Method, apparatus and article for dual-sided playing cards

Abstract

A dual-sided card deck allows for the contemporaneous play of two separate card games. The deck is comprised of a plurality of cards having a first set of values on a first side and a second set of values on a second side. A first card game is played using values assigned to symbols provided on the first side of each of the plurality of cards to determine the outcome of the first game. The outcome of a second card game is determined using the same hand of cards used to play the first game, but using values assigned to symbols provided on the second side of each of the plurality of cards held during the first game. To deter card counting, the symbols appearing on the first side of the plurality of cards can be pseudo-randomly generated and linked to the symbols appearing on the second side of the plurality of cards.

1 . A plurality of playing cards for wagering, each of the playing cards in the plurality of playing cards comprising: 
 a first side; and    a second side opposed to, the first side;    the first side bearing at least a first primary symbol, the first primary symbol selected from a first set of primary symbols, each of the first primary symbols in the first set of primary symbols indicative of a playing card identity according to a first set of game rules, the first set of game rules defining values of various combinations of the playing card identities; and    the second side bearing at least a first secondary symbol, the first secondary symbol selected from a first set of secondary symbols, each of the first secondary symbols in the first set of secondary symbols indicative of a playing card identity according to a second set of game rules, the second set of game rules defining values of various combinations of the playing card identities independently of the first primary symbols.    
   
   
       2 . The plurality of playing cards according to  claim 1  wherein the first set of secondary symbols is different than the first set of primary symbols.  
   
   
       3 . The plurality of playing cards according to  claim 1  wherein the first set of secondary symbols is identical to the first set of primary symbols.  
   
   
       4 . The plurality of playing cards according to  claim 1  wherein the first side bears at least a second primary symbol, the second primary symbol selected from a second set of primary symbols, each of the second primary symbols in the second set of primary symbols indicative of the playing card identity in combination with the first primary symbols from the first set of primary symbols according to the first set of game rules, the first set of game rules defining values of various combinations of the playing card identities.  
   
   
       5 . The plurality of playing cards according to  claim 4  wherein the first set of primary symbols comprises a standard set of playing card rank symbols 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, and A.  
   
   
       6 . The plurality of playing cards according to  claim 5  wherein the second set of primary symbols comprises a standard set of playing card suit symbols ♥,  , ♦, and  .  
   
   
       7 . The plurality of playing cards according to  claim 6  wherein the second side bears at least a second secondary symbol, the second secondary symbol selected from a second set of secondary symbols, each of the second secondary symbols in the second set of secondary symbols indicative of the playing card identity in combination with the first secondary symbols from the first set of secondary symbols according to the second set of game rules, the second set of game rules defining values of various combinations of the playing card identities.  
   
   
       8 . The plurality of playing cards according to  claim 7  wherein the first set of secondary symbols comprises a standard set of playing card rank symbols 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, and A.  
   
   
       9 . The plurality of playing cards according to  claim 8  wherein the first set of secondary symbols comprises a standard set of playing card suit symbols ♥,  , ♦, and  .  
   
   
       10 . The plurality of playing cards according to  claim 9  wherein the first and second primary symbols on the first side of any of the playing cards where the second primary symbol on the first side is one of the ♥ and the ♦ are a first color and the first and the second primary symbols on the first side of any of the playing cards where the second primary symbol on the first side is one of the   and the   is a second color, and wherein the first and the second secondary symbols on the second side of any of the playing cards where the second secondary symbol on the second side is one of the ♥ and the ♦ are the first color and the first and the second secondary symbols on the second side of any of the playing cards where the second secondary symbol on the second side is one of the   and the   is the first color.  
   
   
       11 . The plurality of playing cards according to  claim 1  wherein the first set of game rules are game rules for one of Blackjack, Poker, Baccarat, Caribbean Stud Poker, and LET IT RIDE.  
   
   
       12 . The plurality of playing cards according to  claim 11  wherein the second set of game rules are game rules for one of Blackjack, Poker, Baccarat, Caribbean Stud Poker, and LET IT RIDE.  
   
   
       13 . The plurality of playing cards according to  claim 11  wherein the second set of game rules are identical to the first set of game rules.  
   
   
       14 . The plurality of playing cards according to  claim 11  wherein the second set of game rules are different than the first set of game rules.  
   
   
       15 . The plurality of playing cards according to  claim 1  wherein the first set of secondary symbols comprises at least a subset of standard slot machine symbols including a cherry, a bar, and a bell.  
   
