Title:

Kind
Code:

A1

Abstract:

A method, apparatus, and computer readable storage which determines and tracks a player's error in a game of skill such as video poker. The player error is stored in a player's slot club account so that a beginning player may be entitled to additional complimentaries from the casino. The method includes (a) reading account information on a player's slot club card; (b) allowing the player to complete the hand; (c) calculating expected value points for the hand which incorporate a numerical computation of the player's error; and (d) accumulating the expected value points in the player's slot club account using information stored on the slot club card.

Inventors:

Shackleford, Michael (Las Vegas, NV, US)

Muskin, Jon (Chevy Chase, MD, US)

Muskin, Jon (Chevy Chase, MD, US)

Application Number:

10/460238

Publication Date:

12/16/2004

Filing Date:

06/13/2003

Export Citation:

Assignee:

SHACKLEFORD MICHAEL

MUSKIN JON

MUSKIN JON

Primary Class:

International Classes:

View Patent Images:

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Primary Examiner:

HU, KANG

Attorney, Agent or Firm:

MUSKIN & FARMER LLC (Lansdale, PA, US)

Claims:

1. A method of tracking casino players playing a hand of a game involving skill, the method comprising: reading account information on a player's slot club card; allowing the player to complete the hand; calculating expected value points for the hand which incorporate a numerical computation of the player's error; and accumulating the expected value points in the player's slot club account using information stored on the slot club card.

2. A method as recited in claim 1, wherein the game comprises video poker.

3. A method as recited in claim 2, further comprising: deciding whether to offer a promotion to the player using the accumulated expected value points in the slot club account.

4. A method as recited in claim 3, wherein the promotion comprises converting accumulated expected value points to an incentive dollar amount for discounts.

5. A method as recited in claim 4, wherein the promotion comprises placing playable money for the incentive dollar amount in the player's slot club account.

6. A method as recited in claim 4, wherein the promotion comprises sending a check to the player for the incentive dollar amount.

7. A method as recited in claim 6, wherein the check is cashable only at a particular casino or casino group.

8. A method as recited in claim 2, further comprising accumulating standard comp points in the player's slot club account based on the player's wager which do not incorporate error separate from the expected value points.

9. A method as recited in claim 8, further comprising deciding whether to offer a promotion to the player using information incorporating both the accumulated expected value points in the slot club account and standard comp points in the slot club account.

10. A method as recited in claim 8, further comprising aggregating the standard comp points and the expected value points into one value.

11. A method as recited in claim 10, wherein the aggregating is performed by a casino computer not a video poker machine implementing the hand.

12. A method as recited in claim 10, further comprising deciding whether to offer a promotion to the player using the aggregated points.

13. A method as recited in claim 10, further comprising converting the value to an incentive dollar amount for discounts.

14. A method as recited in claim 13, wherein a promotion comprises placing playable money for the incentive dollar amount in the player's slot club account.

15. A method as recited in claim 13, wherein the promotion comprises sending a check to the player for the incentive dollar amount.

16. A method as recited in claim 15, wherein the check is cashable only at a particular casino or casino group.

17. A method as recited in claim 2, wherein the calculation of expected value points also takes into consideration the player's choice of machine.

18. A method as recited in claim 17, wherein the calculated expected value points incorporates an optimal return for the machine.

19. A method as recited in claim 2, wherein the expected value points are not automatically disclosed to the player electronically.

20. A method as recited in claim 2, wherein the expected value points comprise an equivalent of (optimal value of the dealt hand−expected value of played hand)*bet.

21. A method as recited in claim 21, wherein the expected value points take into consideration a return of the player's machine choice.

22. A method as recited in claim 2, wherein the expected value points comprise an equivalent of (optimal strategy house edge for machine+optimal value of the dealt hand−expected value of played hand)*bet.

23. A method as recited in claim 2, wherein the expected value points take into consideration cash back given to the player.

24. A method as recited in claim 23, wherein the expected value points comprise an equivalent of (optimal strategy house edge for machine−cash back percentage+optimal value of the dealt hand−expected value of played hand)*bet.

25. A method as recited in claim 3, wherein the deciding takes into consideration cash back already given or allotted to the player.

26. A method as recited in claim 2, wherein the expected value points take into consideration cash back given to the player and a return of the player's machine choice.

27. A method as recited in claim 2, further comprising computing a player's skill level as (total expected value points/total amount wagered).

28. A method as recited in claim 2, further comprising computing a player's skill level as (optimal strategy return−(expected value points/total amount bet)).

29. A method as recited in claim 2, further comprising computing a player's skill level as (optimal strategy return+cash back−(expected value points/total amount bet)).

30. A method as recited in claim 2, further comprising computing a future expected loss of the player using the expected value points.

31. A method as recited in claim 2, further comprising computing a future expected daily loss of the player as (average house edge*average hands per day*average wager).

32. A method as recited in claim 2, further comprising computing an average expected value of hands played by the player.

33. A method as recited in claim 2, further comprising: inputting, by a casino employee, the player's identification information on a computer; outputting the player's standard information; and outputting expected value information based on the accumulated expected value points.

34. A method as recited in claim 33, wherein the expected value information comprises a measure of the player's skill.

35. A method as recited in claim 33, wherein the expected value information is equivalent to the average expected value of the player's hands.

36. A method as recited in claim 2, further comprising: inputting, by a casino player, the player's slot club card into a card reader; outputting on a display standard points accumulated by the player stored in the player's slot club account identified on the slot club card; and keeping the expected value points shielded from the player on the display.

37. A method as recited in claim 2, further comprising: identifying the player as an advantage player based on the player's expected return.

38. A method as recited in claim 2, further comprising: identifying the player as an advantage player if the player's (expected total return)>a predetermined expert return.

39. A method as recited in claim 38, further comprising identifying the player as an advantage player if a total number of hands player>a predetermined sample of hands.

40. A method as recited in claim 2, further comprising: identifying the player as an advantage player if the player's (expected total expected value points/amount wagered)<a predetermined amount.

41. A method as recited in claim 40, further comprising identifying the player as an advantage player if a total number of hands player>a predetermined sample of hands

42. A method as recited in claim 2, further comprising: offering a comp amount based on the expected value points and reduced by an amount of standard comps already given.

43. A method as recited in claim 2, wherein the calculated expected value points is a floating point number which is transmitted to a casino computer where the expected value points are accumulated in the player's slot club account.

44. A method as recited in claim 2, wherein the calculated expected value points is a floating point number which is transmitted to a casino computer using an integer representation, the casino computer accumulating the expected value points in the player's slot club account.

45. A method as recited in claim 2, wherein a unit that performs the calculating is installed as a plug-in on a video poker machine implementing the game of video poker.

46. A method of tracking casino players playing a hand of a video poker game, the method comprising: reading account information on a player's slot club card; allowing the player to complete the hand of video poker; calculating expected value points for the hand which incorporate the player's error; accumulating the expected value points in the player's slot club account using information stored on the slot club card; deciding whether to offer a promotion to the player using the accumulated expected value points in the slot club account; computing a player's skill level as (optimal strategy return+cash back−(expected value points/total amount bet)); computing a future expected daily loss of the player as (average house edge* average hands per day*average wager); identifying the player as an advantage player if the player's (expected total return /amount wagered)>a predetermined amount; offering a comp amount based on the expected value points and reduced by an amount of standard comps already given; computing an average expected value of hands played by the player; inputting, by a casino employee, the player's identification information on a computer; outputting the player's standard information; and outputting expected value information based on the accumulated expected value points, inputting, by a casino player, the player's slot club card into a card reader; outputting on a display standard points accumulated by the player stored in the player's slot club account identified on the slot club card; and keeping the expected value points shielded from the player on the display, wherein the expected value points comprise an equivalent of (optimal strategy house edge for machine+optimal value of the dealt hand−expected value of played hand)*bet, wherein the promotion comprises converting accumulated expected value points to an incentive dollar amount for discounts, wherein the promotion comprises placing playable money for the incentive dollar amount in the player's slot club account, wherein the promotion comprises sending a check to the player for the incentive dollar amount, wherein the check is cashable only at a particular casino or casino group, wherein the calculated expected value points is a floating point number which is transmitted to a casino computer where the expected value points are accumulated in the player's slot club account, wherein the expected value information is equivalent to the average expected value of the player's hands, wherein a unit that performs the calculating is installed as a plug-in on a video poker machine implementing the game of video poker.

47. A method of tracking casino players playing a hand of a game involving skill, the method comprising: reading account information on a player's slot club card; allowing the player to complete the hand; calculating expected value points for the hand which incorporate a numerical computation of the player's error; combining the expected value points with standard comp points; and accumulating the combined points in the player's slot club account using information stored on the slot club card.

48. A method as recited in claim 47, further comprising maintaining a ratio of the expected value points to the standard comp points in the player's slot club account.

49. A method as recited in claim 47, wherein the game comprises video poker.

50. A method as recited in claim 49, further comprising: deciding whether to offer a promotion to the player using the accumulated combined points in the slot club account.

51. A method as recited in claim 50, wherein the promotion comprises converting the combined points into an incentive dollar amount for discounts.

52. A method as recited in claim 51, wherein the promotion comprises placing playable money for the incentive dollar amount in the player's slot club account.

53. A method as recited in claim 52, wherein the promotion comprises sending a check to the player for the incentive dollar amount.

54. A method as recited in claim 53, wherein the check is cashable only at a particular casino or casino group.

55. A method as recited in claim 47, wherein the accumulating accumulates the standard comp points and accumulates an extra standard comp point or points when the expected value points reach a certain level.

