Abstract:
A series of strategy cards that provide a convenient means for players of a Texas Hold&#39;em Poker game to judge the strength of their pre-flop hands, otherwise referred to as their hold card sets or combinations. The relative strength of hold cards in Texas Hold&#39;em Poker changes based on the number of players that are in a pot. The relative strength information is presented to the player in an easy to understand matrix that utilizes ordinal rankings and possibly a color coding scheme. The strategy systems may be shaded based on expected value, and the hold card sets may be abbreviated to allow both easy reference and allow printing onto small form factors that are convenient for pocket storage.

Description:
PRIORITY CLAIM 
       [0001]    This application claims priority to U.S. Provisional Patent Application No. 60/910,615 filed on Apr. 6, 2007, the contents of which are incorporated herein by reference in their entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    This invention relates generally to systems and methods for playing a card game such as Texas Hold&#39;em poker, and, more specifically, to a strategy system usable by a player to ascertain a relative strength of the player&#39;s hold cards and methods of using the strategy system during a poker game. 
       BACKGROUND OF THE INVENTION 
       [0003]    Texas Hold&#39;em poker is a popular variant of Poker. The game is typically played with between two to ten players. Texas Hold&#39;em poker derives its name because each player has two sure-down cards, the value of which remains hidden from other opponents (commonly referred to as “hold cards”). In addition to the “hold cards”, five “Community” cards are revealed (in stages, called the “Flop”, “Turn” and “River”) by the dealer who deals to all players. From the seven cards available to each player (the two hold cards and the five community cards), each player builds a five card poker hand, and then wagers on this hand. 
         [0004]    Like most variants of poker, the objective of Texas Hold&#39;em is to win pots, where a pot is the sum of the money wager by oneself and other players in a hand. A pot is won either at the end of the hand by forming the best five card poker hand out of the seven cards available, or by wagering to cause other players to fold and thus abandon their claim to the pot. In the event of a tie (two or more players having the same ranked hand), the pot is described as “split” and each player receives a proportional share. 
         [0005]    There are variants of the Texas Hold&#39;em poker based on rules of wagering (two popular variants being: Limit and No-Limit). These variants dictate the locations in the game where players can wager on their cards, and also the maximum and minimum wager amounts that can be made at each opportunity. These variants do not affect the odds and probabilities of the game, just the wagered amount. 
         [0006]    Similarly, there are also variants of Texas Hold&#39;em poker which describe fixed wagers (entry fees, or “antes”) that each player needs to make in order to play each hand, and also some variants dictate forced wagers (referred to as “blinds”) that are rotated around based on dealer position. As above, these variations adjust the “pot” or money wagered on each hand, and not the probabilities of the game. 
         [0007]    The ranking of poker hands is based on a variety of ways that the five cards can be arranged into patterns. The ranking of hands is ordered based on the probability of these hands being dealt at random, with the “higher” or better hands having the smallest chance of occurring, and the “weaker” hands having the higher probability. 
         [0008]    In Texas Hold&#39;em poker, all suits are equivalent and two hands that are the same rank and different only in the suit are equivalent. 
         [0009]    Cards are ranked from highest to lowest as follows: Ace, King, Queen, Jack, Ten, Nine, Eight, Seven, Six, Five, Four, Three, Two, Ace. The Ace being special as it can be either ranked as either “High” or “Low” depending on where it will contribute to the highest hand ranking. 
         [0010]    The ranking of hands is described below from a strongest hand to a weakest hand. 
         [0011]    Straight Flush All card of the same suit, and numerically adjacent. e.g. Four, Five, Six, Seven, Eight of Spades. In the event that two (or more) players have a straight flush, the player with the highest card in their flush wins. The highest possible straight flush is: Ten, Jack, Queen, King, and Ace (commonly referred to as a “Royal Flush”). The Ace can also be used to represent a “one” in a Straight Flush to form the lowest Straight Flush of: Ace, Two, Three, Four, Five. (commonly referred to as a “Wheel”) 
         [0012]    Four of a Kind All four cards of the same value, with one extra card (called a “Kicker”) e.g. a hand with all (four) Fives in it. In the event that two (or more) players have four of a kind, the player with the highest set of cards wins. In the event that all players have the same four cards, the value of one remaining card, the “kicker”, is used as a tie-breaker, with the player holding the higher card being declared the winner. In the event that the kicker card is also the same value, the hand is a tie. 
