Multi-player bingo game with multiple cards per player

• US 20050064932A1
• Filed: 09/15/2004
• Published: 03/24/2005
• Est. Priority Date: 09/15/2003
• Status: Active Grant

• Current Assignee: IGT (International Game Technology)
• Original Assignee: IGT (International Game Technology)
• Inventors: Cannon, Lee E.
• Granted Patent: US 8,430,738 B2
• Time in Patent Office: Days
• US Class Current: 463/19
• CPC Class Codes: G07F 17/3213 Details of moving display elements, e.g. spinning reels, tumbling members
• CPC Class Codes: G07F 17/3225 Data transfer within a gaming system, e.g. data sent between gaming machines and users
• CPC Class Codes: G07F 17/3267 Game outcomes which determine the course of the subsequent game, e.g. double or quits, free games, higher payouts, different new games
• CPC Class Codes: G07F 17/3276 wherein the players compete, e.g. tournament
• CPC Class Codes: G07F 17/3286 Type of games
• CPC Class Codes: G07F 17/329 Regular and instant lottery, e.g. electronic scratch cards
• CPC Class Codes: G07F 17/34 depending on the stopping of moving members in a mechanical slot machine, e.g. "fruit" machines

Abstract

The invention is directed to methods and gaming units for conducting a multi-player wagering game in which at least one of the players may win the occurrence of the wagering game by matching a game-winning pattern, or one of a plurality of game-winning patterns, of game indicia on one or more game arrays having unique combinations of game indicia based on matching the game indicia on the game arrays to game indicia randomly selected for the occurrence of the wagering game. Each player matching a game-winning pattern may receive game-winning award, and may receive a game-winning award for each game array on which a game-winning pattern is matched. The method and gaming unit may further include an alternate outcome display wherein an outcome of a second wagering game may be displayed that corresponds to the outcome for the player on the one or more game arrays for the occurrence of the multi-player wagering game.

Claims

1. A method for providing a multi-player wagering game on a gaming network having a plurality of gaming units wherein each player has at least one game array having a unique combination of indicia from a range of game indicia for an occurrence of the wagering game, wherein individual game indicia are randomly selected from the range of game indicia during the occurrence of the wagering game and transmitted to the gaming units over the gaming network, and wherein at least one of the players wins the occurrence of the wagering game by matching a game-winning pattern, or one of a plurality of game-winning patterns, of game indicia on at least one of the player'"'"'s game arrays with the randomly selected game indicia, the method comprising:

enrolling a plurality of players at corresponding gaming units for an occurrence of the multi-player wagering game, wherein each occurrence of the multi-player wagering game includes at least a predetermined total number of game arrays, and wherein each player may have a plurality of game arrays for the occurrence of the multi-player wagering game;

randomly selecting game indicia from the range of game indicia;

determining whether each randomly selected game indicia matches any of the game indicia of the at least one game array for each player in the order that the randomly selected game indicia are selected;

determining that at least one game array for the occurrence of the multi-player wagering game has matched a game-winning pattern of game indicia on the player'"'"'s game array with the randomly selected game indicia in the fewest number of randomly selected game indicia; and

determining a game-winning award amount for each player having at least one game array matching a game-winning pattern in the fewest number of randomly selected game indicia, wherein each player receives a game-winning award for each of the at least one game arrays matching the game-winning pattern in the fewest number of randomly selected game indicia.

2. A method for providing a multi-player wagering game in accordance with claim 1, wherein each player may have up to one-half of the predetermined total number of game arrays for an occurrence of the multi-player wagering game.

3. A method for providing a multi-player wagering game in accordance with claim 1, wherein each occurrence of the multi-player wagering game includes exactly the predetermined total number of game arrays.

4. A method for providing a multi-player wagering game in accordance with claim 3, comprising enrolling a player in a different occurrence of the multi-player wagering game when the number of game arrays for the player plus the total number of game arrays for all the players is greater than the predetermined total number of game arrays.

5. A method for providing a multi-player wagering game in accordance with claim 1, wherein the game-winning award amount for each player is equal to a total game-winning award amount for the occurrence of the multi-player wagering game divided by the number of game arrays matching the game-winning pattern in the fewest number of randomly selected game indicia.

6. A method for providing a multi-player wagering game in accordance with claim 1, comprising beginning randomly selecting game indicia once the total number of game arrays for the players is greater than or equal to the predetermined total number of game arrays.

