# Patent application title: Method and Apparatus for Generation of Luck and Skill Scores

##
Inventors:
Adam Bloom (Great Neck, NY, US)

IPC8 Class: AA63F924FI

USPC Class:
463 16

Class name: Amusement devices: games including means for processing electronic data (e.g., computer/video game, etc.) in a chance application

Publication date: 2008-10-09

Patent application number: 20080248851

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# Patent application title: Method and Apparatus for Generation of Luck and Skill Scores

##
Inventors:
Adam Bloom

Agents:
John Santalone, Esq.;Levin Santalone LLP

Assignees:

Origin: LARCHMONT, NY US

IPC8 Class: AA63F924FI

USPC Class:
463 16

## Abstract:

The present invention generally relates to games that involve luck and
skill, such as poker. Specifically, the subject invention provide means,
method and apparatus for the generation of statistics relating to a
player's luck and skill as exhibited in prior games ("luck and skill
statistics" or "luck and skill scores"). In the preferred embodiments,
statistics or scores are generated for participants in a poker game.
These statistics quantify how lucky or skillful a player has been over a
given period of time. The data can be used to enhance the experience of
the viewing public, and to aid a player's self-assessment.## Claims:

**1.**A method of quantifying a player's luck and skill in a game of chance and skill, said method comprises:calculating luck and skill scores for the player by using a formula or a set of formulae based on probability of the player winning hands of the game, pot sizes of the hands, and amounts put in the pots by the player; andusing the luck and skill scores to quantify the player's luck and skill.

**2.**The method of claim 1, wherein the game of chance and skill is a poker game.

**3.**The method of claim 2, wherein the formula or set of formulae comprises L = all streets T S = all streets U whereinL is the luck score;S is the skill score;T is change in expected value V on a given street as a result of a card (or cards) being dealt, or as a result of forced bets (blinds and antes); andU is change in expected value V on a given street as a result of players' unforced action, after all action is complete on that street.

**4.**The method of claim 2, wherein the formula or set of formulae comprisesV

_{i}=C

_{i}P

_{i}-B

_{i}L = ( V 1 - V 0 ) + ( V 3 - V 2 ) + ( V 5 - V 4 ) + ( V 7 - V 6 ) N S = ( V 2 - V 1 ) + ( V 4 - V 3 ) + ( V 6 - V 5 ) + ( V 8 - V 7 ) N L + S = V 8 - V 0 N = V 8 N whereinV

_{0}=expected value before blinds and antes are posted and before hole cards dealtV

_{1}=expected value before action preflop (after blinds and antes posted and after hole cards dealt)V

_{2}=expected value after action preflopV

_{3}=expected value before action postflopV

_{4}=expected value after action postflopV

_{5}=expected value before action on the turnV

_{6}=expected value after action on the turnV

_{7}=expected value before action on the riverV

_{8}=expected value after action on the river (the amount actually won or lost in the hand)C=probability of the player winning the handP=pot sizeB=amount put in the pot by the playerL=luck score for the handS=skill score for the hand, andN=normalization factor.

**5.**A method of enhancing the public viewing of a game of chance and skill which comprises generating luck and skill scores for a player by the method of claim 1 and displaying said scores to the public during said game.

**6.**A method of enhancing the public viewing of a poker game which comprises generating luck and skill scores for a player by the method of claim 3 and displaying said scores to the public during said poker game.

**7.**A method of enhancing the public viewing of a poker game which comprises generating luck and skill scores for a player by the method of claim 4 and displaying said scores to the public during said poker game.

**8.**A method of improving a player's skill level at poker which comprises generating luck and skill scores for the player by the method of claim

**3.**

**9.**A method of improving a player's skill level at poker which comprises generating luck and skill scores for the player by the method of claim

**4.**

**10.**A method of enhancing the experience of a game of chance and skill on the internet which comprises generating luck and skill scores for a player by the method of claim 1 and displaying said scores to the public or to the players after said game.