56. A method of tracking casino players playing a hand of a video poker, the method comprising: reading account information on a player's slot club card; allowing the player to complete the hand; calculating expected value points for the hand based on the player's machine choice; and accumulating the expected value points in the player's slot club account using information stored on the slot club card.

57. A method of marketing to casino players, the method comprising: computing and accumulating expected value points based on a player's error and the player's wager; computing the player's skill level based on the player's error; considering the player's expected value points and the player's skill level to decide whether to offer the player a promotion or incentive.

58. A method of storing player records, the method comprising: storing standard player information in a player record; storing expected value information based on a player's error and wager alongside the standard player information in the player record; and retrieving the standard player information and the expected value information when requested by a client.

59. A method as recited in claim 58, wherein the expected value information comprises points stored as a floating point number.

60. A method of tracking casino players playing a hand of a game blackjack, the method comprising: receiving account information on a player's slot club card; allowing the player to complete the hand of blackjack; calculating expected value points for the hand which incorporate the player's error; and accumulating the expected value points in the player's loyalty account using information stored on the slot club card.

61. A method as recited in claim 60, further comprising: deciding whether to offer a promotion to the player based on the accumulated expected value points in the loyalty account.

62. A method as recited in claim 60, wherein the expected value points comprise an equivalent of (optimal value of the dealt hand−expected value of played hand)*bet.

63. A method as recited in claim 60, wherein the expected value points comprise an equivalent of (optimal value of the dealt hand−expected value of played hand)*bet.

64. A method as recited in claim 60, further comprising computing a player's skill level as (total expected value points/total amount wagered).

65. A method as recited in claim 60, further comprising computing a future expected loss of the player using the expected value points.

66. A method as recited in claim 60, further comprising computing a future expected daily loss of the player as (average house edge*average hands per day*average wager).

67. A method as recited in claim 60, further comprising computing an average expected value of hands played by the player.

68. A method as recited in claim 60, further comprising sending the player a check with an amount based on the expected value points.

69. A method as recited in claim 60, wherein the expected value points reflect the optimal return on the variation of blackjack game played.

70. A method as recited in claim 60, further comprising accumulating standard comp points in the player's loyalty account based on the player's wager which do not incorporate error separate from the expected value points.

71. A method as recited in claim 70, further comprising deciding whether to offer a promotion to the player using information incorporating both the accumulated expected value points in the loyalty account and standard comp points in the loyalty account.

72. A method as recited in claim 70, further comprising aggregating the standard comp points and the expected value points into one value.

73. A method as recited in claim 72, further comprising determining an award based on the aggregated value.

74. A method as recited in claim 60, further comprising computing a player's skill level as (total expected value points/total amount wagered).

75. A method as recited in claim 60, further comprising computing a player's skill level as (optimal strategy return−(expected value points/total amount bet)).

76. A method as recited in claim 60, further comprising computing a player's skill level as (optimal strategy return+cash back−(expected value points/total amount bet)).

77. A method, comprising: displaying a game of skill hand during a playing session resulting in a player entering a choice on the player's computer; the choice either comprising perfect play or comprising erroneous play; displaying to the player an offered promotion based on erroneous play by the player, wherein the promotion is displayed at a subsequent session later than the playing session.

78. A method as recited in claim 77, wherein the offered promotion is displayed after a sum of the player's error reaches a value.

79. A method as recited in claim 77, wherein the offered promotion is displayed after a sum of the player's ((optimal value of respective dealt hands−expected value of respective played hands)*respective bet) reaches a value.

80. A method as recited in claim 77, wherein the offered promotion is displayed after a sum of the player's ((optimal strategy house edge for game chosen+optimal value of the respective dealt hands−expected value of respective played hands)*respective bet) reaches a value.

81. A method as recited in claim 77, wherein the offered promotion is displayed after a sum of the player's ((optimal strategy house edge for game chosen−cash back percentage+optimal value of the respective dealt hands−expected value of respective played hands)*respective bet) reaches a value.

82. A method as recited in claim 77, wherein the game of skill hand is received from a remote server.

83. A method as recited in claim 77, wherein the promotion includes bonus money placed in a player's gaming account.

84. A computer readable storage medium storing a method of tracking casino players playing a hand of a game involving skill, the storage medium controlling a computer by: reading account information on a player's slot club card; allowing the player to complete the hand; calculating expected value points for the hand which incorporate the player's error; and accumulating the expected value points in the player's slot club account using information stored on the slot club card.

85. A computer readable storage medium as recited in claim 84, wherein the game comprises video poker.

86. An apparatus tracking casino players playing a hand of a game involving skill, the apparatus comprising: an input unit reading account information on a player's slot club card; a game apparatus allowing the player to complete the hand; a calculating unit calculating expected value points for the hand which incorporate the player's error; and an accumulating unit accumulating the expected value points in the player's slot club account using information stored on the slot club card.

87. An apparatus as recited in claim 86, wherein the game apparatus comprises a video poker machine.

88. An apparatus for tracking casino players playing a hand of a game involving skill, the apparatus comprising: means for reading account information on a player's slot club card; means for allowing the player to complete the hand; means for calculating expected value points for the hand which incorporate a numerical measure of the player's error; and means for accumulating the expected value points in the player's slot club account using information stored on the slot club card.

Description:

[0001] 1. Field of the Invention

[0002] The present invention is directed to a method, device, and computer readable storage medium for tracking and marketing to select casino players. More particularly, the present invention relates to an improved system for tracking and marketing to select players.

[0003] 2. Description of the Related Art

[0004] Casinos commonly use player tracking systems to track and market to players. Player tracking systems issue to players a “players card” or “slot club card” to a player, who then uses this card when he plays casino games such as blackjack, craps, slot machines, video poker, etc. Computers are used to keep track of a player's bets. Based on the player's wagers (or “action”), the player may be given incentives (or “complimentaries” or “comps”) by the casino, such as discounts on rooms or food, etc. The more casino action a player gives a casino, generally the greater his or her comps will be. If a player has wagered a small amount, he or she will typically not be given any or much comps, as the casino does not value this player's patronage. In this way, a casino encourages players that they value to return to their casino and gamble some more.

[0005] Certain casino games incorporate an element of player skill. For example, in blackjack and video poker, a player is presented with decisions to make. There exists a mathematical strategy for these games so that the player can reduce the house edge as much as possible by making the mathematically correct decisions. In fact, in certain variations of video poker (such as a game known as “full pay deuces wild”) a player playing the optimal strategy will have a slight advantage over the casino. These optimal strategies are available on the Internet and on strategy cards.

[0006] A drawback of the current comp system is that casinos do not calculate a player's skill when the player plays electronic games such as video poker and video blackjack. Consider a first player who is a beginner at video poker and does not follow the proper strategy perfectly, and a second player who bets the same total amount but plays the hands perfectly. The current system would value these two players equally. However, of course the first player is more valuable to the casino, and this player is also more deserving of incentives in order to compensate for losses due to being a beginner.

[0007] Therefore, what is needed is an improved comp system that takes into consideration a player's skill in determining the player's value and marketing efforts.

[0008] It is an aspect of the present invention to provide improvements and innovations in casino player tracking, complimentary, and marketing systems.

[0009] The above aspects can be obtained by a system that includes (a) reading account information on a player's slot club card; (b) allowing the player to complete the hand; (c) calculating expected value points for the hand which incorporate a numerical computation of the player's error; and (d) accumulating the expected value points in the player's slot club account using information stored on the slot club card.

[0010] These together with other aspects and advantages which will be subsequently apparent, reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accompanying drawings forming a part hereof, wherein like numerals refer to like parts throughout.

[0011] Further features and advantages of the present invention, as well as the structure and operation of various embodiments of the present invention, will become apparent and more readily appreciated from the following description of the preferred embodiments, taken in conjunction with the accompanying drawings of which:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] Reference will now be made in detail to the presently preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout.

[0022] The present invention relates to improving player tracking, evaluation, and marketing systems. The invention relates to determining and using an individual player's skill level in order to present a more complete picture of a player's ability and the player's value to a casino.

[0023] Tracking a player's play can be accomplished either on table games or on machine games. A table game typically requires a casino employee to manually enter a player's plays. On a machine game, the machine can automatically track a player's plays.

[0024] Video poker is a highly popular game in casinos, both in land based and Internet casinos. Five cards are dealt to the player, and the player chooses which of the five cards to keep and which to replace. The goal is for the player to create certain hands which pay according to an active paytable. A video poker machine typically displays a description of the paying hands and how much each hand pays as a multiple of the original bet.

[0025] Video poker comes in many variations, which include (but not limited to): Jacks or Better, Deuces Wild, Joker Poker, etc. Each variation has its own pay table and special rules. For example, in Joker Poker, a wild joker is added to a standard deck. In Deuces wild, all deuces (twos) are wild. Of course, the paytable is adjusted to reflect each game's particular rules.

[0026] Table I below presents a payout chart for “full pay Jacks or Better.”

TABLE I | ||||||

Coins Bet | ||||||

Hand | 1 | 2 | 3 | 4 | 5 | |

Royal flush | 250 | 500 | 750 | 1000 | 4000 | |

Straight flush | 50 | 100 | 150 | 200 | 250 | |

Four of a kind | 25 | 50 | 75 | 100 | 125 | |

Full house | 9 | 18 | 27 | 36 | 45 | |

Flush | 6 | 12 | 18 | 24 | 30 | |

Straight | 4 | 8 | 12 | 16 | 20 | |

Three of a | 3 | 6 | 9 | 12 | 15 | |

kind | ||||||

Two pair | 2 | 4 | 6 | 8 | 10 | |

Jacks or better | 1 | 2 | 3 | 4 | 5 | |

[0027] Video poker should not be played according to “hunches” or what some players may consider common sense. There is a known mathematical strategy for playing the game to reduce (or even eliminate) the house edge as much as possible. Table II presents a sample “simple strategy” for “9/6” Jacks or Better video poker, characterized by paying 9 for a full house and 6 for a flush, per coin bet. The optimal return in 9/6 Jacks or Better is 99.54.