7. A method for providing a multi-player wagering game in accordance with claim 1, comprising:

allowing additional players to enroll in the occurrence of the multi-player wagering game for a predetermined period of time once the total number of game arrays for the players is greater than or equal to the predetermined total number of game arrays;

beginning randomly selecting game indicia after the expiration of the predetermined period of time.

8. A method for providing a multi-player wagering game in accordance with claim 1, comprising displaying each of the game arrays for one of the players at the corresponding gaming unit.

9. A method for providing a multi-player wagering game in accordance with claim 8, comprising displaying each of the game arrays for one of the players at the corresponding gaming unit so that the unique combination of indicia for each game array is visible at the same time.

10. A method for providing a multi-player wagering game in accordance with claim 8, comprising displaying each of the game arrays for one of the players at the corresponding gaming unit so that the unique combination of indicia for one of the game arrays is visible and a portion of each of the other game arrays is visible.

11. A method for providing a multi-player wagering game in accordance with claim 1, comprising providing an alternate outcome display for a player for the occurrence of the multi-player wagering game, wherein the alternate outcome display is a display of an outcome for an occurrence of a second wagering game, wherein the outcome of the second wagering game corresponds to a combined outcome for the game arrays enrolled by the player for the occurrence of the multi-player wagering game.

12. A method for providing a multi-player wagering game in accordance with claim 11, wherein the alternate outcome display comprises a plurality of second wagering games, each second wagering game corresponding to a number of game arrays that may be enrolled by a player for an occurrence of the multi-player wagering game, the method comprising displaying an alternate outcome display of an outcome for an occurrence of the one of the plurality of second wagering games corresponding to the number of game arrays enrolled by the player for the occurrence of the multi-player wagering game, wherein the outcome of the one of the second wagering games corresponds to a combined outcome for the game arrays enrolled by the player for the occurrence of the multi-player wagering game.

13. A method for providing a multi-player wagering game in accordance with claim 1, comprising:

determining a desired statistical distribution of the number of randomly selected game indicia for at least one game array to match a game-winning pattern for an occurrence of the multi-player wagering game;

determining criteria for selecting at least one game-winning pattern for an occurrence of the multi-player wagering game based on the number of game arrays used by the players in an occurrence of the multi-player wagering game such that the statistical distribution of the number of randomly selected game indicia for at least one player to match a game-winning pattern for an occurrence of the multi-player wagering game using the at least one game-winning pattern is approximately the same as the desired statistical distribution;

calculating the total number of game arrays for the players enrolled in the occurrence of the multi-player wagering game; and

selecting at least one game-winning pattern for the occurrence of the multi-player wagering game based on the criteria for selecting at least one game-winning pattern corresponding to the total number of game arrays for the players enrolled in the occurrence of the multi-player wagering game.

14. A method for providing a multi-player wagering game in accordance with claim 1, wherein the game-winning award amount is determined based on the number of randomly selected game indicia required to match the game-winning pattern and the total number of game arrays for the occurrence of the multi-player wagering game.

15. A method for providing a multi-player wagering game in accordance with claim 1, comprising:

awarding a first game-winning award amount to a player in response to determining that a game array enrolled by the player matches the game-winning pattern in the fewest number of randomly selected game indicia and in fewer than a predetermined number of randomly selected game indicia; and

awarding a second game-winning award amount to the player in response to determining that the game array enrolled by the player matches the game-winning pattern in the fewest number of randomly selected game indicia and in more than the predetermined number of randomly selected game indicia, wherein the predetermined number of randomly selected game indicia for the occurrence of the multi-player wagering game is determined based on the total number of game arrays for the occurrence of the multi-player wagering game.

16. A method for providing a multi-player wagering game in accordance with claim 1, wherein the game-winning pattern or plurality of game-winning patterns for the occurrence of the multi-player wagering game is determined based on the total number of game arrays enrolled for the occurrence of the multi-player wagering game.