**11.**A method of enhancing the experience of a poker game on the internet which comprises generating luck and skill scores for a player by the method of claim 3 and displaying said scores to the public or to the players after said poker game.

**12.**A method of enhancing the experience of a poker game on the internet which comprises generating luck and skill scores for a player by the method of claim 4 and displaying said scores to the public or to the players after said poker game.

## Description:

**[0001]**The present invention generally relates to games that involve luck and skill, such as poker. Specifically, the subject invention provide means, method and apparatus for the generation of statistics relating to a player's luck and skill as exhibited in prior games ("luck and skill statistics" or "luck and skill scores"). In the preferred embodiments, statistics or scores are generated for participants in a poker game. These statistics quantify how lucky or skillful a player has been over a given period of time. The data can be used to enhance the experience of the viewing public, and to aid a player's self-assessment.

**BACKGROUND**

**[0002]**Interest in playing and viewing poker has exploded in the last several years. Watching poker on television is more enjoyable now than in the past because there are now miniature cameras installed at the card table which allow the home viewer to see a player's hole cards, which are hidden from the view of his opponents. The player's hole cards are typically displayed on the screen, along with the percentage chance that he will win the hand. As subsequent cards are dealt, these percentages are updated. What makes this exciting is that the announcer can then observe, "John bluffed Greg and got Greg to fold a hand that was a three to one favorite to win, what an aggressive move!" or "John took a really `bad beat` in that hand because Greg's `miracle card` got dealt, allowing Greg to win the hand even though John was a 20:1 favorite to win." In short, exposing the game to viewer scrutiny makes it more interesting.

**[0003]**Poker luck and skill statistics would similarly enhance the experience of the poker game by providing additional statistical information regarding the strength of a player's cards and a player's strategy. It is analogous to the idea of having baseball statistics, like runs-batted-in and on-base percentage. For example, whenever a player wins a World Series of Poker event, the question always arises: Did he get lucky, or was it skill? The question is particularly pertinent when the winner is an amateur and not a professional poker player. Conventional wisdom states that in order to win a particular poker tournament, even a skillful player must also get lucky. While this assessment, which is shared by professional players, is likely to be qualitatively correct, it is not particularly illuminating because it does not answer the questions, "How lucky does the player need to be?" and "How lucky was the winner of that particular game?" To answer these questions, the concept of poker luck and skill scores are used, formulas which provide a quantitative index as to how lucky or skillful a player has been over a given period of time. These formulas are specifically detailed in the next section.

**[0004]**Poker luck and skill statistics can be used by both the poker player and the poker game viewer. The poker viewer's enjoyment of the game is enhanced in the same way that a baseball viewer's enjoyment of the game is enhanced by baseball statistics. For example, when the players' chip stacks are displayed on the screen, their poker luck and skill statistics can be displayed as well. The announcer could then comment, "Greg is up $100,000 in the cash game so far. His cards have not been lucky but he's made up for it by playing well." Or, "Phil is knocked out the tournament complaining about his unlucky bad beats, but we see from his luck score that his cards have actually been quite lucky." A poker fan might attach more significance to wins achieved in the face of lackluster luck scores and high skill scores, and the merits of wins achieved with unusually good luck scores and poor skill scores could be debated.

**[0005]**Additionally, the poker player can use his own poker luck and skill statistics to improve his play. For example, an internet player might observe that using a certain style of play, his success is dependent, or independent, of the quality of his luck score. After a successful game, a player could determine how much his skill reading and bluffing opponents contributed to his victory, and how much his lucky cards played a role.

**[0006]**For a better understanding of the present invention, reference is made to the following description taken in conjunction with the examples.