   
       16 . The plurality of playing cards according to  claim 1  wherein the first set of secondary symbols comprises a set of numbers.  
   
   
       17 . The plurality of playing cards according to  claim 1  wherein the first set of secondary symbols comprises a set of graphics.  
   
   
       18 . The plurality of playing cards according to  claim 1  wherein the first set of secondary symbols comprises a set of graphics, at least some of the graphics in the set of graphics forming at least one rebus.  
   
   
       19 . The plurality of playing cards according to  claim 1  wherein the second set of game rules define values of various combinations of the playing card identities according to a number of playing cards collected having matching secondary symbols on the second side of the playing cards and a relative ordering of the matching secondary symbols with respect to the other secondary symbols comprising the first set of secondary symbols.  
   
   
       20 . The plurality of playing cards according to  claim 1  wherein the second set of game rules define values of various combinations of the playing card identities according to a number of playing cards collected having matching secondary symbols on the second side of the playing cards.  
   
   
       21 . The plurality of playing cards according to  claim 1  wherein the second set of game rules define values of various combinations of the playing card identities according to a cumulative value of a collection of playing cards determined by adding a value represented by the secondary symbols on the second side of the playing cards.  
   
   
       22 . (canceled)  
   
   
       23 . The plurality of playing cards according to  claim 1  wherein a first probability of the first symbol appearing on the first side is dependent on a second probability of the first secondary symbol appearing on the second side.  
   
   
       24 . The plurality of playing cards of  claim 1  wherein two playing cards in the first plurality of playing cards have a same identity.  
   
   
       25 . A set of playing cards for wagering, each of the playing cards comprising: 
 a first side bearing at least a first primary symbol and a second primary symbol, the first primary symbol selected from a standard set of playing card rank symbols comprising 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, and A, and the second primary symbol selected from a standard set of playing card suit symbols ♥,  , ♦, and  , the combination of the first and the second primary symbols on each of the playing cards indicative of a first respective playing card identity; and    a second side bearing at least a first secondary symbol, the first secondary symbol on the second side selected from a first set of secondary symbols, each of the first secondary symbols in the first set of secondary symbols indicative of a respective second playing card identity according to a set of game rules the second playing card identity independent of the first playing card identity.    
   
   
       26 . The set of playing cards according to  claim 25  wherein the first set of secondary symbols comprises at least a subset of standard slot machine symbols including a cherry, a bar, and a bell.  
   
   
       27 . The set of playing cards according to  claim 25  wherein the first set of secondary symbols comprises a set of integers.  
   
   
       28 . The set of playing cards according to  claim 25  wherein the first set of secondary symbols comprises a set of graphics.  
   
   
       29 . The set of playing cards according to  claim 25  wherein the first set of secondary symbols comprises a set of graphics, at least some of the graphics in the set of graphics forming at least one rebus.  
   
   
       30 . The set of playing cards according to  claim 25  wherein the set of playing cards includes fifty-two playing cards, the first side of each of the playing cards bearing a respective combination of the first primary symbol and the second primary symbol, and wherein the first secondary symbol on the second side of the playing card is not discernible from the first primary symbol and the second primary symbol on the first side of the playing card.  
   
   
       31 . A method of producing playing cards having a face and a back, the method comprising: 
 forming at least a first primary symbol on the face of the playing card, the first primary symbol from a first set of primary symbols and indicative of a first playing card identity of a playing card according to a first set of game rules, the first set of game rules defining values of various combinations of the first playing card identities;    pseudo-randomly generating at least a first secondary symbol from a first set of secondary symbols, each of the secondary symbols in the first set of secondary symbols indicative of a second playing card identity according to a second set of game rules, the second set of game rules defining values of the second playing card identities independent of the first playing card identities; and    forming the first secondary symbol on the back of the playing card.    
   
   
       32 . The method according to  claim 31 , the method further comprising: 
 forming at least a second primary symbol on the face of the playing card, the second primary symbol from a second set of primary symbols where the first set of primary symbols is a standard set of playing card ranks and the second set of primary symbols is a standard set of playing card suits.    
   
   
       33 . The method according to  claim 32 , further comprising: 
 pseudo-randomly generating the first and the second primary symbols.    
   
   
       34 . The method according to  claim 31  wherein forming the first secondary symbol on the back of the playing card comprises printing the first secondary symbol on a portion of the back of the playing card.  
   