         [0013]    Full House This is a hand comprising of three cards of the same value, and two cards of another value, e.g. three Kings and two Sevens. In the event that two (or more) players have a full house, the player with the higher ranking of their three card set is determined to have the higher hand. In the event of all players have the same value of the three card set, the hand is disambiguated by the ranking of the other two cards. In the event that all players also have the same value, the hand is a tie. 
         [0014]    Flush This is a hand in which all five cards are the same suit, e.g. Ace, Ten, Seven, Five, Two of Spades. In the event that two (or more) players have a flush, the hands are disambiguated by the value of the highest card in each player&#39;s hand. If there is a tie on this card, the value of the next highest card in each players hand is compared; and so on until a winner is declared. 
         [0015]    Straight This is a hand in which all five cards are numerically linked in order with no gaps, e.g. Eight, Nine, Ten, Jack, Queen. In the event that two (or more) players have a straight, the hands are disambiguated with the winner of the hand being the player whose straight has the highest card at the top of the straight. In the event that two (or more) players have a straight with the same high card, the hand is a tie. The make-up of the suits used to make the straight is of no significance, and all straights with the same value are equivalent (with the exception that if all the cards are the same suit then the hand would have been classified as a Straight Flush—see above). As with a Straight Flush, an Ace can be used at either end of the Straight. 
         [0016]    Three of a Kind This is a hand in which there are three cards of the same value e.g. three Nines. In the event that two (or more) players have three of a kind, then the player with the highest set of three cards is deemed the winner. In the event that two (or more) players have three cards of the same value, then the value of the two remaining cards (called kickers) is used to determine the winning hand as follows: the player with the highest ranked kicker card is determined the winner. In the event that two (or more) players also share the same value for their highest ranked kicker card, the value of the last remaining kicker card is compared and the player with the highest kicker, overall, is determined the winner. In the event that both players also share highest kicker, the hand it deemed a tie. 
         [0017]    Two Pair This is a hand in which there are two sets of cards, both of the same value. E.g. two Aces, and two Eights. In the event that two (or more) players have two pair, then the player with the highest ranked set of two cards is deemed the winner. In the event that two (or more) players share the same highest pair, the player with the highest ranked lower pair is deemed the winner. In the event that two (or more) players have the same two pairs of cards, the remaining single card (called a kicker) is used to determine the winning hand. The player with the highest ranked kicker card is deemed the winner. In the event that two (or more) players also have the same kicker card, then the hand is deemed a tie. 
         [0018]    Pair This is a hand in which there are two cards of the same ranking. E.g. two Kings. In the event that two (or more) players have a pair of cards, the player with the highest ranked pair of cards is determined the winner. In the event that two (or more) players have the same ranked pair, the remaining cards in a players hand (the kickers) are used to determine the higher hand. Each player compares his kicker cards in order from highest to lowest, and the player with the highest distinct kicker card is deemed the winner. In the event that two (or more) players also have the same kicker cards, the hand is deemed a draw. 
         [0019]    High Card This is a hand that cannot be classified by any of the above higher rankings e.g. Queen high. In the event that two (or more) players have a high card hand, the player with the highest distinct card is deemed the winner. In the event that two (or more) players have the same high card, the hands are disambiguated by the next highest card in each players hand, and so on until either a winner is determined, or, if the players have the same hand then a tie is declared. 
         [0020]    It would be desirable to have a method for determining whether it is advantageous to remain in the pot during the poker game. 
       SUMMARY OF THE INVENTION 
       [0021]    According to at least one embodiment of the invention, a strategy system for determining a relative strength or ranking of a set of hold cards during a Texas Hold&#39;em poker game includes a layout of the possible hold card pairs and where each of the hold card pairs is arranged in a selected manner and associated with at least an ordinal ranking that provides a relative ranking of each hold card pairs. In one embodiment, the ordinal rankings may be grouped or otherwise arranged and associated with particular colors (i.e., color coded). Thus, color coding the ordinal rankings may provide a more visually apparent indicator of the relative strengths of each set of hold cards. 