17. A method for providing a multi-player wagering game in accordance with claim 1, comprising:

providing a plurality of game awards that may be awarded to the players during an occurrence of the multi-player wagering game for matching a game-winning pattern in the fewest number of randomly selected game indicia, wherein the plurality of game awards are divided into a plurality of groups of game awards, and wherein each group of game awards has a corresponding range of the number of randomly selected game indicia within which to match the game-winning pattern to receive a game award from the group of game awards;

comparing the number of randomly selected game indicia required to match the game-winning pattern on the player'"'"'s game array to the ranges of the number of randomly selected game indicia corresponding to the groups of game awards in response to determining that the player matched the game-winning pattern in the fewest number of randomly selected game indicia; and

awarding a game award to the player from one of the groups of game awards in response to determining that the number of randomly selected game indicia required to match the game-winning pattern on the player'"'"'s game array is within the range of numbers of randomly selected game indicia corresponding to the one of the groups of game awards.

18. A method for providing a multi-player wagering game in accordance with claim 17, wherein each of the game awards within a group of game awards has a corresponding secondary pattern of game indicia, the method comprising:

comparing the secondary patterns for the game awards in the one of the groups of game awards to game indicia on the player'"'"'s game array matched by the randomly selected game indicia in response to determining that the number of randomly selected game indicia required to match the game-winning pattern on the player'"'"'s game array is within the range of numbers of randomly selected game indicia corresponding to the one of the groups of game awards; and

awarding one of the game awards from the one of the groups of game awards to the player in response to determining that the game indicia on the player'"'"'s game array matched by the randomly selected game indicia matches the secondary pattern corresponding to the one of the game awards.

19. A method for providing a multi-player wagering game in accordance with claim 18, comprising:

providing the player with a secondary game array having a combination of indicia from the range of game indicia;

comparing the secondary patterns for the game awards in the one of the groups of game awards to game indicia on the player'"'"'s secondary game array matched by the randomly selected game indicia in response to determining that the number of randomly selected game indicia required to match the game-winning pattern on the player'"'"'s game array is within the range of numbers of randomly selected game indicia corresponding to the one of the groups of game awards;

awarding one of the game awards from the one of the groups of game awards to the player in response to determining that the game indicia on the player'"'"'s secondary game array matched by the randomly selected game indicia matches the secondary pattern corresponding to the one of the game awards.

20. A method for providing a multi-player wagering game in accordance with claim 18, comprising:

providing the player with one secondary game array having a combination of indicia from the range of game indicia;

comparing the secondary patterns for the game awards in the one of the groups of game awards to game indicia on the one secondary game array matched by the randomly selected game indicia in response to determining that the number of randomly selected game indicia required to match the game-winning pattern on the player'"'"'s game array is within the range of numbers of randomly selected game indicia corresponding to the one of the groups of game awards, wherein the one secondary game array is used regardless of which of the plurality of game arrays enrolled for the player matches the game-winning pattern;

awarding one of the game awards from the one of the groups of game awards to the player in response to determining that the game indicia on the one secondary game array matched by the randomly selected game indicia matches the secondary pattern corresponding to the one of the game awards.

21. A method for providing a multi-player wagering game in accordance with claim 17, wherein each of the game awards other than the lowest game award within a group of game awards has a corresponding secondary pattern of game indicia, the method comprising:

comparing the secondary patterns for the game awards in the one of the groups of game awards to game indicia on the player'"'"'s game array matched by the randomly selected game indicia in response to determining that the number of randomly selected game indicia required to match the game-winning pattern on the player'"'"'s game array is within the range of numbers of randomly selected game indicia corresponding to the one of the groups of game awards;

awarding one of the game awards from the one of the groups of game awards to the player in response to determining that the game indicia on the player'"'"'s game array matched by the randomly selected game indicia matches the secondary pattern corresponding to the one of the game awards; and

awarding the lowest game awards from the one of the groups of game awards to the player in response to determining that the game indicia on the player'"'"'s game array matched by the randomly selected game indicia does not match any of the secondary pattern corresponding to the game awards from the one of the groups of game awards.