**DESCRIPTION OF THE INVENTION AND EMBODIMENTS**

**[0007]**Preferred embodiments of the invention are presented below for the purposes of illustration and description. These embodiments are presented to aid in an understanding of the invention and are not intended to, and should not be construed to, limit the invention in any way. All alternatives, modifications and equivalents that may become obvious to those of ordinary skill upon a reading of the present disclosure are included within the spirit and scope of the present invention. Additionally, the present disclosure is not a primer on games of luck and skill, nor on computer software, systems or apparatus for implementing the methods described herein. Basic concepts known to those skilled in the industry have not been set forth in detail.

**The Primary Luck and Skill Scores**--Preferred Area

**[0008]**The primary luck and skill scores are elegant and simple enough for your average poker enthusiast to understand intuitively. They make use of statistical data which is already commonly displayed on poker programs. The following formulas apply to a game of Texas Hold 'Em, although they are easily generalized to any poker variant.

**[0009]**Let

**[0010]**V

_{0}=expected value before blinds and antes are posted and before hole cards dealt

**[0011]**V

_{1}=expected value before action preflop (after blinds and antes posted and after hole cards dealt)

**[0012]**V

_{2}=expected value after action preflop

**[0013]**V

_{3}=expected value before action postflop

**[0014]**V

_{4}=expected value after action postflop

**[0015]**V

_{5}=expected value before action on the turn

**[0016]**V

_{6}=expected value after action on the turn

**[0017]**V

_{7}=expected value before action on the river

**[0018]**V

_{8}=expected value after action on the river (the amount actually won or lost in the hand)

**[0019]**C=probability of the player winning the hand

**[0020]**P=pot size

**[0021]**B=amount put in the pot by the player

**[0022]**L=luck score for the hand

**[0023]**S=skill score for the hand

**[0024]**N=normalization factor

**[0025]**Note that N can be set equal to 1, P

_{1}(the total value of the blinds and antes), the total amount of the stacks of all the players at the table, or even to the total amount of the stacks of all the players (in a tournament structure.)

**[0026]**Note that V

_{0}=P

_{0}=0.

**[0027]**Then

**V i**= C i P i - B i ( 1 ) L = ( V 1 - V 0 ) + ( V 3 - V 2 ) + ( V 5 - V 4 ) + ( V 7 - V 6 ) N ( 2 ) S = ( V 2 - V 1 ) + ( V 4 - V 3 ) + ( V 6 - V 5 ) + ( V 8 - V 7 ) N ( 3 ) L + S = V 8 - V 0 N = V 8 N ( 4 )

**[0028]**Let us examine a specific example, using a normalization factor N=P

_{1}. Suppose that the blinds are $50-$100 and the table is three-handed with Player X in the small blind, Player Y in the big blind, and Player Z on the button. Before the hole cards are dealt, each player has an equal probability of 1/3 of winning the hand. After the blinds are posted and after the hole cards are dealt, but before betting, the probabilities of X, Y, and Z winning the hand are 40%, 20%, and 40%, respectively. Z calls $100, X folds, and Y checks. With X folding, the probabilities of X, Y, and Z winning the hand change to 0%, 40%, and 60%, respectively. After the flop is dealt, the probabilities of Y and Z winning the hand change to 20% and 80%, respectively. Y bets $200, Z raises to $400, and Y calls $200. After the turn card is dealt, the probabilities of winning for Y and Z change to 10% and 90%. Y and Z check the turn. After the river card is dealt, the probabilities for Y and Z winning change to 100% and 0% when Y completes his draw. Y bets $1000, and Z calls. Using equations (1)-(4), we can then generate the following analysis for this hand:

**TABLE**-US-00001 Player X Player Y Player Z Player X Player Y Player Z Player X Player Y Player Z i C

_{i}C

_{i}C

_{i}B

_{i}B

_{i}B

_{i}P

_{i}V

_{i}V

_{i}V

_{i}0 0.33 0.33 0.33 0 0 0 0 0 0 0 1 0.4 0.2 0.4 50 100 0 150 10 -70 60 2 0 0.4 0.6 50 100 100 250 -50 0 50 3 0 0.2 0.8 50 100 100 250 -50 -50 100 4 0 0.2 0.8 50 500 500 1050 -50 -290 340 5 0 0.1 0.9 50 500 500 1050 -50 -395 445 6 0 0.1 0.9 50 500 500 1050 -50 -395 445 7 0 1 0 50 500 500 1050 -50 550 -500 8 0 1 0 50 1500 1500 3050 -50 1550 -1500 L S Player X 0.04 -0.40 Player Y 4.80 5.53 Player Z -4.87 -5.13