   
       35 - 37 . (canceled)  
   
   
       38 . The method according to  claim 31  wherein pseudo-randomly generating at least a first secondary symbol further comprises pseudo-randomly generating the first secondary symbol and a second secondary symbol, the second secondary symbol from a second set of secondary symbols, the combination of the first and the second secondary symbols indicative of the second playing card identity according to the second set of game rules where the first set of secondary symbols comprises a standard set of playing card ranks and the second set of secondary symbols comprises a standard set of playing card suits.  
   
   
       39 . The plurality of playing cards according to  claim 38  wherein if the second primary symbol on the playing card is one of the ♥ and the ♦ then forming the first and the second primary symbols comprises printing with a first color and if the second primary symbol on the playing card is one of the   and the   then forming the first and the second primary symbols comprises printing with a second color and if the second secondary symbol on the playing card is one of the ♥ and the ♦ then forming the first and the second secondary symbols comprises printing with the second color and if the second secondary symbol on the playing card is one of the   and the   then forming the first and the second secondary symbols comprises printing with the first color.  
   
   
       40 . The method according to  claim 31 , further comprising: 
 removing the playing card from a printer after forming one of the first primary symbol and the first secondary symbol;    reinserting the playing card in the printer before forming the other one of the first primary symbol and the first secondary symbol.    
   
   
       41 . The method according to  claim 31  wherein both the first primary symbol and the first secondary symbol are formed before removing the playing card from a symbol forming device.  
   
   
       42 . A device for producing playing cards, the device comprising: 
 a housing;    a media path extending through the housing along which playing card stock passes;    at least a one printhead coupled to receive print data, the at least one printhead proximate the media path and operable to print on the playing card stock passing the printhead along the media path; and    at least one processor configured to pseudo-randomly generate at least a number of first secondary identifiers, each of the first secondary identifiers corresponding to a respective first secondary symbol, the first secondary symbols being from a first set of secondary symbols, where the at least one processor is coupled to provide print data representing the first secondary symbols and representing at least a number of first primary symbols, the first primary symbols from a first set of primary symbols, the at least one processor configured to cause the printhead to print the first secondary symbol on a back of the playing card stock and to print the first primary symbol on a face of the playing card stock, where each of the primary symbols in the first set of primary symbols indicative of a playing card identity according to a first set of game rules, the first set of game rules defining values of various combinations of the playing card identities and each of the secondary symbols in the first set of secondary symbols indicative of a playing card identity according to a second set of game rules.    
   
   
       43 . The device according to  claim 42  wherein the processor is further configured to pseudo-randomly generate at least a first number of first primary identifiers representing respective ones of the first primary symbols.  
   
   
       44 . The device according to  claim 42  wherein the processor is further configured to pseudo-randomly generate at least a first number of primary identifiers representing respective combinations of the first primary symbol and a second primary symbol, the second primary symbol from a second set of primary symbols.  
   
   
       45 . The device according to  claim 42 , further comprising: 
 at least a second printhead opposed across the media path with respect to the first printhead to print on the opposite side of the playing card stock from the first printhead.    
   
   
       46 . A method of producing playing cards having a face and a back, the face bearing a first primary symbol from a first set of primary symbols and a second primary symbol from a second set of primary symbols, the first and the second primary symbols pre-printed on the face of the playing card and indicative of an a first playing card identity of a playing card according to a first set of game rules, the first set of game rules defining values of various combinations of the first playing card identities, the method comprising: 
 pseudo-randomly generating at least a first secondary symbol from a first set of secondary symbols, each of the secondary symbols in the first set of secondary symbols indicative of a second playing card identity according to a second set of game rules, the second set of game rules defining values of the second playing card identities the second playing card identities independent of the first playing card identities; and    forming the first secondary symbol on the back of the playing card.    
   
   
       47 . The method according to  claim 46  wherein the first set of primary symbols is a standard set of playing card ranks and the second set of primary symbols is a standard set of playing card suits, and wherein pseudo-randomly generating at least a first secondary symbol from a first set of secondary symbols comprises pseudo-randomly generating the first secondary symbol from at least a subset of standard slot machine symbols.  
   
   
       48 . (canceled)  
   
   
       49 . A device for producing playing cards from preprinted playing card stock, the preprinted playing card stock bearing a first and a second symbol selected from a standard set of playing card rank symbols and a standard set of playing card suit symbols, respectively, the device comprising: 
 a housing;    a media path extending through the housing along which the playing card stock passes;    at least a one printhead coupled to receive print data, the at least one printhead proximate the media path and operable to print on the playing card stock passing the printhead along the media path; and    at least one processor configured to pseudo-randomly generate at least a number of first secondary identifiers, each of the first secondary identifiers corresponding to a respective first secondary symbol, the first secondary symbols from a first set of secondary symbols, where the at least one processor is coupled to provide the print data representing the first secondary symbols to cause the printhead to print the first secondary symbols on a back of the playing card stock.    
   