22. A gaming unit for conducting a multi-player wagering game over a gaming network having a plurality of gaming units operatively coupled together, wherein each player has at least one game array having a unique combination of indicia from a range of game indicia for an occurrence of the wagering game, wherein individual game indicia are randomly selected from the range of game indicia during the occurrence of the wagering game and transmitted to the gaming units over the gaming network, wherein at least one of the players wins the occurrence of the wagering game by matching a game-winning pattern, or one of a plurality of game-winning patterns, of game indicia on at least one of the player'"'"'s game arrays with the randomly selected game indicia, comprising:

an input device for inputting a plurality of input selections;

a currency-accepting mechanism that is capable of allowing a player to deposit a medium of currency;

a display device;

a value-dispensing mechanism that is capable of dispensing value to the player;

a gaming unit controller operatively coupled to the input device, the currency-accepting mechanism, the output device, and the value-dispensing mechanism,

the gaming unit controller being programmed to allow the currency-accepting mechanism to accept a deposit of an amount of a medium of currency by a player at the gaming unit,

the gaming unit controller being programmed to allow the input device to receive input for a player'"'"'s enrollment in an occurrence of the multi-player wagering game, wherein each occurrence of the multi-player wagering game includes at least a predetermined total number of game arrays, wherein each player may have a plurality of game arrays for the occurrence of the multi-player wagering game,

the gaming unit controller being programmed to receive randomly selected game indicia from the range of game indicia transmitted to the gaming units over the gaming network,

the gaming unit controller being programmed to determine whether each randomly selected game indicia matches any of the game indicia of each game array in the order that the randomly selected indicia is selected,

the gaming unit controller being programmed to determine whether the game arrays have matched a game-winning pattern of game indicia on the player'"'"'s game arrays with the randomly selected game indicia in the fewest number of randomly selected game indicia, and

the gaming unit controller being programmed to award the player a game-winning award amount for each of the plurality of game arrays matching a game-winning pattern in the fewest number of randomly selected game indicia in response to determining that at least one game array matched the game-winning pattern of game indicia in the fewest number of randomly selected game indicia.

23. A gaming unit for providing a multi-player wagering game in accordance with claim 22, wherein the gaming unit controller is programmed to receive input for the player'"'"'s enrollment of up to one-half of the predetermined total number of game arrays for an occurrence of the multi-player wagering game.

24. A gaming unit for providing a multi-player wagering game in accordance with claim 22, wherein each occurrence of the multi-player wagering game includes exactly the predetermined total number of game arrays.

25. A gaming unit for providing a multi-player wagering game in accordance with claim 24, wherein the gaming unit controller is programmed to enroll the player in a different occurrence of the multi-player wagering game in response to the gaming unit controller or the gaming network determining that the number of game arrays for the player plus the total number of game arrays for all the players is greater than the predetermined total number of game arrays.

26. A gaming unit for providing a multi-player wagering game in accordance with claim 22, wherein the gaming unit controller is programmed to award the player the game-winning award amount equal to a total game-winning award amount for the occurrence of the multi-player wagering game divided by the number of game arrays matching the game-winning pattern in the fewest number of randomly selected game indicia.

27. A gaming unit for providing a multi-player wagering game in accordance with claim 22, wherein the gaming unit controller is programmed to cause the display device to display each of the game arrays for the player.

28. A gaming unit for providing a multi-player wagering game in accordance with claim 27, wherein the gaming unit controller is programmed to cause the display device to display each of the game arrays for the players so that the unique combination of indicia for each game array is visible at the same time.

29. A gaming unit for providing a multi-player wagering game in accordance with claim 27, wherein the gaming unit controller is programmed to cause the display device to display each of the game arrays for the players so that the unique combination of indicia for one of the game arrays is visible and a portion of each of the other game arrays is visible.

30. A gaming unit for providing a multi-player wagering game in accordance with claim 22, comprising a second display device operatively coupled to the gaming unit controller, the gaming unit controller being programmed to determine an outcome of a second wagering game corresponding to a combined outcome for the game arrays enrolled by the player for the occurrence of the multi-player wagering game, and to cause the second display device to display the outcome for the occurrence of the second wagering game.

31. A gaming unit for providing a multi-player wagering game in accordance with claim 22, comprising a second display device operatively coupled to the gaming unit controller,

the gaming unit controller being programmed to select one of a plurality of second wagering games for display at the second display device based on the number of game arrays enrolled in the occurrence of the multi-player wagering game, wherein each of the plurality of second wagering games corresponds to a number of game arrays that may be enrolled by a player for an occurrence of the multi-player wagering game,

the gaming unit controller being programmed to determine an outcome of the selected second wagering game corresponding to a combined outcome for the game arrays enrolled by the player for the occurrence of the multi-player wagering game, and

the gaming unit controller being programmed to cause the second display device to display the outcome for the occurrence of the selected second wagering game.