**[0029]**Let us examine the results of this analysis to gain an intuitive understanding of the mathematical formulation of the luck score L and the skill score S. Note that for purposes of analysis, after a player folds his hand (as player X did), C

_{i}is set to zero because the player can no longer win the hand, and B

_{i}holds a constant value because the player can no longer change the amount he has already put into the pot. We then observe that the net amount actually lost or won by a player in a given hand is given by the value V

_{8}, the expected value after the action on the river is complete. The question we seek to answer, then, is what portion of V

_{8}was obtained by luck, and what portion was obtained by skill? As a hand progresses, like in the example above, the expected value for a given player will change as a result of two processes: cards are dealt, and action (checking, betting or folding) is taken. In short, the changes in expected value that arise as a result of cards being dealt are attributed to luck, while changes in expected value that arise as a result of players' unforced action are attributed to skill. This statement is captured by equations (2) and (3). Note that in equations (2) and (3), the changes in expected value are divided by N. In the example above, N is set equal to P

_{1}, the total value of the blinds and antes. This is done to "normalize" the statistics, so that a meaningful comparison of luck and skill scores can be made between hands in different games, or between hands which occur early and late in a tournament. In other words, the amount won or lost on a given hand is considered relative to the size of the blinds and antes. Alternatively, by changing the value of N, the amount won or lost on the hand can be considered relative to the total amount of the stacks of all the players at the table, or to the total amount of the stacks of all the players in a tournament structure. N can also be set to 1 so that the statistics are not normalized.

**[0030]**Equation (4) demonstrates that V

_{8}/N, the normalized amount won (or lost) by the player in the hand, is the sum of the normalized amount attributable to luck and the normalized amount attributable to skill. In the example above, player Y's $1,550 win is attributable to both good luck (L=4.80) and skill (S=5.53), with slightly more skill than luck. Player Z's $1,500 loss is attributable to both bad luck (L=-4.87) and lack of skill (S=-5.13), with slightly more lack of skill than bad luck. Player X's $50 loss is attributable to good luck (L=0.07) with a greater lack of skill (S=-0.40). Understandably, the amounts of luck and skill involved in Player X's small loss are orders of magnitude less than the amounts involved with Player Y's larger win and Player Z's larger loss.

**[0031]**Now that we have examined the luck score and skill score for a given hand, what is the overall luck score l and overall skill score s for a given number of hands over a given time period? There are two ways this can be reported. The overall scores for a given number of hands can be either: the average of the scores for each individual hand,

**l**= L (5)

**s**= S (6)

**or the sum of the scores for each individual hand**,

**l**= all hands L ( 7 ) s = all hands S ( 8 )

**[0032]**A few comments about the luck and skill scores are in order. It is important to note that the way luck and skill are calculated does not imply that the best strategy is to maximize expected value for each and every given hand. Rather, the best strategy is to maximize expected value over the game, which encompasses all the hands. So, for example, an aggressive player might incur a negative skill score for a given hand while deliberately creating a table image. However, this move might allow him to maximize his skill score for a later, larger pot when his opponents don't give him credit for a premium hand.