         [0022]    A strategy system for playing Texas Hold&#39;em Poker includes a plurality of matrices, where separate systems or matrices may be generated for different numbers of players in a given hand. The matrices indicate the ranking of each possible combination of starting hold card pairs such that a player with a first set of hold cards may easily determine their relative chances of winning or drawing in the present hand in the event the player were to play these cards to the end of the hand. The respective rankings may take the form of ordinal ranking indicators, a color coded grid or scheme, or a combination of both and where each grid may include a number that represents the ranking of the relative strength of that set of hold cards. The generated matrices are computed based on a probability that the player&#39;s set of hold cards will comprise a portion of the winning hand against all other possible combinations of hands while excluding the player&#39;s set of hold cards from the computation. 
         [0023]    In one embodiment, the strategy system is determined using a Monte Carlo simulation because determining an exact solution while superimposing a number of probabilities in view of a large array of card combinations becomes mathematically unfeasible, if not impossible. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0024]    Preferred and alternative embodiments of the present invention are described in detail below with reference to the following drawings: 
           [0025]      FIG. 1  is a strategy system for determining a relative strength of a set of hold cards with respect to a first number of players at a card game according to an embodiment of the invention; 
           [0026]      FIG. 2  is a strategy system for determining a relative strength of a set of hold cards with respect to a second number of players at a card game according to another embodiment of the invention; 
           [0027]      FIG. 3  is a kit for viewing a number of strategy systems based on a number of players at a card game according to another embodiment of the invention; and 
           [0028]      FIG. 4  is a strategy system for determining a relative strength of a set of hold cards with individual cards represented along horizontal and vertical axes according to another embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0029]    In the following description, certain specific details are set forth in order to provide a thorough understanding of various embodiments of the invention. In other instances, well-known systems, methods, and rules associated with card games, and in particular poker card games, may not be shown or described in detail to avoid unnecessarily obscuring descriptions of the embodiments of the invention. 
         [0030]    A common mistake when playing Texas Hold&#39;em poker is for players to enter into a pot with “poor” hold cards. Poor hold cards are cards that have a low probability of maturing into the winning hand by the time all the community cards are dealt. Because of the many variables that must continually be taken into consideration (e.g., the number of players in the current hand, the number of players remaining in the current game, the current minimum wager per player to stay in the hand, the wagering aggressiveness or non-aggressiveness of opposing players, etc.), many players find it difficult to distinguish between good hold cards and poor hold cards. The present invention relates generally to a strategy system and method of comparing a relative strength of different combinations of hold cards when pre-computed probabilities are assigned to every possible combination of hold cards as these probabilities are further superimposed with a number of players at the table and/or the number of players “in the pot” (i.e., in the current hand). The strategy system ranks, sorts and displays each set of hold card combinations with an assigned ordinal ranking and may also display groups of the hold card combinations in a color coded grid for easy reference. 
         [0031]    When a player is dealt their two hold cards, they must make a decision whether to play these cards (typically requiring a wager), or fold them. This decision is sometimes referred to as “pre-flop” wagering decision, and needs to be made before any additional cards are seen. Thus, it would be advantageous if the player could make their pre-flop wagering decision based on some probability that the hold cards held by the player may eventually become part of a winning hand (ignoring any bluffing the player and/or his opponents may perform). For Texas Hold&#39;em poker, the winning hand is based on the highest five cards out of seven cards (a set of hold cards and five community cards). 
         [0032]    Over the course of a poker game, the primary objective of the players is not to win every individual pot, but rather to make mathematically and strategically correct decisions. As a result of making such decisions, the players may hopefully be able to maximize their time in the game and consequently win more money than they lose over the course of a game and particularly over the course of a tournament (a continually running poker event that may take days). 
         [0033]    The strategy system as described herein ranks the strengths of the starting hands depending on the number of players that are in the pot. For example, a good set of hold cards when playing with a small number of players may actually be a poor set of hold cards when playing with many opponents (and vice versa). In one embodiment, the strategy system allows players to look at their hold cards, find the appropriate matrix for the number of players in the current hand, and then look up the strength of their hold cards relative to all other possible starting hold cards. Armed with this information, the player may advantageously make improved mathematical and strategic decisions on how to continue playing out the present poker hand. 