32. A gaming unit for providing a multi-player wagering game in accordance with claim 22, wherein:

the gaming unit controller is programmed to select a predetermined number of randomly selected game indicia from a plurality of predetermined numbers of game indicia based on the total number of game arrays enrolled in the occurrence of the multi-player wagering game;

the gaming unit controller is programmed to compare the number of randomly selected game indicia required for the player to match the game-winning pattern to selected predetermined number of game indicia in response to determining that a game array enrolled by the player matches the game-winning pattern in the fewest number of randomly selected game indicia;

the gaming unit controller is program to award the player a first game-winning award amount in response to determining the number of randomly selected game indicia required for the player to match the game-winning pattern is less than the selected predetermined number; and

the gaming unit controller is program to award the player a second game-winning award amount in response to determining the number of randomly selected game indicia required for the player to match the game-winning pattern is greater than the selected predetermined number.

33. A gaming unit for providing a multi-player wagering game in accordance with claim 22, wherein the game-winning pattern or plurality of game-winning patterns for the occurrence of the multi-player wagering game is determined based on the total number of game arrays enrolled for the occurrence of the multi-player wagering game.

34. A method for providing a multi-player wagering game on a gaming network having a plurality of gaming units wherein each player has at least one game array having a unique combination of indicia from a range of game indicia for an occurrence of the wagering game, wherein individual game indicia are randomly selected from the range of game indicia during the occurrence of the wagering game and transmitted to the gaming units over the gaming network, and wherein at least one of the players wins the occurrence of the wagering game by matching a game-winning pattern, or one of a plurality of game-winning patterns, of game indicia on at least one of the player'"'"'s game arrays with the randomly selected game indicia, the method comprising:

enrolling a plurality of players at corresponding gaming units for an occurrence of the multi-player wagering game, wherein each occurrence of the multi-player wagering game includes at least a predetermined total number of game arrays, and wherein each player may have a plurality of game arrays for the occurrence of the multi-player wagering game;

randomly selecting game indicia from the range of game indicia;

determining whether each randomly selected game indicia matches any of the game indicia of the at least one game array for each player in the order that the randomly selected game indicia are selected;

determining that at least one game array for the occurrence of the multi-player wagering game has matched a game-winning pattern of game indicia on the player'"'"'s game array with the randomly selected game indicia in the fewest number of randomly selected game indicia;

determining a game outcome for a player based on the game indicia of the player'"'"'s game arrays matching the randomly selected game indicia;

providing an alternate outcome display of a second wagering game at the gaming unit, wherein the second wagering game has a plurality of wagering options, and wherein the number of game arrays for the player corresponds to one of the wagering options of the second wagering game; and

displaying a second wagering game outcome at the alternate outcome display corresponding to the game outcome for the player for the multi-player wagering game, wherein the displayed second wagering game outcome is an outcome for the one of the wagering options corresponding to the number of game arrays for the player.

35. A method for providing a multi-player wagering game in accordance with claim 34, wherein each wagering option has a corresponding expected win frequency, and wherein the expected win frequency for a wagering option corresponding to the number of game arrays for the player is approximately equal to the expected win frequency for the plurality of game arrays.

36. A method for providing a multi-player wagering game in accordance with claim 35, wherein the second wagering game is a spinning reel game having a plurality of paylines, and wherein each wagering option is a number of paylines on which wagers are made.

37. A method for providing a multi-player wagering game in accordance with claim 36, wherein the total multi-player wagering game wager amount is equal to the number of game arrays for the player multiplied by the wager amount per game array for the occurrence of the multi-player wagering game, wherein the total second wagering game wager amount is equal to the number of paylines for the wagering option multiplied by the wager amount per payline for second wagering game outcome, and wherein the total multi-player wagering game wager amount is equal to the total second wagering game wager amount.

38. A method for providing a multi-player wagering game in accordance with claim 37, wherein the total multi-player wagering game wager amount is equal to a fixed total wager amount regardless of the number of game arrays for the player for the occurrence of the multi-player wagering game.

39. A method for providing a multi-player wagering game in accordance with claim 37, wherein the wager amount per game array is equal to a fixed wager amount per game array regardless of the number of game arrays for the player for the occurrence of the multi-player wagering game.

40. A method for providing a multi-player wagering game in accordance with claim 37, wherein the wager amount per payline is equal to a fixed wager amount per payline regardless of the number of game arrays for the player for the occurrence of the multi-player wagering game.