TABLE II | |

1 | Full house or better |

2 | 4 to a royal flush |

3 | Straight, three of a kind, or flush |

4 | 4 to a straight flush |

5 | Two pair |

6 | High pair |

7 | 3 to a royal flush |

8 | 4 to a flush |

9 | Low pair |

10 | 4 to an outside straight |

11 | 2 suited high cards |

12 | 3 to a straight flush |

13 | 2 unsuited high cards (if more than 2 pick then pick lowest 2) |

14 | Suited 10/J, 10/Q, or 10/K |

15 | One high card |

16 | Discard everything |

[0028] The way this strategy works is as follows. When a player is dealt a particular hand, the player will keep the set of cards that have the highest rank in Table II. For example, if a player is dealt the following hand: A 8 5 2 2, the highest ranked hand that the player can make in Table II is #9 low pair (the pair of 2's). Thus, the player should keep the pair of 2's and discard the other cards. The strategy in Table II, if played perfectly on a 9/6 Jacks or Better game, will return to a player 99.46%. Longer and more advanced strategies can improve on this return marginally, as far as the optimal strategy return of 99.54%. Note there are more optimal strategies for this game and this is merely presented as an example

[0029] A beginning player that does not make the optimal play (the above example strategy in Table II is close, but not optimal) is basically giving money to the casino. For example, consider the player that gets dealt: A 8 5 2 2, as in the example above. The correct play is to keep the pair of 2's. If the player is playing a one dollar machine and puts in $5, the expected value of keeping the pair of 2's would be $4.12. However, if a beginning player keeps the pair of 2's but also the A (as a “kicker”), then his expected value would be only $3.38. Thus, the player just gave 74 cents to the casino, on average. Of course, making the wrong play may result in a bigger win than playing correctly, however what is more important than the instant result is the long term average for a player's skill level.

[0030] An improved player tracking system would keep long term track of the players unnecessary cost for each hand dealt. A beginning player that makes more mistakes should be entitled and considered for special promotions and marketing efforts by the casinos. More on ways of computing this cost and ways to track it will be described below.

[0031] As an example of ways to play a hand, consider a player that is dealt: 2 hearts; 4 spades; 8 hearts; 9 clubs, and queen spades. The player can keep or discard each of the 5 cards, for 32 possible ways to play the hand. A table can be created for each way to play the hand, and a breakdown of the number of paying (and losing) hands possible. Table III and Table IV, based on 9/6 Jacks or Better, represent such a table for the example hand given. For example, given that the play keeps all of his cards, row 1 indicates that this results in only 1 way to make a non-paying hand (“nothing”). This has an expected value of 0. If the 2, 4, 8 and queen are kept, row 3 indicates that there are 44 ways to make a non-paying hand, and 3 ways to make a high pair (i.e. 3 other queens to match the kept queen). The expected value here is 0.06, that is for every $1 bet, the player can expect on average to return 6% or 6 cents. From Tables III and IV it is clear that the best play is to keep only the queen, as it is the play with the highest expected value.

TABLE III | |||||

High | Two | 3 of a | |||

Kept cards | Nothing | pair | pair | kind | Straight |

2h, 4s, 8h, 9c, Qs | 1 | 0 | 0 | 0 | 0 |

2h, 4s, 8h, 9c | 47 | 0 | 0 | 0 | 0 |

2h, 4s, 8h, Qs | 44 | 3 | 0 | 0 | 0 |

2h, 4s, 8h | 1024 | 21 | 27 | 9 | 0 |

2h, 4s, 9c, Qs | 44 | 3 | 0 | 0 | 0 |

2h, 4s, 9c | 1024 | 21 | 27 | 9 | 0 |

2h, 4s, Qs | 913 | 132 | 27 | 9 | 0 |

2h, 4s | 14295 | 780 | 711 | 281 | 128 |

2h, 8h, 9c, Qs | 44 | 3 | 0 | 0 | 0 |

2h, 8h, 9c | 1024 | 21 | 27 | 9 | 0 |

2h, 8h, Qs | 913 | 132 | 27 | 9 | 0 |

2h, 8h | 14258 | 780 | 711 | 281 | 0 |

2h, 9c, Qs | 913 | 132 | 27 | 9 | 0 |

2h, 9c | 14423 | 780 | 711 | 281 | 0 |

2h, Qs | 12248 | 2955 | 711 | 281 | 0 |

2h | 148980 | 15357 | 8874 | 4102 | 382 |

4s, 8h, 9c, Qs | 44 | 3 | 0 | 0 | 0 |

4s, 8h, 9c | 1024 | 21 | 27 | 9 | 0 |

4s, 8h, Qs | 913 | 132 | 27 | 9 | 0 |

4s, 8h | 14359 | 780 | 711 | 281 | 64 |

4s, 9c, Qs | 913 | 132 | 27 | 9 | 0 |

4s, 9c | 14423 | 780 | 711 | 281 | 0 |

4s, Qs | 12083 | 2955 | 711 | 281 | 0 |

4s | 148534 | 15357 | 8874 | 4102 | 828 |

8h, 9c, Qs | 897 | 132 | 27 | 9 | 16 |

8h, 9c | 14183 | 780 | 711 | 281 | 240 |

8h, Qs | 12200 | 2955 | 711 | 281 | 48 |

8h | 148455 | 15357 | 8874 | 4102 | 907 |

9c, Qs | 12136 | 2955 | 711 | 281 | 112 |

9c | 148290 | 15357 | 8874 | 4102 | 907 |

Qs | 118674 | 45456 | 8874 | 4102 | 589 |

None | 1205537 | 213648 | 71802 | 31502 | 5979 |

[0032]

TABLE IV | ||||||

Full | 4 of a | Str | Royal | |||

Kept cards | Flush | house | kind | flush | flush | Exp Value |

2h, 4s, 8h, 9c, Qs | 0 | 0 | 0 | 0 | 0 | 0.00000 |

2h, 4s, 8h, 9c | 0 | 0 | 0 | 0 | 0 | 0.00000 |

2h, 4s, 8h, Qs | 0 | 0 | 0 | 0 | 0 | 0.06383 |

2h, 4s, 8h | 0 | 0 | 0 | 0 | 0 | 0.09436 |

2h, 4s, 9c, Qs | 0 | 0 | 0 | 0 | 0 | 0.06383 |

2h, 4s, 9c | 0 | 0 | 0 | 0 | 0 | 0.09436 |

2h, 4s, Qs | 0 | 0 | 0 | 0 | 0 | 0.19704 |

2h, 4s | 0 | 18 | 2 | 0 | 0 | 0.23244 |

2h, 8h, 9c, Qs | 0 | 0 | 0 | 0 | 0 | 0.06383 |

2h, 8h, 9c | 0 | 0 | 0 | 0 | 0 | 0.09436 |

2h, 8h, Qs | 0 | 0 | 0 | 0 | 0 | 0.19704 |

2h, 8h | 165 | 18 | 2 | 0 | 0 | 0.26192 |

2h, 9c, Qs | 0 | 0 | 0 | 0 | 0 | 0.19704 |

2h, 9c | 0 | 18 | 2 | 0 | 0 | 0.20086 |

2h, Qs | 0 | 18 | 2 | 0 | 0 | 0.33500 |

2h | 328 | 288 | 52 | 2 | 0 | 0.29658 |

4s, 8h, 9c, Qs | 0 | 0 | 0 | 0 | 0 | 0.06383 |

4s, 8h, 9c | 0 | 0 | 0 | 0 | 0 | 0.09436 |

4s, 8h, Qs | 0 | 0 | 0 | 0 | 0 | 0.19704 |

4s, 8h | 0 | 18 | 2 | 0 | 0 | 0.21665 |

4s, 9c, Qs | 0 | 0 | 0 | 0 | 0 | 0.19704 |

4s, 9c | 0 | 18 | 2 | 0 | 0 | 0.20086 |

4s, Qs | 165 | 18 | 2 | 0 | 0 | 0.39605 |

4s | 326 | 288 | 52 | 4 | 0 | 0.30707 |

8h, 9c, Qs | 0 | 0 | 0 | 0 | 0 | 0.25624 |

8h, 9c | 0 | 18 | 2 | 0 | 0 | 0.26007 |

8h, Qs | 0 | 18 | 2 | 0 | 0 | 0.34684 |

8h | 325 | 288 | 52 | 5 | 0 | 0.30909 |

9c, Qs | 0 | 18 | 2 | 0 | 0 | 0.36263 |

9c | 490 | 288 | 52 | 5 | 0 | 0.31464 |

Qs | 327 | 288 | 52 | 2 | 1 | 0.47442 |

None | 2982 | 2124 | 344 | 18 | 3 | 0.34198 |

[0033]

[0034] The method starts with operation

[0035] From operation

[0036] Once the discarded cards are determined, the method then proceeds to operation

[0037] In this way, every possible card combination is produced. The return (according to a selected paytable) is stored for each of the combinations and averaged for each of the 32 possible ways to hold/discard cards.