         [0034]    Because the odds change depending on the number of players in the pot, the strategy system provides a packet or a kit of cards with ordinal rankings of all the possible starting hold cards correlated with the number of players in the pot. By way of example, the packet or kit may provide ordinal rankings of the hold cards correlated to 1+N players, where N&gt;1. 
         [0035]    In one embodiment, the strategy system may be generated based on the probability of a win or a draw and thus may advantageously guide a player in the player&#39;s decision to stay in or abandon a particular pot, especially when the player has an amount of money invested in the poker game. Another way to describe this combined win/draw probability is that it is the inverse of the probability that the player may lose their money in a given hand and moreover over a course of an entire poker game. 
       Superposition of Probabilities 
       [0036]    One of the subtleties of poker is the way cards are grouped between the different rankings of hands Straights (cards numerically in order), Flushes (cards of the same suit) and modal combinations of similar cards (Pairs, Three of a Kind, Full Houses, etc.). For instance, having two cards of the same value, which means having at least a pair, also increases the probability of getting: Two Pair, Three of a Kind, a Full House or Four of a Kind, while decreasing the probability of making a Flush, Straight or Royal Flush. 
         [0037]    Conversely, having two hold cards of the same suit, increases the probability of making a Flush or Royal Flush, and decreases the probability of making other types of hands. 
         [0038]    Two hold cards that are “connected” (numerically different by just one number), increases the probability that a hand could make a Straight. Two hold cards that are “loosely connected” (numerically different by no more than four), increases the probability that a Straight could be made using both of the hold cards. 
         [0039]    All other things being equal, having higher valued hold cards increases the probability of winning the hand, by either using the hold cards directly to make a higher ranked hand, or using one of the hold cards as a high kicker to win over an otherwise equivalent hand. 
         [0040]    As can be seen from the above discussion, the value of the hold cards is a superposition of the probabilities that the holds cards could make each of the possible ranked hands. For instance, if the player has Eight and Nine of Spades, the respective probabilities that the hold cards could make a Straight Flush, Four of a Kind, a Full House, etc. are calculated and then combined to determine an overall strength of the hold cards. 
         [0041]    In addition to the probabilities of making the different hands, the probability of which hand could be the winning hand is also determined. Hence, this is one reason why the relative strength of the ranking hold cards varies in relationship to the number of players. 
         [0042]    More players in the pot, generally means that a higher ranked hand will be needed to win. By way of example, a hand such as a pair has a greater chance of being the winning hand when there are just two people in the pot. When more players remain in the pot, however, typically a higher ranked hand is needed to win. To illustrate this, imagine a hand in which the community cards form a Partial Straight (a Straight missing just one card). With just two players, the chances are small that one of the players has the card needed to complete the straight. However, if there are ten players in the pot (each with two cards), the chances are much higher that someone will have the card needed to complete the Straight. Because of the changes in probabilities of the rankings of hands winning, the relative strength of the hold cards change as the superposition of these probabilities changes. 
         [0043]    When playing with a small number of players, pairs of cards are good (with obviously the higher the value of the pair the better), as are any set of hold cards that has an Ace in them (which is valuable both to make a pair if another Ace appears, but also as a high-card kicker in the event of a tie in the rest of the hand). Whilst having two cards that are suited is always better than having the same two cards unsuited, the chances of making a Flush are small (as are the chances of needing a Flush to win), and so there is only a small difference between the ranking of hold cards that are the same but different only if they are suited or not. 
         [0044]      FIG. 1  shows a strategy system  100  showing ordinal ranking indicia  102  (numbered 1-169) that provide a relative strength of each set of hold cards  104  that are possible with two players in the pot. For purposes of the description herein, each “set” of hold cards  104  indicates the two hold cards that are dealt to each player to start a new hand of cards in the game of Texas Hold&#39;em poker. Further, a “set” of hold cards may be paired, meaning two cards having the same rank within a deck of playing cards (e.g. AA, KK, QQ, JJ, 10-10, 9-9, 8-8, 7-7, 6-6, 5-5, 4-4, 3-3, and 2-2). In the illustrated embodiment, the strategy system  100  is fairly symmetrical along a leading diagonal, which is indicated by a dashed line  106 . Each pair of suited hold cards  104  are characterized with the letter “s” either located next to the hold cards  104  or at least proximate thereto. Each pair of unsuited hold cards  104  are without any special characterization or symbol. Alternatively, the unsuited hold cards  104  may be characterized with a unique character or symbol and the suited hold cards may be without such a character or symbol. In yet another embodiment, the unsuited and suited hold cards  104  may have different fonts, formats, type setting, color, etc. to distinguish one from the other. In one embodiment of the strategy system  100 , the paired sets of hold cards  104  are positioned along the leading diagonal  106  with the suited sets of hold cards  104  located to the right of the diagonal  106  and the unsuited sets of hold cards  104  located to the left of the diagonal  106 . 