41. A method for providing a multi-player wagering game in accordance with claim 37, comprising determining a game award amount for the player for matching the game-winning pattern of game indicia on one of the game arrays with the randomly selected game indicia, wherein the game award amount is proportionate to the wager amount per game array for the occurrence of the multi-player wagering game.

42. A method for providing a multi-player wagering game in accordance with claim 37, comprising:

allowing the player to select a number of paylines for the spinning reel game of the alternate outcome display; and

enrolling the number of game arrays corresponding to the selected number of paylines of the second wagering game for the player for the occurrence of the wagering game.

43. A method for providing a multi-player wagering game in accordance with claim 42, comprising:

allowing the player to select a wager amount per payline for the spinning reel game of the alternate outcome display; and

calculating the wager amount per game array equal to the total second game wager amount divided by the number of game arrays enrolled for the occurrence of the multi-player wagering game.

44. A method for providing a multi-player wagering game in accordance with claim 43, comprising:

allowing the player to select one of the plurality of wagering options for the second wagering game of the alternate outcome display; and

enrolling the number of game arrays corresponding to the selected wagering option of the second wagering game for the player for the occurrence of the wagering game.

45. A method for providing a multi-player wagering game on a gaming network having a plurality of gaming units wherein each player has at least one game array having a unique combination of indicia from a range of game indicia for an occurrence of the wagering game, wherein individual game indicia are randomly selected from the range of game indicia during the occurrence of the wagering game and transmitted to the gaming units over the gaming network, and wherein at least one of the players wins the occurrence of the wagering game by matching a game-winning pattern, or one of a plurality of game-winning patterns, of game indicia on at least one of the player'"'"'s game arrays with the randomly selected game indicia, the method comprising:

enrolling a plurality of players at corresponding gaming units for an occurrence of the multi-player wagering game for a predetermined enrollment time period, wherein each player may have a plurality of game arrays for the occurrence of the multi-player wagering game;

beginning the occurrence of the multi-player wagering game in response to determining that the number of game arrays enrolled for the occurrence of the multi-player wagering game within the enrollment time period is equal to a predetermined total number of game arrays;

determining a range of the total number of game arrays required to begin the occurrence of the multi-player wagering game in response to determining that the number of game arrays enrolled for the occurrence of the multi-player wagering game within the enrollment time period is less than the predetermined total number of game arrays;

beginning the occurrence of the multi-player wagering game in response to determining that the number of game arrays enrolled for the occurrence of the multi-player wagering game after the enrollment time period is within the required range of the total number of game arrays;

randomly selecting game indicia from the range of game indicia;

determining whether each randomly selected game indicia matches any of the game indicia of the at least one game array for each player in the order that the randomly selected game indicia are selected;

determining that at least one game array for the occurrence of the multi-player wagering game has matched a game-winning pattern of game indicia on the player'"'"'s game array with the randomly selected game indicia in the fewest number of randomly selected game indicia; and

determining a game-winning award amount for each player having at least one game array matching a game-winning pattern in the fewest number of randomly selected game indicia, wherein each player receives a game-winning award for each of the at least one game arrays matching the game-winning pattern in the fewest number of randomly selected game indicia.

46. A method for providing a multi-player wagering game in accordance with claim 45, wherein the range of the total number of game arrays is the range of numbers from one less than the predetermined total number of game arrays to one more than the total number of game arrays.

47. A method for providing a multi-player wagering game in accordance with claim 45, comprising:

determining a second range of the total number of game arrays required to begin the occurrence of the multi-player wagering game in response to determining that the number of game arrays enrolled for the occurrence of the multi-player wagering game within a second enrollment time period is less than the lowest total number of game arrays in the required range of the total number of game arrays, wherein the second required range is larger than the original required range; and

beginning the occurrence of the multi-player wagering game in response to determining that the number of game arrays enrolled for the occurrence of the multi-player wagering game after the after the enrollment time period is within the second required range of the total number of game arrays.

48. A method for providing a multi-player wagering game in accordance with claim 45, comprising enrolling a player in a different occurrence of the multi-player wagering game when the number of game arrays for the player plus the total number of game arrays for all the players is greater than the predetermined total number of game arrays during the enrollment time period, and is greater than the upper limit of the required range after the enrollment time period.