**[0033]**There are many intuitive and practical advantages to calculating the luck and skill scores in the way described above. First, the luck and skill scores are calculated using information which is already displayed to the poker television viewer: percentage chance of winning, pot size, and amount each player is putting in the pot. Second, the scores give mathematical validity to the intuitive concept that a skilled poker player will "get his money in with the best of it"; in other words, increase the pot size when he is statistically favored to win. When a player holding the worse hand bluffs another player out of a pot, this is reflected positively in the bluffer's skill score and negatively in the loser's skill score. When a player "sucks out" on the river, this is reflected positively in his luck score and negatively in his opponent's luck score. A final advantage to calculating luck and skill scores in this way is that knowledge of the board cards that would have been dealt had players stayed in the hand until showdown is not required. If a player folds before the flop, for example, whether or not he would have had the best hand on the river does not affect his luck or skill scores.

**[0034]**It should be noted that the formula for the expected value V is easily adjusted to the situation in which there is a chance of a split pot. Equation (1) then becomes

**V**= ( CP - B ) + e P f ( 9 )

**Where**

**[0035]**e=the probability of the player winning a split pot

**[0036]**f=the number of players sharing in the split pot

**[0037]**C=probability of the player winning the pot (without splitting)

**[0038]**P=pot size

**[0039]**B=amount put in the pot by the player

**[0040]**The expected value V is also easily adjusted to the situation in which there is a side pot. Equation (1) then becomes

**V**=(CP-B)+(cp-b) (10)

**Where**

**[0041]**C=the probability of winning the main pot

**[0042]**P=size of the main pot

**[0043]**B=amount put into the main pot by the player

**[0044]**c=the probability of winning the side pot

**[0045]**p=the size of the side pot

**[0046]**b=amount put into the side pot by the player

**[0047]**The luck and skill scores as described above are also easily generalized to any poker variant with different numbers of streets or cards. Equations (2) and (3) then become

**L**= all streets T ( 11 ) S = all streets U ( 12 )

**Where**

**[0048]**T=change in expected value V on a given street as a result of a card (or cards) being dealt, or as a result of forced bets (blinds and antes)

**[0049]**U=change in expected value V on a given street as a result of players' unforced action, after all action is complete on that street

**The Secondary Luck and Skill Scores**--Other Areas

**[0050]**There may be debate over what formulas best capture a player's luck and skill, just as there is debate over whether a baseball player's prowess is best measured by home runs, slugging percentage, on-base percentage, or runs-batted in. Perhaps there will be other luck and skill scores proposed which use slightly different formulas than those illustrated above. Although it is believed that the primary luck and skill scores as described in the earlier section are the best mode for practicing the invention, other luck and skill scores derived from different formulas may provide additional insight as well. These other formulas are termed "secondary poker luck and skill statistics" herein, and are considered part of the present invention. As an example, a different scheme for calculating poker luck, and the rationale behind it, is detailed below.

**[0051]**A player's luck score L

_{n}for the n

^{th}hand is as follows:

**L n**= 1 - p - 1 h - 1 ( 13 )

**where**

**[0052]**p=placing in the hand (1

^{st}, 2

^{nd}, 3

^{rd}, . . . ) if all the players had played their cards until showdown (i.e., no one folds), and

**[0053]**h=the total number of players dealt cards in the given hand.

**[0054]**If there is a tie for a placing, then a player's luck score L

_{n}for the n

^{th}hand is determined as follows. Assume that q players are tied for p

^{th}place. Then each tied player's luck score is the average of the luck score for p

^{th}place, (p+1)

^{th}place, . . . , and (p+s-1)

^{th}place:

**L n**= 1 q i = p p + q - 1 1 - i - 1 h - 1 ( 14 )

**[0055]**Simplifying via the well-known relation

**j**= 1 m j = m ( m + 1 ) 2

**we obtain**

**L n**= 1 - p + q - 3 2 h - 1 = [ 1 - p - 1 h - 1 ] - q - 1 2 ( h - 1 ) ( 15 )

**[0056]**Equation (3) demonstrates that the luck score of a player tied for p

^{th}place is the luck score the player would have received if he were untied for p

^{th}place, reduced by the factor

**q**- 1 2 ( h - 1 ) .

**[0057]**The player's luck score l for the period of interest, for example all the hands of a single tournament, is then the average of all the individual luck scores for each hand:

**l**= 1 k n = 1 k L n ( 16 )

**where**

**[0058]**L

_{n}is the luck score for the n

^{th}hand of k total hands.

