, said second interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a second action sequence, wherein said hand strength hierarchy of said player comprises a first hand in said first interval having a hand strength immediately below said value of said variable and a second hand in said second interval having a hand strength immediately above said value of said variable, the computer readable program code in said article of manufacture comprising;
computer readable program code configured to cause said computer to determine a ratio between (i) a difference between said hand strength of said second hand and said value of said variable and (ii) a difference between said hand strength of said second hand and said hand strength of said first hand;
computer readable program code configured to cause said computer to output a value representing a fraction of said first hands equal to said ratio with which to undertake said second action sequence.
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32. An article of manufacture comprising:
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a computer usable medium having computer readable program code embodied therein for generating a virtual hand for a card game having a hand strength ranking corresponding to a value of a action sequence triggering variable representing a dividing point between first and second intervals of a card hand strength hierarchy for a player, said first interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a first action sequence, said second interval corresponding to a subset of hands from said player'"'"'s card hand strength hierarchy with which said player undertakes a second action sequence, wherein said hand strength hierarchy of said player comprises a first hand in said first interval having a hand strength immediately below said value of said variable and a second hand in said second interval having a hand strength immediately above said value of said variable, the computer readable program code in said article of manufacture comprising;
computer readable program code configured to cause said computer to determine a first ratio between (i) a difference between said value of said variable and said hand strength of said first hand and (ii) a difference between said hand strength of said second hand and said hand strength of said first hand;
computer readable program code configured to cause said computer to output a value representing a fraction of said second hands equal to said first ratio with which to undertake said first action sequence. - View Dependent Claims (33)
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Specification