   
       50 . The device according to  claim 49  wherein the at least one processor comprises a first processor configured to pseudo-randomly generate at least a first number of identifiers and a second processor configured to provide the print data representing the first secondary symbols.  
   
   
       51 . A method of contemporaneously playing two card games with a dual-sided card deck, the method comprising: 
 dealing a number of playing cards to at least a first player, each playing card having at least a first primary symbol on a first side and at least a first secondary symbol on a second side, the first primary symbols from a first set of primary symbols and the first secondary symbols from a first set of secondary symbols;    determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards; and    determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards.    
   
   
       52 . The method according to  claim 51  wherein the first set of game rules is one of blackjack rules and baccarat rules, the first set of primary symbols is a set of stand playing card rank symbols, and determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards comprises: 
 determining a value for each of the playing cards corresponding to the rank symbol on the first side of the playing card;    summing each of the determined values for the number of playing cards; and    comparing the sum of the values to at least one other value.    
   
   
       53 . The method according to  claim 52  wherein the second set of game rules is one of blackjack rules and baccarat rules, the first set of secondary symbols is a set of stand playing card rank symbols, and determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises: 
 determining a value for each of the playing cards corresponding to the rank symbol on the second side of the playing card;    summing each of the determined values for the number of playing cards; and    comparing the sum of the values to at least one other value.    
   
   
       54 . The method according to  claim 51  wherein the first set of game rules is poker, the first set of face symbols is a set of stand playing card rank symbols, and determining the outcome of the first game comprises: 
 determining a rank and suit for each of the playing cards corresponding to the first primary identifier and a second primary identifier, respectively;    determining a number of combinations of the playing cards having identical ranks and the number of playing cards in each determined combination;    determining a number of combinations of the playing cards having identical suits and the number of playing cards in each determined combination; and    comparing the determined number of combinations of playing cards having identical ranks and identical suits and the number of playing cards in each combination to at least one other hand of playing cards employing a set of predefined rankings.    
   
   
       55 . The method according to  claim 51  wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining an existence or absence of a particular one of the first secondary symbols on at least one of the playing cards.  
   
   
       56 . The method according to  claim 51  wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining a quantity of the playing cards having identical first secondary symbols.  
   
   
       57 . The method according to  claim 51  where the first set of secondary symbols comprises at least a cherry symbol, a bell symbol and a bar symbol, and wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining a quantity of the playing cards having identical first secondary symbols.  
   
   
       58 . The method according to  claim 51  where the first set of secondary symbols comprises a number of graphics, at least some of the graphics forming a rebus, and wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining whether the player correctly solves the rebus formed by the first secondary symbols on the playing cards.  
   
   
       59 . The method according to  claim 51  where the first set of secondary symbols comprises a number of graphics, at least some of the graphics representing at least one prize, and wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining whether the existence of at least one playing card in the number of playing cards bearing one of the first secondary symbols representing one of the prizes.  
   
   
       60 . A method of playing a wagering game, the method comprising: 
 dealing a number of hands of playing cards to each of a number of players, each playing card having at least a first primary symbol on a first side and at least a first secondary symbol on a second side, the first primary symbols from a first set of primary symbols and the first secondary symbols from a first set of secondary symbols;    determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand; and    for each of a number of winning hands determined based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand, determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards.    
   
   
       61 . The method of  claim 60  wherein determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand comprises determining the outcome of the first game based on a value of the hand of playing cards based on a value of the first primary symbol on each of the playing card in the hand.  
   
   
       62 . The method of  claim 60  wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first primary symbol on the second side of at least one of the number of playing cards comprises determining the outcome of the second game based on value of the hand of playing cards based on a value of the first primary symbol on each of the playing card in the hand.  
   
   
       63 . The method of  claim 60  wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining the outcome of the second game based a number of the playing cards in the hand that each have a same one of the first secondary symbols.  
   
   
       64 . The method of  claim 60 , further comprising: 
 for each of a number of winning hands determined based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand; providing the player a first payout; and    for each of a number of winning hands determined based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards of each hand, providing the player a second payout.    
   