[0038] From operation

[0039] The method illustrated in

[0040]

[0041] The method starts with operation

[0042] From operation

[0043] From operation

[0044]

[0045] The method starts with operation

[0046] From operation

[0047] From operation

[0048] From operation

[0049] From operation

[0050] Operation

[0051] The formula based approach comprises operation

[0052] From operation

[0053] From operation

[0054] From operation

[0055] It is noted that any combination of the cycling or formula based approaches can be used. For example, all possible replacement cards can be cycled through; or the formula based approach can be used to all situations; or a mixture of the two approaches can be used (i.e. for 1-2 discards, the cards can be cycled through. For more 3-5 discards, the formula based approach is used). The preferred method is to use the cycling approach for 1-2 cards and the formula based approach for all others.

[0056] Appendix A illustrates an example of C++ code used which illustrates the formulaic approach to determine the amount of winning combinations of hands with 4 discards, which can then be used to calculate the expected value of the dealt hand. Other numbers of discards can be accomplished similarly.

[0057] An example of the above formula based method follows:

[0058] A player is playing Jacks or Better at the 25 cent coinage level and plays 5 coins. The player is dealt the following cards: 2 of hearts, 4 of spades, 8 of hearts, 9 of clubs, queen of spades. The method will determine the expected value of keeping just the queen of spades. Following is the logic the computer would follow to determine the number of combinations of each possible hand on the draw. The computer would loop through all combinations of ranks.

[0059] Royal flush: The 10, jack, king, and aces of spades are all still in the deck, therefore there is 1 royal flush combination.

[0060] Straight flush: The possible spans for a straight flush are 8 to queen and 9 to king. All necessary cards are still in the deck, therefore number of combinations is 2.

[0061] Four of a kind: For the ranks 3, 5, 6, 7, 10, jack, king, and ace all four cards are still in the deck, therefore there is one combination each for a total of 8. All three other queens are also still in the deck and the player can still get any of the 44 kickers with the three queens. So the number of four of a kinds is 8+44=52.

[0062] Full house: The queen can be either part of the three of a kind or pair. If the queen is part of the three of a kind then there are 3 ways to pick 2 queens from the remaining 3. There are 12 ranks left for the pair. 8 of them have all four cards left and 4 have just three left. Of the ranks with all four cards left there are 6 ways to choose 2 cards out of 4. Of the 4 ranks with 3 left there are 3 ways to choose 2 cards out of 3. So the total number of full houses, queens up, is 3*(8*6+4*3)=180. For the number of full houses where the queen is part of the pair there are 3 ways to choose one more queen out of the three left. Of the other 12 ranks there are 4 ways to choose 3 out of 4 cards for the 8 ranks with all four cards remaining. Of the other 4 ranks with 3 cards left there is only 1 way to pick 3 out of 3 cards. So the number of full houses where the queen is the pair is 3*(8*4+4*1)=108. So the total number of full houses is 180+108=288.

[0063] Flush: Spades are the only possible suit for the flush. The player discarded the 8 of spades so there are 11 spades left in the deck. There are 330 ways to pick 4 spades out of 11 to complete the flush. However 3 of those will result in a straight flush or royal flush. So the number of flush combinations is 330−3=327.

[0064] Straight: There are three possible spans for a straight: 8 to queen, 9 to king, and 10 to ace. The player already discarded an 8 and 9, which will cut down the number of straight combinations. Let n8=number of 8's left in deck, and so on for each rank. The number of possible straights can be expressed as: n8*n9*n10*nJ+n9*n10*nJ*nK+n10+nJ+nK+nA=3*3*4*4+3*4*4*4+4*4*4*4=592. However 3 of these combinations result in a straight flush or royal flush. So the final number of straight combinations is 592−3=589.

[0065] Three of a kind: There are two types of three of a kind in this situation: (1) queen is in the three of a kind, (2) queen is a singleton. To determine the number of type (1) three of a kind there are 3 ways to pick 2 out of the three queens left in the deck. There are also 44 non-queens left in the deck. The number of ways to pick 2 cards out of 44 is 44*43/2=946. However we know from the full house section that 8*6+4*3 that 60 of these combinations result in a pair. So there are 3*(946−60)=2658 ways to form a type (1) three of a kind. For the type (2) full houses there are 12 ranks left for the three of a kind, and 11 for the other singleton. The program would circulate through all 132 combinations of three of a kind and singleton ranks. 4*3=12 will result in both ranks having only three cards left, in which case there will be 1*3=3 ways to complete the three of a kind. 8*4=32 ways will result in the 3 of a kind coming from a rank with all 4 cards left and the singleton from a rank with 3. Then there were will be 4*3=12 ways to complete the three of a kind. 4*8=32 ways will result in the three of a kind coming from a rank with 3 cards left and the singleton from a rank with 4 cards left. There are 1*4=4 ways to complete the three of a kind. 8*7=56 ways will result in both the three of a kind and the singleton coming from ranks with all four cards left. There will be 4*4=16 ways to complete each three of a kind. So the total number of type (2) three of a kinds is (12*3+32*12+32*4+56*16)=1444. The total number of three of a kinds is 2658+1444=4102.

[0066] Two pair: There are two types of two pairs: (1) queen is part of a pair, (2) queen is the singleton. Of the type (1) two pairs there are 3 possible ranks for the other queen. There are 8*7=56 ways the other pair and singleton can both come from ranks with 4 cards left, for a total of 6*4=24 combinations each. There are 8*4=32 ways the three of a kind can come from a rank of 4 and the singleton from a rank of 3, for a total of 6*3=18 each. There are 4*8=32 ways the three of a kind can come from a rank of 3 and the singleton from a rank of 4, for a total of 3*4=12 combinations each. There are 4*3=12 ways both the other pair and the singleton can come from ranks with 3 left each, for a total of 3*3=9 combinations each. So the total number of type (1) two pairs is 3*(56*24+32*18+32*12+12*9)=7236. Of the type (2) two pairs there are 8*7/2=28 ways both pairs can come from ranks 4, and there are 6*6 ways to pick the suits from each set. There are 8*4=32 ways to pick one pair from a rank of 4 and one from a rank of 3, and there are 6*3=18 ways to pick the suits from each set. There are 4*3/2=6 ways to pick both pairs from ranks of 3, and there are 3*3=9 ways to pick the suits from each set. So the total number of type (2) two pairs is (28*36+32*18+6*9)=1638. The total number of two pairs is therefore 7236+1638=8874.

[0067] Pair: There are two types of pairs: (1) pair of queens, (2) pair of another high card. For the type (1) pairs the program picks one of 3 suits for the other queen and then will cycle through all 12*11*10/6=220 ways to pick 3 ranks out of 12 for the singletons. 8*7*6/6=56 of those ways will result in all 3 singletons coming from ranks of 4, for 4{circumflex over ( )}3=64 ways to pick the suits each. (8*7/2)*4=112 of those ways will result in 2 singletons coming from ranks of 4 and one from a rank of 3, for 4{circumflex over ( )}2*3=48 ways to pick the suits each. 8*(4*3/2)=48 of those ways will result in 1 singleton coming from a rank of 4 and two from a rank of 3, for 4*3{circumflex over ( )}2=36 ways to pick the suits. 4*3*2/6=4 ways result from all three singletons coming from ranks of 3, or 3{circumflex over ( )}3=27 ways to pick the suits. So the number of type (1) pairs is 3*(56*64+112*48+48*36+4*27)=32388 combinations of type (1) pairs. For the type (2) pairs there are 3 ranks to choose from for the other pair. All three ranks have all four cards left so each has 4*3/2=6 ways to arrange the suits. There are 11*10/2=55 ways to pick the ranks of the other two singletons. 7*6/2=21 ways result in both singletons from ranks of 4, for 4{circumflex over ( )}2=16 ways to pick the suits. 7*4=28 ways result in one singleton from a rank of 4 and one from a rank of 3, for 4*3=12 ways to pick the suits. 4*3/2=6 ways result in both singletons from ranks of 3, for 3{circumflex over ( )}2=9 ways to pick the suits. So the number of type (2) pairs is 3*6*(21*16+28*12+6*9)=13068. The total number of pairs is 32388+13068=45456.

[0068] Non-paying hand: There are 47*46*45*44/24=178365 ways to pick 4 replacement cards out of 47 left in the deck. The total number of paying combinations is 59691, adding up the totals for each type of hand. 178365−59691=118674 ways to have a non-paying hand.

[0069] Table V below summarizes the number of combinations of each hand and the product of each combination and what it pays under the 9/6 Jacks or Better pay table with maximum coins played, for the above example.

TABLE V | |||

Hand | Pays | Probability Combinations | Return Combinations |

Royal flush | 800 | 1 | 800 |

Straight flush | 50 | 2 | 100 |

Four of a kind | 25 | 52 | 1300 |

Full house | 9 | 288 | 2592 |

Flush | 6 | 327 | 1962 |

Straight | 4 | 589 | 2356 |

Three of a kind | 3 | 4102 | 12306 |

Two pair | 2 | 8874 | 17748 |

Pair | 1 | 45456 | 45456 |

Nothing | 0 | 118674 | 0 |

Total | 178365 | 84620 | |

[0070] The expected value of this hand is the return combinations divided by the probability combinations, or 84620/178365=0.4744. In other words for each $1 bet the player can expect to get back 47.44 cents. In the case of the player betting 5 quarters this hand is now worth $1.25*0.4744=59.3 cents.

[0071] The above describes how to calculate the optimal value of a dealt hand, and an expected value of the way a player plays the hand. Calculating the player error involves these two values and can provide the player error, which can then be used for marketing purposes.