**[0059]**Let us examine a concrete example. Consider the case of Players A, B, C, D, and E who play a hand of poker. Without regard for the action that actually transpires (who stays in the hand until showdown and who folds), we consider the relative strength of each player's final hand if they all stayed in the hand until showdown. We determine, by knowing all the players' hole cards and all the board cards, that A, B, C, D, and E would have placed first, second, third, fourth, and fifth respectively. Applying equation (1) we find the following:

**TABLE**-US-00002 Player Luck Score A 1 B 0.75 C 0.5 D 0.25 E 0

**[0060]**Simply put, the first place player will always have a luck score of 1, the last place player will always have a luck score of 0, and the remaining players will be distributed at equal intervals between 0 and 1.

**[0061]**If A and B have the same strength hands, which beat the same strength hands of C, D, and E, then A and B can be said to have tied for first place, with C, D, and E tying for third place. Equation (3) then yields:

**TABLE**-US-00003 Player Luck Score A 0.875 B 0.875 C 0.25 D 0.25 E 0.25

**[0062]**Simply put, the luck score of A and B is the average of the luck scores for untied first and second place, and the luck score of C, D, and E is the average of the luck scores for untied third, fourth and fifth place.

**[0063]**Several points should be raised about the features of this secondary luck score. First, it is clear that a player's average luck score, in the absence of cheating, will tend towards 0.5 with a variance that decreases as then number of hands increases. Expressed as a percentage, the primary luck score becomes more intuitive for the average poker player or fan: the average luck score is 50%, the luckiest possible score is 100%, and the unluckiest score is 0%. It is clear that after numerous hands, a professional poker player's average lifetime luck score will be minimally different from 50%. Therefore, if the professional has a better than average winning record, this can be attributed to skill, because the luck score has evened out. However, a professional player's luck score at a tournament's final table, which would involve far fewer hands, is of significance because it may well be different from 50%. It would be of great interest to correlate the professional's luck score at the final table with his placing in the tournament.

**[0064]**Second, it is important to note that the formula considers the strength of the hands as if no one folded, regardless of the fact that often poker hands are not played to showdown. The reason for this is that a player cannot claim that his cards are unlucky if he folds before he can be the recipient of his lucky cards, even if folding was the prudent strategy. In fact, if folding is the prudent strategy, then it may have been made so by a skillful opponent who bet in order to induce the fold. Conversely, one might consider a player who is dealt pocket aces more than his statistical fair share to be lucky--but not if the pocket aces are always beaten at showdown by another player who doesn't fold and makes a better hand! It is therefore simpler to avoid the issue of whose cards were better earlier in the hand and consider only the relative strength of each player's final hand had it been played to showdown.

**[0065]**Third, the formulation of the secondary luck score only takes into account how each player's hand places relative to the others. It does not take into account, for example, how much stronger the first place hand is compared to the second place hand. Nor does the secondary luck score consider the absolute strength of a player's hand. The reason for this is that it is unclear whether having a much stronger hand is luckier or not. If a player's hand is much stronger than his opponent's, then the player can make larger bets with more confidence and thus win more money. On the other hand, if the opponent possesses a relatively weak hand, the opponent is more likely to fold, denying the player a chance to make a big win. It is therefore simpler to avoid this issue and consider only the relative placing of each player's hand.

**[0066]**It is arguable that this secondary luck score is not the best quantitative measure of a player's luck, precisely because it does not take into account factors like whose hand was the strongest on earlier streets, and how much stronger the hand was. Also, to compute the secondary luck score, even if the hand doesn't go to showdown, knowledge of the board cards that would have been dealt is required. This information is not usually displayed to the poker player or viewer. The primary luck and skill scores are better compared to the secondary luck score in both these respects.