         [0045]    By way of example, the ordinal ranking indicia  102  for an Ace-Ace hold card combination is ranked as “#1” and an Ace-King suited hold card combination is ranked as “#8.” In one embodiment, the ordinal ranking indicia  102  may be grouped and respectively color coded to provide a quick, visual check of the relative strength of the set of hold cards  104 . By way of example, the sets of hold cards  104  may be arranged into color coded grid combinations that cooperate with a color coded legend  108  for easy reference. Alternatively stated, the color coding scheme described above provides a quick reference to the strength of a set of hold cards  104 , and thus permits the player to merely glance at the color of the appropriate square in the grid. In one embodiment, the color scheme is represented as a rainbow spectrum. In another embodiment, the color coding scheme may be used to represent only sets of hold cards  104  that have a positive expected value; whereas sets of hold cards  104  with a zero or negative expected value are not colored. 
         [0046]      FIG. 2  shows another strategy system  200  with the relative strengths of sets of hold cards  204  when there are ten players in the pot. In this embodiment, there is a significant shift in the strengths of relative strengths of sets of hold cards  204 , which is further apparent by the ordinal ranking indicia  202 . Having suited cards becomes significantly more important, as does the value of having connected or even loosely connected cards. For instance, the difference between Ace-Ten unsuited and Ace-Nine unsuited when playing with ten players, for example, carries a much greater significance (e.g., the strength of the hold cards and the willingness to stay in the hand). With Ace-Ten, there is a chance of making a straight using both cards, but with Ace-Nine, there is only the chance of making a straight with one of the hold cards, which has a much smaller probability. In addition and with ten players playing the hand, there is a much greater chance that the pot will be split between two or more players if four of the community cards are used to make a straight. In addition, the kickers, which in the present example would be the “nine” and the “ten,” may be the difference between winning or losing the hand. 
       Generation of the Probabilities 
       [0047]    Generating a table of probabilities cannot be performed in isolation. There are only 52 cards in a deck, and each card can only be used once. If a player is holding Ace-King suited in his hand, the probability of this hand making a Full House, Flush, Straight, Two Pair, etc. can be calculated, but to get a true estimate of the chances of this hand winning, this hand should be compared to all other possible hands held by the indicated number of opponents and all possible combinations of community cards. When this calculation is performed, it should be taken into account that there is one less Ace and one less King that can be used by the opposing players and the community cards. For example, because one player holds an Ace and King, it is impossible for another player to have four Aces or four Kings, and also less likely that another player will make a straight containing an Ace or a King. 
         [0048]    As the number of players increases above two, the combinatorial mathematics involved in comparing every single possible variation of a starting hand for each player, combined with every possible combination of starting cards for each opponent, combined with every possible combination of community cards that could be dealt, rapidly makes this problem impossible to solve using a comparison of all combinations. This class of problem is classified or referred to as an np-complete because the vast number of combinations means that this problem cannot be calculated with exactness. 
         [0049]    Accordingly, the generation and superposition of the possibilities is achieved using a mathematical technique called a Monte Carlo simulation. To generate the probability combination, hundreds of millions of hands of poker were randomly dealt and then a record was made if a particular player would have won (or drawn) the hand, had that player stayed in the pot. 
         [0050]    For each set of hold cards, a tally is kept if the hold cards are involved in a winning or tying hand. Next, the possible starting hands are ranked according to their strengths, with the hand that won the most number of times being given a rank #1 (R1), and the hand that won the least number of times being given a rank #169 (R169). The ranking is based on any/all possible hold cards held by opponents. 