[0072] One way the player error can be calculated is by:

[0073] The players expected value loss can be calculated by:

[0074] In other words, the latter formula is the expected amount (not necessarily the actual amount) that the casino gains from the error made by the player. This expected value loss (or even just the player error) can be stored as “expected value points” for purposes of tracking and storing. The casino can keep track of the expected value points, either cumulatively (maintains only a total) or individually (maintains each entry separately), in a player's loyalty account (or slot club account), to be explained below in more detail. Generally, “loyalty account” and “slot club account” represent the same concept and can typically be used interchangeably. In this way, the casinos can specially market incentives, promotions, and other offers to the beginning players which can compensate them for their mistakes. The more expected value points a player may accrue, the casino may offer more incentives, or there may be a greater likelihood of offering an incentive. Expected value points are basically a measure of a player's expected loss, and can be calculated in numerous ways. Expected value points incorporate a computation of the player's error, but also may incorporate other variables such as the amount wagered, etc.

[0075] Note that the preferred way of calculating expected value points are non-fixed numbers which are a measure of the magnitude of the player's error, a system can alternatively assign fixed (or discrete) numerical values to a player's error. For example, if a player plays a hand perfectly it will be scored as a ‘0’; if a minor error is made (which falls within a predetermined range of error or a predetermined categorization of errors) it can be scored as a ‘1’; if a major error is made it can be scored as a ‘2’, or any such system using any range of discrete values, which then can be optionally multiplied by a conversion factor. Of course, since this method has reduced accuracy, it is not the preferred method.

[0076] Note that if a player chooses not to play the full amount of coins, on some paytables he will suffer a loss of expected return. For example, in the paytable in Table I, by playing 5 coins, the return on a royal flush is disproportionate to the return by playing 1-4 coins. Therefore, it is of course to the player's advantage in this case to play all 5 coins. The expected value point calculation considers the aspect of a player playing less than 5 coins as well, by calculating the EV for all possible hands. It is noted that the optimal strategy could be different depending on the number of coins played, because if less than full coins are played because the player will not seek royal flushes as aggressively. The system should preferably know the optimal return for each of number coins played. Generally, though, the majority of players play the full number of coins.

[0077] Further, casinos may wish to track or compute just the (optimal value of the dealt hand−expected value of played hand) or (1−this value) as a measure of the player's skill level (typically skill level is independent of amount bet). This can also be computed by tracking the amount of expected value points and dividing by the total amount bet. More on skill levels will be discussed below.

[0078] The choice a player makes regarding the variation of video poker as well as the paytable offered also affects the player's return and should ideally also be considered by the casino. For example, for the variation of video poker known as Deuces Wild, a paytable known as “full pay” optimally returns 100.77%. Table VI below illustrates a paytable for full pay deuces wild. This means that someone who knows the optimal strategy for this paytable of Deuces Wild can make 0.77% on every bet, on average. On the other hand, Table VII illustrates an alternative payable of “Deuces Wild,” which returns 98.91% if the player uses optimal strategy.

TABLE VI | |||||

Full Pay Table | |||||

Coins Bet | |||||

Hand | 1 | 2 | 3 | 4 | 5 |

Natural royal flush | 250 | 500 | 750 | 1000 | 4000 |

Four deuces | 200 | 400 | 600 | 800 | 1000 |

Wild royal flush | 25 | 50 | 75 | 100 | 125 |

Five of a kind | 15 | 30 | 45 | 60 | 75 |

Straight flush | 9 | 18 | 27 | 36 | 45 |

Four of a kind | 5 | 10 | 15 | 20 | 25 |

Full house | 3 | 6 | 9 | 12 | 15 |

Flush | 2 | 4 | 6 | 8 | 10 |

Straight | 2 | 4 | 6 | 8 | 10 |

Three of a kind | 1 | 2 | 3 | 4 | 5 |

[0079]

TABLE VII | |||||

Coins Bet | |||||

Hand | 1 | 2 | 3 | 4 | 5 |

Natural royal flush | 250 | 500 | 750 | 1000 | 4000 |

Four deuces | 200 | 400 | 600 | 800 | 1000 |

Wild royal flush | 25 | 50 | 75 | 100 | 125 |

Five of a kind | 15 | 30 | 45 | 60 | 75 |

Straight flush | 9 | 18 | 27 | 36 | 45 |

Four of a kind | 4 | 8 | 12 | 16 | 20 |

Full house | 4 | 8 | 12 | 16 | 20 |

Flush | 3 | 6 | 9 | 12 | 15 |

Straight | 2 | 4 | 6 | 8 | 10 |

Three of a kind | 1 | 2 | 3 | 4 | 5 |

[0080] A casino would prefer that a player play the version in Table VII over that in Table VI. This concept also applies across to other variations of video poker as well (such as “Joker Poker”) which also have their own sets of pay tables and returns. The casino would prefer that a player play a version of Joker Poker that pays 94.1% over either of the Deuces wild versions illustrated in Tables VI and VII. Of course, these return percentages reflect play at the optimal strategy level. The player's choice of machine can also be considered a part of the player's “error,” as it is in his interest to choose the machine with the highest return percentage.

[0081] The expected value point formula given above can be optionally modified to take into consideration the machine choice. This formula is as follows:

[0082] Wherein the optimal strategy house edge is the house edge when the player knows and plays the optimal strategy. This number is equivalent to (1−optimal player return). Thus, the house edge on a game that returns 98.91% is 1.09%. Thus, the above formula adds on the house edge to the player error. The expected value of a player's play is due to both mistakes by the player and the house edge, and the above formula accounts for both.

[0083] Alternatively, it is also possible to incorporate the machine choice without regard for the player's error. This can be done by computing and storing only the (optimal strategy house edge*bet). This gives the casino a picture of a player's machine choice, but not his play. This alternative may be easier to implement by casinos, because casinos currently maintain a list of machines with identification numbers, and there is no need to track actual player decisions. Of course, this system is less powerful than the above formulas.

[0084] Some casinos typically give a “cash back” allowance on every video poker bet (i.e. 0.5%). For example, if a player wagers $5 on a hand of video poker, the player will get 2.5 cents added to his player loyalty account. A player that plays full pay deuces wild perfectly (player advantage of 100.77%) with a 0.5% cash back allowance gets back 1.27% on each bet. Of course, this isn't a very attractive proposition for the casino. This cash back can also be worked into the formula for expected value points as follows:

[0085] Using the above formula to calculate the expected value points, it is easy for the casino to see if they are, on average, making or losing money on each game played and how much. All of the above formulas may be rehashed in different ways but still produce an identical or comparable result. It should not matter how the calculation is actually done. Further, the above formula considering the cash back is the preferred formula to use.

[0086] Each casino typically maintains an electronic list (or database) of video poker machines (variation and paytable) they currently carry and an identification number. Such a list should also include the (optimal) player return for each one. The player return for each game should already be well known from the game literature; if not, it can be pre-computed by dealing every possible combination of cards, playing them optimally, as described above, and taking the average return. The player return can also be electronically stored on each machine as well.

[0087] A skill level, as discussed above, can optionally be computed for each player as well. This number can provide a casino employee with an idea of a player's skill level or expected return. One way to compute this is:

[0088] While this calculation is optional, presenting a casino employee with this data may assist in the casino's evaluation of a player's abilities. The higher the above calculation is, the greater a player's skill. For the purposes of the above formula, any method can be used to calculate the expected value points. Further, a less preferred method would be to divide the expected value points by the product of the average bet and total number of hands instead of the total amount bet, or dividing the total player error (not considering the wager) by the total number of hands (these methods can be applied to the alternative formulas below also). Alternatively, another less preferred method is to just divide the expected value points by the total number of hands, but preferably maintaining each coinage separately. Of course, depending on what information the system stores, other formulas can be devised which produces equivalent results.

[0089] A player's skill level can be helpful in certain situations. For example, consider a first player who plays $50,000 in action and a second player who plays $1,000,000 in action. However, both players have accumulated the same number expected value points (i.e. 1000). However, a casino may not value these two players equally. From the numbers, the second player plays better than the first (i.e. the second player has a higher expected return). Therefore, the first player (with the lower expected return) may receive preferential treatment because he will likely lose more in the same period of time than the second player. Therefore, a more informative evaluation of a player's play history could optionally and preferably take into consideration both his expected value points and his skill level. Of course, an evaluation can also merely take into consideration either one of these values as well. On the other hand, a casino may prefer the second player because the second player shows more loyalty to the casino. It is entirely up to the casino to weigh any of the variables discussed herein (or others) in any way, individually or in combination with other variables, to determine the players they value.

[0090] A more advanced way of computing a player's skill level which also takes into consideration the player's machine choice is as follows:

[0091] wherein the optimal strategy return is what a machine returns if a player uses optimal strategy, and is equivalent to (1−the optimal strategy house edge). Thus, for example, if a player loses 1% due to errors on a Jacks or Better 9/6 machine which has a 99.54% optimal strategy return, his skill level using the previous formula would be 98.54%.

[0092] Another way of calculating a player's skill rating which considers both the player's machine choice and cash back is as follows:

[0093] Thus, if the above described player were to get 0.5% cash back from the casino on every bet, his skill level would be 99.04%. The above formula is preferred as it considers the most possible factors.

[0094] If a player plays different games with different optimal strategy returns, then a weighted average may be used (for example one way is to weight each strategy return by the amount bet on that variation). Further, the preferred and simpler way of computing skill is the above formula: optimal strategy return−(expected value points/total amount bet). However, in some cases this may not practical, for example if the expected value point formula used takes into consideration a factor not relevant to a skill determination.