**Venues in Which to Use the Luck and Skill Scores**

**[0067]**Televised Events.

**[0068]**If the event is televised, the poker luck and skill scores could be displayed alongside each player's name at the end of each hand, or they could be displayed at the same time the current standings and chip counts are shown. The commentator could then analyze the action using this information. For example, the commentator might tell the viewers that "Bob the amateur wins a big pot this hand using a large amount of skill and a lesser amount of good luck." The commentator might observe that "Phil the poker professional has gone broke in this cash game; despite a positive amount of skill, he lost because of a greater amount of bad luck." The luck and skill scores would thus help answer in an objective way how skillful and lucky a player had been during the game.

**[0069]**In order to calculate the luck and skill scores, you have to know the hole cards dealt to each player, as well as the community cards that are dealt. If the game is on the internet, these data can easily be obtained and computed. For a televised event, particularly the World Series of Poker Main Event, the number of entrants (over 5,000 in 2005 and 8,000 in 2006) and the number of hands played probably preclude complete data collection. One possible solution is to start collecting this data only after all but twenty players have been eliminated, and present to viewers the overall scores for these final tables. Alternatively, the luck and skill scores for individual hands (and not the overall scores) can be easily captured from featured tables earlier in the tournament.

**[0070]**Live Casino Games.

**[0071]**During a live casino game, data collection can be automated by using a previously patented device, the "Card Game Dispensing Shoe with Barrier and Scanner" (U.S. Pat. No. 6,582,301 B2). The dispensing shoe can record the cards that are dealt. A device to record the amounts put into the pot by the players and to record when they fold would also be necessary. Taken together with the data from the shoe, the overall luck and skill scores could be generated, and presented to the players involved in a live casino game once the game is over.

**[0072]**Internet Games.

**[0073]**If the game is on the internet, all the necessary data is easily captured. At the end of a tournament or cash game, each player's standing, overall luck score, and overall skill score could be calculated and listed. Each player could then assess his own performance by seeing how much skill and luck (or lack thereof) contributed to his success or failure. It would be very interesting to analyze the data from numerous games to see how lucky the winners typically are, or to determine which poker variants empirically require more or less luck to win.

**[0074]**Video Poker Machines.

**[0075]**These machines, described by others, essentially convert a conventional poker table (using a human dealer, real playing cards, and chips) to a computerized, electronic facsimile. Players using these machines make bets and view their cards via computer terminals around the table. Players place these bets and view their cards the same way that they do while playing on the internet. These machines allow players to congregate around the table while playing each other via the computer, without the need for a human dealer. A "home game" version of these machines is also possible, where each player holds a compact, easily portable, computerized tablet which is wirelessly linked to the tablets held by his opponents. Data collection to calculate the luck and skill scores via these machines is as easy as it would be on the internet. The scores could then be displayed to the players at the end of a cash game or at the conclusion of a tournament.

**[0076]**The invention comprises the methods, apparatus and systems which implement the formulas described above, including computer-implemented systems. Where the invention is carried out by means of computer apparatus, the invention encompasses suitable executable computer instructions, including routines, subroutines, programs, objects, data structures and the like that perform certain functions or manipulate or implement the data of interest.

**[0077]**The invention can be practiced with any suitable combination of processing, input/output devices, display devices, and/or general-purpose or special-purpose processors or logic circuits programmed with the methods of the invention. Such devices can include, for example, personal computers, servers, client devices, personal data assistants (PDAs), hand-held devices, laptops, programmable electronics, computer networks, such as, for example, a personal computer network, a mainframe, and a suitable distributed computing environment that includes any of the foregoing.

**[0078]**While the invention has been described with reference to specific embodiments thereof, it should be understood that the invention is capable of further modifications and that this disclosure is intended to cover any and all variations, uses, or adaptations of the invention which follow the general principles of the invention. All such alternatives, modifications and equivalents that may become obvious to those of ordinary skill in the art upon reading the present disclosure are included within the spirit and scope of the invention.

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