   
       65 . The method of  claim 60 , further comprising: 
 for each of a number of winning hands determined based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards of each hand, enhancing a payout to the player.    
   
   
       66 . A method of playing a wagering game, the method comprising: 
 dealing a number of hands of playing cards to each of a number of players, each playing card having at least a first primary symbol on a first side and at least a first secondary symbol on a second side, the first primary symbols from a first set of primary symbols and the first secondary symbols from a first set of secondary symbols;    determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand; and    for each of a number of losing hands, determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards.    
   
   
       67 . The method of  claim 66  wherein determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand comprises determining the outcome of the first game based on value of the hand of playing cards based on a value of the first primary symbol on each of the playing card in the hand.  
   
   
       68 . The method of  claim 66  wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining the outcome of the second game based on value of the hand of playing cards based on a value of the first secondary symbol on each of the playing card in the hand.  
   
   
       69 . The method of  claim 66  wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining the outcome of the second game based a number of the playing cards in the hand that each have a same one of the first secondary symbols.  
   
   
       70 . The method of  claim 66  wherein determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards comprises determining the outcome of the second game based at least one of the playing cards in the hand having a particular one of the first secondary symbols.  
   
   
       71 . A method of playing a card game, the method comprising: 
 for each of a number of players, determining if the player placed a primary wager;    dealing a number of hands of playing cards to each of a number of players who placed a respective one of the primary wagers, each playing card having at least a first primary symbol on a first side and at least a first secondary symbol on a second side, the first primary symbols from a first set of primary symbols and the first secondary symbols from a first set of secondary symbols;    determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand;    determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards; and    for each of a number of winning hands, if any, determined based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards of each hand, providing the player an award.    
   
   
       72 . The method according to  claim 71 , further comprising: 
 determining an amount of the award according to a predetermined payout schedule.    
   
   
       73 . The method according to  claim 71 , further comprising: 
 determining an amount of the award based at least on a value assigned to at least the first secondary symbol.    
   
   
       74 . The method according to  claim 71 , further comprising: 
 determining an amount of the award based at least one of a good and a service represented by at least the first secondary symbol.    
   
   
       75 . A method of playing a card game, the method comprising: 
 for each of a first number of players, determining if the player placed a primary wager;    dealing a number of hands of playing cards to each of the players who placed a respective one of the primary wagers, each playing card having at least a first primary symbol on a first side and at least a first secondary symbol on a second side, the first primary symbols from a first set of primary symbols and the first secondary symbols from a first set of secondary symbols;    determining an outcome of a first game according to a first set of game rules based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand;    for each of a second number of players, determining if the player placed a secondary wager; and    for each of the players who placed a secondary wager, determining an outcome of a second game according to a second set of game rules based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards in the respective hand of playing cards.    
   
   
       76 . The method of  claim 75 , further comprising: 
 for each of a number of winning hands determined based at least in part on the first primary symbol on the first side of at least one of the number of playing cards of each hand; providing the player a first payout; and    for each of a number of winning hands determined based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards of each hand, providing the player a second payout.    
   
   
       77 . The method of  claim 75 , further comprising: 
 for each of a number of winning hands determined based at least in part on the first secondary symbol on the second side of at least one of the number of playing cards of each hand, enhancing a base payout to the player.    
   
   
       78 . The method of  claim 75  wherein the second number of players is equal to the first number of players.  
   
   
       79 . A device for producing playing cards, the device comprising: 
 means for pseudo-randomly generating at least a number of first secondary identifiers;    means for associating the number of first secondary identifiers with respective ones of a number of first secondary symbol, the first secondary symbols from a first set of secondary symbols, each of the secondary symbols in the first set of secondary symbols indicative of a playing card identity according to one set of game rules; and    means for printing the first secondary symbols on a back of a playing card stock where a face of the playing card stock bears a first and a second primary symbols, the first and the second primary symbols from a standard set of playing card ranks and a standard set of playing card suits, respectively.    
   
   
       80 . The device according to  claim 79 , further comprising: 
 means for pseudo-randomly generating at least a number of first primary identifiers;    means for associating the number of first primary identifiers with respective ones of the number of first primary symbols; and    means for printing the first primary symbols on the face of the playing card stock.    
   
   
       81 . The device according to  claim 80  wherein the means for pseudo-randomly generating at least a number of first secondary identifiers is independent of the first primary identifiers.  
   
   
       82 . The device according to  claim 80  wherein the means for pseudo-randomly generating at least a number of first secondary identifiers is dependent of the first primary identifiers.