[0095] A player's expected win/loss can also be estimated for a future session. For example, assuming a casino is reviewing a player's record and wishes to decide whether to offer him comps or special incentives to return. The player's future losses per day may be calculated as follows:

[0096] The expected return in the above formula can be computed using the formula given above. Further, the above formula can optionally be multiplied by the number of days of an expected visit.

[0097] It is also noted that the above formulas for calculating expected value points are merely examples, but a number of alternative formulas can also be used. The general principle is to generate a number which reflects a player's skill level and/or correlates to a monetary amount that a beginning player would be penalized over the long run. It is noted that the player error is different from the player's win/loss. It is possible that a beginning player could have a large win yet have a high number of expected value points. It is also noted that typically the method does not take into account the player's final hand on the draw.

[0098] A casino may wish to disburse a dollar amount in comps based on the expected value points. Expected value comps are a dollar amount and can be computed as follows:

[0099] wherein the constant is used to convert expected value points to an actual dollar amount. The casino may set this constant at a level of their choosing. Of course, if the conversion to be an equal one, the constant can be set to 1. A non-linear formula can also be used. Also, separate “levels” or discrete award amounts can be used. For example, a casino may issue an award (cash back, check, etc.) in the amount of $25, $50, $100, etc., wherein the expected value points (or expected value points*constant) should fall within respective ranges to earn a respective award amount.

[0100] Further, the present invention can optionally take into consideration comps already given based on the standard comp system. As discussed above, the standard comp system returns an amount to each player based on their wagers, but not their skill level. The comp system described herein can work alongside the current standard comp system. If a player is comped a certain amount using the standard comp system, a casino may not want to double comp the player according to expected value points (depending on formulas used to calculate them). Instead, the comps the player has already received can be subtracted from his “expected value comps” (comps based on expected value points).

[0101] One way that a dollar amount of expected value comps to be disbursed can be computed is as follows:

[0102] Wherein, the standard comps already given is a dollar amount already given based on the current comp system. Thus, the formula above rewards a player extra above and beyond what he would normally get for his beginner status. Thus, for example, if a casino gives a player comp points based on 0.5% cash back, and he plays $200, the player receives $1 in standard comps. If the player has also earned $5 in expected value comps due to his error, a casino may wish to subtract to award the player $5−$1=$4 in extra comps based on expected value points. A casino may especially wish to limit comps in this manner if the constant used to convert expected value points to dollars is high or equal to 1. The standard comps already given in the above formula can also optionally be multiplied by a conversion constant. It is further noted that adjusting the comps between the two types as described is entirely optional and a casino may or may not wish to do so depending on their preferences and the way their system is configured. In some cases, awarding both sets of comps independently makes sense, in other cases, the award may be too high without adjusting.

[0103] Further, in another embodiment of the present invention, standard comp points (based purely on a player's action) can be aggregated with points based on player error. For example, standard comp points can be accumulated in the conventional manner. However, expected value points can also be tracked and accumulated by the apparatus implementing the game. When the accumulated values (1 or more) of expected value points exceeds a predetermined number, a standard comp point or points is added (or “kicked in”) to the player's slot club account, and then the total expected value points accumulated therein should preferentially be subtracted from the predetermined number. For example, for every x expected value points earned (calculated using any formula), y standard comp points are kicked in to the player. A simpler way of performing this is to add in 1 standard comp point for every x expected value points. Carryovers of expected value points can be maintained from hand to hand.

[0104] Thus, using this method, it is not necessary for the system to separately store both standard comp points and expected value points in a player's slot club account. Thus, this method should be easier to implement than storing both values in a slot club account database. However, this embodiment is less preferred because it is not as powerful as having both components stored and available for viewing and calculations. An optional ratio can also be stored in the player's slot club account indicated the proportion of comp points were obtained from expected value points (player error).

[0105] In this manner, a beginning player can be compensated for his mistakes by using standard comp points. He may or may not know that he has received extra points due to his errors.

[0106] Combining points based on player error with points based on gaming action can be done with the following formula:

[0107] wherein the standard component is any standard formula or counter used to allocate comps (i.e. constant, wager, wager*constant, f(wager), etc.), and the error component can be any of the respective formulas described herein, such as: (optimal value of the dealt hand−expected value of played hand)*bet. The coefficients a and b are conversion factors chosen by the casino based on their own preferences of how much they wish to weight both variables. One possible choice of coefficients would be a=1 (so the player always gets his standard comp points) and b=0.1 (where the player gets 10% of his error converted to comp points), but of course any choice of coefficients can be used.

[0108] An example of how the above formula can work is as follows. Suppose a casino routinely gives a player 1 comp point for every $2 bet. Each comp point may for example be equivalent to a penny, but of course casinos are free to choose values and/or significance of their comp points. If a=1 and b=0.1, then the player always gets his standard comp points. In addition, the player also gets 0.1*error (calculated using a formula as per the casinos choosing). Thus, the player's aggregated total incorporates both points resulting from his wager (action) as well as points resulting from his error.

[0109] If a casino aggregates both the standard comp points and the expected value comp points immediately after play, the casino may wish to also include a number which represents which portion (or percentage) of the total points are due to standard comp points (or expected value comp points). For example, if one aggregate number is maintained, and a percentage of 30 is also maintained, this could represent that 30% of the aggregated points are due to standard comp points (or of course expected value comp points depending on the nomenclature the casino uses). This ratio (or percentage, etc) gives the casino more information and allows the casino to calculate the player's skill as well by separating a players total into the two components and then using any of the formulas presented herein to calculate skill.

[0110] The previously described method for aggregating standard comps and comps based on player error can be computed and aggregated at the machine level itself immediately after each hand. However, the two types of points (the standard comp points and the expected value corn points) can also be stored separately in the player's slot club account and aggregated at a later time. In this manner, aggregated comp points can be computed by:

[0111] Wherein, a and b are conversion factor coefficients chosen by the casino. One possible choice of coefficients is a=1 (so the player gets full value from his standard comp points) and b=0.1 (the player gets 10% of his expected value comp points converted into the aggregated amount), but of course the casino is free to choose coefficients which suit their particular needs.

[0112] Having an aggregated amount of comp points instead of two separate ones allows a casino employee to deal with one number representing comp points instead of two separate numbers. This is a simpler system, although maintaining and making available the two separate numbers is more powerful because the casino employees have more information at their disposal. Before aggregating, the casino may wish to subtract one type of comp from the other (or any percentage of one from any percentage of the other, etc.)

[0113] It is also noted that casinos may wish to keep the expected value points shielded from the players, and in this case the casinos of course can choose to do so as they please. Depending on a casino's preferences, they can simply aggregate the standard comp points and expected value comp points (either instantly or later on), or maintain them separately, and choose to disclose or not disclose what they wish. Casinos are of course free to use all of the data described herein in any manner they wish.

[0114]

[0115] The method starts with operation

[0116] The method then proceeds to optional operation

[0117] From operation

[0118] From operations

[0119] Or alternatively, the method can begin at (or continue from any of the other operations) operation

[0120]

[0121] A video poker machine

[0122] The slot club interface unit

[0123] The casino communication unit

[0124] If no such floating point unit (or capability) exists, floating point numbers may still be rounded or transmitted by using an integer representation of the floating point number. This can comprise multiplying the number by 100 and transmitting the number as an integer. Further, an integer method could be used wherein each 1% of a penny (or other denomination) counts as a “subpoint.” Subpoints are accumulated, and when the subpoint total reaches 100, a regular penny is added to the expected value points and 100 is subtracted from the subpoints. On a high denomination machine, the subpoints may exceed 100 by a factor of several times; in this case, then int(subpoints/100) is added to the expected value points, and the subpoints are adjusted to equal mod (subpoints, 100).

[0125] The casino database

[0126] The components in

[0127] Therefore, as a result of the above system, the casino management, having access to the casino database using the casino marketing computer

[0128] Further, when different types of comp points (expected value points and standard comp points) are maintained (as discussed above) and transmitted separately, the casino communication unit

[0129] The above described methods and apparatus store a players expected value points and possibly additional information (which can include any of the variables or computations discussed herein), in addition to the standard information, in the player's loyalty account.

[0130]

[0131] A database

[0132] The player record

[0133] The expected value information

[0134] If the casino chooses to aggregate to the types of points at the onset without separating them, then one aggregate value (not pictured) need be stored in the record instead of both.

[0135] The information stored regarding the expected value (and any other information discussed herein) can be used in numerous ways to market to beginning or desirable players. Beginning players can receive and appreciate special offers which the experienced player may not receive. Such targeted marketing should ideally also increase house profits as well.

[0136] Such offers, marketing, or incentives can comprise offering free or discounted rooms or food, offering cash back upon return to the casino, sending targeted, advertisements for the casino, offering discounts on gift shop items or shows, gift certificates that can be used for any of the above, or any other standard way a casino may attempt to attract players. A casino may also send a check back to a player based on his expected value points.

[0137] Another way of providing an incentive would be to issue a check cashable only at the casino or specified group of casinos (so the player must visit) or credit a player's slot club account electronically with “playable money.” U.S. Pat. No. 6,244,958 teaches how a player's slot club account can actually store playable money to be used for wagering (note that this is different than comp points). A casino that wishes to market to a desirable play based on criteria discussed herein can credit a player's account with an amount of money (may be based on expected value information, such as a fraction of expected value points earned).

[0138]

[0139] The method starts with operation

[0140] The method then proceeds to operation

[0141] From operation

[0142] More than one criterion can be used as well. For example, a casino can choose as marketing criteria all players with a skill below a certain level and with standard comp points (or expected value comps, or aggregated comps, etc.) above a certain level.