       Representing the Relative Strength of the Hold Cards 
       [0051]    Because there is no difference in poker between suits (Hearts, Clubs, Diamonds, Spades) in the hand rankings, there are only 169 possible combinations of sets of hold cards. These 169 combinations represent each possible permutation of the two hold cards, which may be suited (both cards being the same suit) or unsuited (the cards being of different suits). The ordinal ranking indicia  102  ranking number between #1 and #169 showing the relative strength of each set of hold cards relative to the other possible sets of hold cards. 
         [0052]    Referring now to both  FIGS. 1 and 2 , the sets of hold card combinations are displayed on a 13×13 matrix, array or system with the suited sets of hold cards arranged over an upper right portion of the array and the unsuited sets of hold cards arranged over a lower portion of the array, and the respective portions separated by the leading diagonal. It is appreciated and understood that unique matrices may be generated for each number of players in the pot. 
         [0053]    To read the strength of each set of hold cards, the player selects an appropriate card for the number of players in the pot, and then looks at the strategy system to find the player&#39;s hold card combination. Each particular system may include color coded regions, which permits the player to quickly reference and determine the strength of their set of hold cards. In one embodiment, the color scheme is a rainbow scheme, although other colors could be used. 
         [0054]    By way of example and as shown in  FIG. 3 , a kit or package  300  may include strategy systems  302 ,  303 ,  304 ,  305 ,  306 ,  307 ,  308 ,  309  and  310 , for a 2-player pot, a 3-player pot, a 4-player pot, a 5-player pot, a 6-player pot, a 7-player pot, a 8-player pot, a 9-player pot, and a 10-player pot, respectively. Although nine strategy systems are shown in the kit  300 , it is appreciated that the kit  300  may include a greater or less number of systems. 
         [0055]    In one embodiment, the kit  300  may take the form of a poster, a foldable pamphlet, or some equivalent form. 
         [0056]    In another embodiment, hold cards with a positive expected value, which means the hold cards have greater than one 1/nth of a chance of winning with N players in the pot, are shaded with colors. Hold cards with a negative expected value are shaded in gray. As an explanatory example, one can imagine playing against an automaton that always stayed in the pot regardless of automaton&#39;s hold cards. If an opposing player only played with hold cards marked with a color on the matrix, the opposing player would, over the course of many games be more likely to increase their winnings because their selected hold cards would more often than not have a higher strength than the automaton&#39;s hold cards. 
         [0057]      FIG. 4  shows a strategy system  400  having a matrix or array of respective card rankings or strengths according to another embodiment of the invention. This strategy system is a simplified version of the above-described strategy systems. One difference from the above-described strategy systems is that the illustrated strategy system of  FIG. 4  represents the hold cards as individual cards arranged respectively along a horizontal and a vertical axis of the matrix. In addition, the right hand triangular portion of the matrix is used for “suited” hold card pairs while the left hand triangular portion of the matrix is used for “unsuited” hold card pairs. The relative rankings or strengths may again be represented with different colors, for example RED may represent a great set of hold cards and LIGHT GRAY may represent an inferior set of hold cards. But, the illustrated strategy system  400  is not dependent on the number of players at the table or in the pot. Specifically, the rankings (i.e., the color coding scheme) have been normalized to remove the relationship between the relative ranking and the number of players in the pot. 
         [0058]    These and other changes can be made in light of the above detailed description. In general, in the following claims, the terms used should not be construed to limit the invention to the specific embodiments disclosed in the specification and the claims, but should be construed to include all types of card games and card combinations thereof, to include but not limited to poker-type card games that operate in accordance with the claims. 
         [0059]    As discussed above, it is appreciated that the ordinal ranking indicia located on the systems, which provide the strength indication, relate to more than the rules of the game or a presentation of information relating to the game. The indicia provide a structure so as to present information without reference to a separate chart in a simple and effective manner that enables an assessment by the player in the short time available to make a decision while playing the game. 
         [0060]    While the preferred embodiment of the invention has been illustrated and described, as noted above, many changes can be made without departing from the spirit and scope of the invention. For example, other color schemes, display criteria, and probability superpositions may be employed to achieve similar objectives and advantages as described above. Accordingly, the scope of the invention is not limited by the disclosure of the preferred embodiment. Instead, the invention should be determined by reference to the claims that follow.