[0143] Ideally, the casino should determine based on their specific data which set of marketing criteria will result in the most profits. Any of the numbers, variables, and calculations described herein can be compared to fall within or outside of predetermined range(s) in order to qualify for additional marketing efforts.

[0144] From operation

[0145] A casino may offer a credit to players for any of the above based on the expected value points. For example, if a player's expected value points in the player's loyalty account indicate that a player lost $100 due to player error, the casino may offer the player complimentaries based on this amount.

[0146] Casinos can issue an award amount based on either standard comp points, expected value comp points (which can be computed as either any formula for expected value points optionally multiplied by a constant) or a combination of the two types of points (or concepts). The awarded amount can be computed by converting the respective comp amount (standard comps, expected value comps, aggregated comps) to a dollar amount, for example by multiplying by a constant (1 can be used for an even conversion from comp points to dollars). A dollar amount award can further be optionally reduced/increased by multiplying by or adding/subtracting a constant. An award can also be adjusted to be a fixed selected amount (i.e. $25, $50, $75, $100, or any number), by checking a range for the fixed amounts and awarding the fixed amount that corresponds to the respective range the award amount falls between. This may be done so a player would not get an award (such as a check) for an odd amount, such as $23.28, in which the player may wonder how the amount was determined. For example, if a player's expected value points=98, and the conversion factors used to convert this to dollars is 1, the player can get an award of $98. A casino may optionally wish to reduce this amount by multiplying by 0.75, resulting in $73.5. The casino may further wish to subtract $5 from this award, resulting in $68.5. Lastly, the casino can optionally convert this to an even amount of $75. Again, casinos are free to choose parameters to suit their marketing preferences.

[0147] For example, in an embodiment of the present invention, if a player has earned what amounts to $20 in standard comp points and $50 in expected value comp points, the casino may wish to award the player $20+$50=$70 in general comps. Alternatively, the casino may wish to typically restrict certain awards to certain type of comps. For example, the casino may wish to issue checks to be cashed at the casino only based on expected value points (or use the expected value points for the sole purpose of issuing checks). Thus, in this case, the casino would award this player $20 in general comps but send a $50 check to the player. Similarly, a casino may wish to issue discounts on hotel rooms based on expected value points, but apply standard comp points to food and beverage. Casinos are free to mix, match, configure, and use these systems in any manner they wish to suit their preferences. Further, any measure of comp points (i.e. standard comp points, expected value comps, and aggregated points (either aggregated immediately or later on) can be used in any manner described herein.

[0148] Once comp points are used they are typically subtracted from the player's account. Any kind of comp points may also expire after a predetermined amount of time, at the casinos option.

[0149] Sometimes a manual review of a player's player (or loyalty) account is performed. This may occur when a player calls a casino to ask for complimentaries. In this case, a special display can be produced for a player which includes expected value information as described above.

[0150] Casinos can also maintain a separate list of preferred players based on their characteristics. For example, such a list may contain players with expected value points over a predetermined amount, or any other combination of criteria. The list may be shared with other casinos.

[0151]

[0152] Player information

[0153] Alongside the player information is expected value information

[0154] The player's comps given

[0155] In the embodiment of the present invention described herein wherein comps are computed based on action and error, and these comps are aggregated into a single comp amount, then this single amount can be presented to the casino employee (not pictured), in place of or in addition to the comps available amount display for each of the components. For example, the display in

[0156] The display in

[0157] If the points based on action and error are aggregated into one value immediately upon play, if the ratio is maintained (as discussed above), the data can then be split into its components to display both sets.

[0158] Of course, a display according to the present invention may include any combination of the above information or additional information (whether described herein or elsewhere) as needed.

[0159] It is also noted that the expected value points and related information would typically not be automatically presented to the player, as this information is typically used for casino marketing purposes. The player can check his/her total standard points by inserting his/her card into most slot machines, which indicate total standard points in a small display by the card reader. On the other hand, a casino employee may mention the expected value points at their discretion, for example if questioned by a casino patron about why their comps were at the level they were at.

[0160] In an additional embodiment, expected value points may expire after a certain time. For example, if a certain amount of time goes by, comps based on the expected value points are no longer able to be utilized by the player.

[0161] Also, the present invention can identify “advantage” players, either automatically or by a casino employee upon reviewing a player's record. An advantage player can be defined as a player who plays at an expected return high enough that the casino does not care for his business, and may take such action as eliminating cash back points, prohibiting play games vulnerable to a player advantage, or barring from casino property. As stated above, some variations/paytables of video poker may have a high expected return. If a casino offers a full pay deuces wild game, and also offers a player 0.5% cash back on all bets, a player that plays optimal strategy will have an expected return of 101.27 (including cash back). A player that bets large denominations and plays very quickly can theoretically beat the house for a sizable amount of money in the long run. The present invention can identify advantage players by their skill level (as discussed above). Once identified, a casino may choose to reduce or not issue comps at all to such players, or even bar them. One way an expert player can be identified as follows:

[0162] Wherein the expected total return is the expected amount that the player should have received from his wagers, which can also take into consideration cash back by the casino. Note that this is not the actual amount, as the method is not concerned with the player's actual losses. A preferred formula for expected total return for use in this case is:

[0163] The above formula results in a value of 100% when the player is playing even with the house, and over 100% when the player is playing at an advantage. Note that if the player plays different versions of a game with different optimal strategy house edges, then a weighted average can be used for the optimal strategy house edge.

[0164] A preferred predetermined expert return is 100%, although other returns can be used as well, for example the casino may allow a player to return 100.1% before labeling him an advantage player.

[0165] The predetermined sample of hands is used so that a player isn't labeled an advantage player if he plays a number of hands which isn't a large enough sample of his play. A preferred predetermined sample of hands is 1000, although of course the casino can set this amount as to their preferences.

[0166] An alternative formula to that can be used to identify an advantage player is:

[0167] Wherein the predetermined expert threshold is set by the casino but can preferably be zero (equivalent to 100 in the previous methodology), and the expected value point formula can be any logical formula including the ones described above, but preferably uses the formula which incorporates the cash back.

[0168]

[0169] The method starts with operation

[0170] If the check in operation

[0171] If the check in operation

[0172] Further, the invention is not limited to video poker. The same methods/embodiments described herein can also be used for blackjack as well, either electronic or table based. Of course, if the blackjack game is table based, an input mechanism must be used to enter the cards dealt and the player's play. Cards may be scanned electronically by a video camera and inputted into the system electronically and automatically.

[0173] For blackjack, a table of the optimal value of a dealt hand and an expected value of a dealt/played hand can be found on the Internet or in blackjack literature such as Professional Blackjack, Fourth Edition, by Stanford Wong, pages 302-333. These values can simply be substituted in the formulas above to implement the present invention. Hence the figures herein (except for

[0174] The methods/embodiments described herein can also be applied to other games of skill as well, such as Pai Gow Poker, 3 Card Poker, Carribean Stud Poker, and any game where there is a mathematical way of playing each hand.

[0175] In another embodiment of the present invention, the invention can also be applied to Internet casinos. Internet casinos are casinos which use a server to generate random numbers and transmit hand comprising values of cards (or dice, etc.) to a client computer, wherein a player can play casino games on the client computer for real money. The internet casino may wish to email special offers to players based on their expected value points or skill level. Such special offers can include bonus money which can automatically or manually be placed in the player's gaming account. A player's gaming account is an account which stores an amount representing real money which a player owns and uses to play with.

[0176] It is noted that generally, comp points may represent a “raw form” while dollar amounts are actual monetary amounts. In some cases, casinos may implement systems wherein one point=one dollar, and thus these terms may be used interchangeably. In other cases, a conversion between these two concepts (for some or all of types of comp points) may be needed an implemented by multiplying/dividing by a conversion factor or putting the subject for conversion into a formula.

[0177] It is also noted that any and/or all of the above embodiments, configurations, variations of the present invention described above can mixed and matched and used in any combination with one another. Any claim herein can be combined with any others (unless the results are nonsensical). Further, any mathematical formula given above also includes its mathematical equivalents, and also variations thereof such as multiplying any of the individual terms of a formula by a constant(s) or other variable.

[0178] Moreover, any description of a component or embodiment herein also includes hardware, software, and configurations which already exist in the prior art and may be necessary to the operation of such component(s) or embodiment(s).

[0179] The many features and advantages of the invention are apparent from the detailed specification and, thus, it is intended by the appended claims to cover all such features and advantages of the invention that fall within the true spirit and scope of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and accordingly all suitable modifications and equivalents may be resorted to, falling within the scope of the invention.

APPENDIX A |

// (c) Michael Shackleford, The Wizard of Odds |

// This routine illustrates calculating the number of possible ranks for a given hand using |

// the formulaic approach, for 1 card held. The other scenarios can be done similarly. |

// There is already a matrix call “indeck” that holds the distribution of the remaining |

// deck. The r and s that get passed are the rank and suit of the one card. Ranks are |

// numbered 0 to 12. The totals hold the number of combinations of each hand. Total[9] |

// is for royal flushes, and so on down. |

void fast1(int r, int s, int total[]) |

{ |

int i,j,k,l,numcom; |

if (r>=4) |

if (r!=12) |

total[8]+=indeck[r−4][s]*indeck[r−3][s]*indeck[r−2][s]*indeck[r−1][s]; |

else |

total[9]=indeck[r−4][s]*indeck[r−3][s]*indeck[r−2][s]*indeck[r−1][s]; |

if ((r>=3)&&(r<=11)) |

if (r!=11) |

total[8]+=indeck[r−3][s]*indeck[r−2][s]*indeck[r−1][s]*indeck[r+1][s]; |

else |

total[9]=indeck[r−3][s]*indeck[r−2][s]*indeck[r−1][s]*indeck[r+1][s]; |

if ((r>=2)&&(r<=10)) |

if (r!=10) |

total[8]+=indeck[r−2][s]*indeck[r−1][s]*indeck[r+1][s]*indeck[r+2][s]; |

else |

total[9]=indeck[r−2][s]*indeck[r−1][s]*indeck[r+1][s]*indeck[r+2][s]; |

if ((r>=1)&&(r<=9)) |

if (r!=9) |

total[8]+=indeck[r−1][s]*indeck[r+1][s]*indeck[r+2][s]*indeck[r+3][s]; |

else |

total[9]=indeck[r−1][s]*indeck[r+1][s]*indeck[r+2][s]*indeck[r+3][s]; |

if (r<=8) |

if (r!=8) |

total[8]+=indeck[r+1][s]*indeck[r+2][s]*indeck[r+3][s]*indeck[r+4][s]; |

else |

total[9]=indeck[r+1][s]*indeck[r+2][s]*indeck[r+3][s]*indeck[r+4][s]; |

if (r==12) |

total[8]+=indeck[0][s]*indeck[1][s]*indeck[2][s]*indeck[3][s]; |

else if (r==0) |

total[8]+=indeck[12][s]*indeck[1][s]*indeck[2][s]*indeck[3][s]; |

else if (r==1) |

total[8]+=indeck[12][s]*indeck[0][s]*indeck[2][s]*indeck[3][s]; |

else if (r==2) |

total[8]+=indeck[12][s]*indeck[0][s]*indeck[1][s]*indeck[3][s]; |

else if (r==3) |

total[8]+=indeck[12][s]*indeck[0][s]*indeck[1][s]*indeck[2][s]; |

if (r>=4) |

total[4]+=indeck[r−4][4]*indeck[r−3][4]*indeck[r−2][4]*indeck[r−1][4]; |

if ((r>=3)&&(r<=11)) |

total[4]+=indeck[r−3][4]*indeck[r−2][4]*indeck[r−1][4]*indeck[r+1][4]; |

if ((r>=2)&&(r<=10)) |

total[4]+=indeck[r−2][4]*indeck[r−1][4]*indeck[r+1][4]*indeck[r+2][4]; |

if ((r>=1)&&(r<=9)) |

total[4]+=indeck[r−1][4]*indeck[r+1][4]*indeck[r+2][4]*indeck[r+3][4]; |

if (r<=9) |

total[4]+=indeck[r+1][4]*indeck[r+2][4]*indeck[r+3][4]*indeck[r+4][4]; |

if (r==12) |

total[4]+=indeck[0][4]*indeck[1][4]*indeck[2][4]*indeck[3][4]; |

else if (r==0) |

total[4]+=indeck[12][4]*indeck[1][4]*indeck[2][4]*indeck[3][4]; |

else if (r==1) |

total[4]+=indeck[12][4]*indeck[0][4]*indeck[2][4]*indeck[3][4]; |

else if (r==2) |

total[4]+=indeck[12][4]*indeck[0][4]*indeck[1][4]*indeck[3][4]; |

else if (r==3) |

total[4]+=indeck[12][4]*indeck[0][4]*indeck[1][4]*indeck[2][4]; |

total[4]−=(total[8]+total[9]); |

if (indeck[13][s]==12) |

total[5]=495; |

else if (indeck[13][s]==11) |

total[5]=330; |

else if (indeck[13][s]==10) |

total[5]=210; |

else if (indeck[13][s]==9) |

total[5]=126; |

else if (indeck[13][s]==8) |

total[5]=70; |

total[5]−=(total[8]+total[9]); |

/* four of a kind */ |

for (i=0; i<=12; i++) |

{ |

if ((i!=r)&&(indeck[i][4]==4)) |

total[7]++; |

if ((i!=r)&&(indeck[r][4]==3)) |

total[7]+=indeck[i][4]; |

} |

/* full house */ |

for (i=0; i<=12; i++) |

{ |

if (i!=r) |

{ |

if (indeck[r][4]==3) |

{ |

if (indeck[i][4]==4) |

total[6]+=30; |

else if (indeck[i][4]==3) |

total[6]+=12; |

else if (indeck[i][4]==2) |

total[6]+=3; |

} |

else if (indeck[r][4]==2) |

{ |

if (indeck[i][4]==4) |

total[6]+=14; |

else if (indeck[i][4]==3) |

total[6]+=5; |

else if (indeck[i][4]==2) |

total[6]++; |

} |

else if (indeck[r][4]==1) |

{ |

if (indeck[i][4]==4) |

total[6]+=4; |

else if (indeck[i][4]==3) |

total[6]++; |

} |

} |

} |

/* three of a kind */ |

for (i=0; i<=11; i++) |

{ |

for (j=i+1; j<=12; j++) |

{ |

if ((i!=r)&&(j!=r)) |

{ |

if (indeck[i][4]==4) |

total[3]+=4*indeck[j][4]; |

else if (indeck[i][4]==3) |

total[3]+=indeck[j][4]; |

if (indeck[j][4]==4) |

total[3]+=4*indeck[i][4]; |

else if (indeck[j][4]==3) |

total[3]+=indeck[i][4]; |

if (indeck[r][4]==3) |

total[3]+=(3*indeck[i][4]*indeck[j][4]); |

else if (indeck[r][4]==2) |

total[3]+=(indeck[i][4]*indeck[j][4]); |

} |

} |

} |

/* two pair */ |

for (i=0; i<=11; i++) |

{ |

for (j=i+1; j<=12; j++) |

{ |

if ((i!=r)&&(j!=r)) |

{ |

if ((indeck[i][4]==2)&&(indeck[j][4]==2)) |

{ |

total[2]++; |

total[2]+=(indeck[r][4]*4); |

} |

else if ((indeck[i][4]==2)&&(indeck[j][4]==3)) |

{ |

total[2]+=3; |

total[2]+=(indeck[r][4]*9); |

} |

else if ((indeck[i][4]==3)&&(indeck[j][4]==2)) |

{ |

total[2]+=3; |

total[2]+=(indeck[r][4]*9); |

} |

else if ((indeck[i][4]==2)&&(indeck[j][4]==4)) |

{ |

total[2]+=6; |

total[2]+=(indeck[r][4]*16); |

} |

else if ((indeck[i][4]==4)&&(indeck[j][4]==2)) |

{ |

total[2]+=6; |

total[2]+=(indeck[r][4]*16); |

} |

else if ((indeck[i][4]==3)&&(indeck[j][4]==3)) |

{ |

total[2]+=9; |

total[2]+=(indeck[r][4]*18); |

} |

else if ((indeck[i][4]==3)&&(indeck[j][4]==4)) |

{ |

total[2]+=18; |

total[2]+=(indeck[r][4]*30); |

} |

else if ((indeck[i][4]==4)&&(indeck[j][4]==3)) |

{ |

total[2]+=18; |

total[2]+=(indeck[r][4]*30); |

} |

else if ((indeck[i][4]==4)&&(indeck[j][4]==4)) |

{ |

total[2]+=36; |

total[2]+=(indeck[r][4]*48); |

} |

else if ((indeck[i][4]==1)&&(indeck[j][4]==4)) |

total[2]+=(indeck[r][4]*6); |

else if ((indeck[i][4]==1)&&(indeck[j][4]==3)) |

total[2]+=(indeck[r][4]*3); |

else if ((indeck[i][4]==1)&&(indeck[j][4]==2)) |

total[2]+=(indeck[r][4]); |

else if ((indeck[i][4]==4)&&(indeck[j][4]==1)) |

total[2]+=(indeck[r][4]*6); |

else if ((indeck[i][4]==3)&&(indeck[j][4]==1)) |

total[2]+=(indeck[r][4]*3); |

else if ((indeck[i][4]==2)&&(indeck[j][4]==1)) |

total[2]+=(indeck[r][4]); |

} |

} |

} |

/* pair */ |

for (j=0; j<=10; j++) |

for (k=j+1; k<=11; k++) |

for (l=k+1; l<=12; l++) |

if ((r!=j)&&(r!=k)&&(r!=l)) |

{ |

if (r>=9) |

total[1]+=(indeck[r][4]*indeck[j][4]*indeck[k][4]*indeck[l][4]); |

if (j>=9) |

{ |

if (indeck[j][4]==4) |

numcom=6; |

else if (indeck[j][4]==3) |

numcom=3; |

else if (indeck[j][4]==2) |

numcom=1; |

else |

numcom=0; |

total[1]+=(numcom*indeck[k][4]*indeck[l][4]); |

} |

if (k>=9) |

{ |

if (indeck[k][4]==4) |

numcom=6; |

else if (indeck[k][4]==3) |

numcom=3; |

else if (indeck[k][4]==2) |

numcom=1; |

else |

numcom=0; |

total[1]+=(numcom*indeck[j][4]*indeck[l][4]); |

} |

if (l>=9) |

{ |

if (indeck[l][4]==4) |

numcom=6; |

else if (indeck[l][4]==3) |

numcom=3; |

else if (indeck[l][4]==2) |

numcom=1; |

else |

numcom=0; |

total[1]+=(numcom*indeck[j][4]*indeck[k][4]); |

}} |

total[0]=178365; |

for (i=1; i<=9; i++)total[0]−=total[i]; |

} |