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A gaming device having unisymbol display reels, wherein each symbol on a display of the gaming device represents or is included on a different reel. The present invention structures the paylines of the gaming device such that the gaming device can include different reel strips having different winni

A gaming device having unisymbol display reels, wherein each symbol on a display of the gaming device represents or is included on a different reel. The present invention structures the paylines of the gaming device such that the gaming device can include different reel strips having different winning symbols or different proportions of winning symbols, while still maintaining payout symbols and payout combinations that have uniform odds and uniform payouts.

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The invention is claimed as follows: 1. A method of operating a gaming device having a slot game, said method comprising: (a) providing a plurality of unisymbol display reels in the slot game, at least one of said unisymbol display reels having a different probability of generating at least one sym

The invention is claimed as follows: 1. A method of operating a gaming device having a slot game, said method comprising: (a) providing a plurality of unisymbol display reels in the slot game, at least one of said unisymbol display reels having a different probability of generating at least one symbol than another one of said unisymbol display reels; (b) displaying a plurality of columns each having X number of said unisymbol display reels, where X is at least one; (c) displaying a plurality of rows each having Y number of said unisymbol display reels, where Y is at least one; and (d) providing a plurality of paylines associated with said unisymbol display reels in said rows and columns, each said payline associated with a same number of each of the unisymbol display reels having said different probabilities such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different of said paylines. 2. The method of claim 1, which includes at least one column having X-W number of said unisymbol display reels, where W is less than X. 3. The method of claim 1, which includes at least one row having Y-Z number of said unisymbol display reels, where Z is less than Y. 4. The method of claim 1, wherein at least one of said columns has X-W number of said unisymbol display reels, where W is less than X and at least one of said rows has Y-Z number of said unisymbol display reels, where Z is less than Y. 5. The method of claim 4, wherein the W number of unisymbol display reels is different from the Z number of unisymbol display reels. 6. The method of claim 1, wherein the unisymbol display reels in each of said plurality of columns have the same probability of generating symbols. 7. The method of claim 6, wherein each payline is associated with one unisymbol display reel from each column. 8. The method of claim 1, wherein the unisymbol display reels in each of said plurality of rows have the same probability of generating symbols. 9. The method of claim 8, wherein each payline is associated with one unisymbol display reel from each row. 10. The method of claim 1, which is provided through a data network. 11. The method of claim 10, wherein the data network is an internet. 12. A method of operating a gaming device having a slot game, said method comprising: (a) providing a plurality of unisymbol display reels, at least one of said unisymbol display reels having a different probability of generating at least one symbol than another one of said unisymbol display reels; (b) displaying a plurality of first groups of said unisymbol display reels, each having X number of said unisymbol display reels, where X is at least one; (c) displaying a plurality of second groups of said unisymbol display reels, each having Y number of said unisymbol display reels, where Y is at least one; and (d) providing a plurality of paylines associated with said unisymbol display reels in said first and second groups, wherein each payline is associated with one of each of the unisymbol display reels having said different probabilities such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 13. The method of claim 12, wherein at least one of the first groups includes X-W number of said unisymbol display reels, where W is less than X. 14. The method of claim 12, wherein at least one of the second groups includes Y-Z number of said unisymbol display reels, where Z is less than Y. 15. The method of claim 12, which includes at least one column having X-W number of said unisymbol display reels, where W is less than X and at least one row having Y-Z number of said unisymbol display reels, where Z is less than Y. 16. The method of claim 15, wherein the W number of unisymbol display reels is different from the Z number of unisymbol display reels. 17. The method of claim 12, wherein the unisymbol display reels in each of said plurality of first groups have the same probability of generating said symbols. 18. The method of claim 17, wherein each payline is associated with a same number of unisymbol display reels from the same group. 19. The method of claim 12, wherein the unisymbol display reels in each of said plurality of second groups have the same probability of generating said symbols. 20. The method of claim 19, wherein each payline is associated with a same number of unisymbol display reels from the same group. 21. The method of claim 12, which is provided through a data network. 22. The method of claim 21, wherein the data network is an internet. 23. A method of operating a gaming device, said method comprising: displaying a plurality of unisymbol display reels arranged in a matrix of rows and columns, where at least one unisymbol display reel has a different probability of generating at least one symbol than another one of said unisymbol display reels, and where (a) at least one column of the unisymbol display reels has a different number of the unisymbol display reels than another of the columns, or (b) at least one row of the unisymbol display reels has a different number of the unisymbol display reels than another of the rows; and providing a plurality of paylines associated with said unisymbol display reels in said columns and rows, each payline associated with at least one unisymbol display reel in each column such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 24. The method of claim 23, which includes displaying each column of unisymbol display reels to include a set of symbols that is different from sets of symbols of the unisymbol display reels of the other columns. 25. The method of claim 23, which includes displaying each row of unisymbol display reels to include a set of symbols that is different from sets of symbols of the unisymbol display reels of a plurality of other rows. 26. The method of claim 23, wherein the columns and rows are positioned orthogonally with respect to one another. 27. The method of claim 23, which is provided through a data network. 28. The method of claim 27, wherein the data network is an internet. 29. A method of operating a gaming device having a slot game, said method comprising: (a) providing a plurality of unisymbol display reels in the slot game, where at least one of said unisymbol display reels has a different number of at least one symbol than another one of said unisymbol display reels; (b) displaying a plurality of columns each having X number of said unisymbol display reels, where X is at least one; (c) displaying a plurality of rows each having Y number of said unisymbol display reels, where Y is at least one; and (d) providing a plurality of paylines associated with said unisymbol display reels in said rows and columns, wherein each payline is associated with the same number of each of the unisymbol display reels having different numbers of at least one symbol such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 30. The method of claim 29, which includes at least one column having X-W number of said unisymbol display reels, where W is less than X. 31. The method of claim 29, which includes at least one row having Y-Z number of said unisymbol display reels, where Z is less than Y. 32. The method of claim 29, which includes at least one column having X-W number of said unisymbol display reels, where W is less than X and at least one row having Y-Z number of said unisymbol display reels, where Z is less than Y. 33. The method of claim 32, wherein the W number of unisymbol display reels is different from the Z number of unisymbol display reels. 34. The method of claim 29, wherein the unisymbol display reels in each of said plurality of columns have the same number of each symbol. 35. The method of claim 34, wherein each payline is associated with one unisymbol display reel from each column. 36. The method of claim 29, wherein the unisymbol display reels in each of said plurality of rows have the same number of each symbol. 37. The method of claim 36, wherein each payline is associated with one unisymbol display reel from each row. 38. The method of claim 29, which is provided through a data network. 39. The method of claim 38, wherein the data network is an internet. 40. A method of operating a gaming device having a slot game, said method comprising: (a) providing a plurality of unisymbol display reels, where at least one of said unisymbol display reels has a different number of at least one symbol than another one of said unisymbol display reels; (b) displaying a plurality of first groups of said unisymbol display reels, each having X number of said unisymbol display reels, where X is at least one; (c) displaying a plurality of second groups of said unisymbol display reels, each having Y number of said unisymbol display reels, where Y is at least one; and (d) providing a plurality of paylines associated with said unisymbol display reels in said first and second groups, where each payline is associated with the same number of each of the unisymbol display reels having different numbers of at least one symbol such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 41. The method of claim 40, wherein at least one of the first groups includes X-W number of said unisymbol display reels, where W is less than X. 42. The method of claim 40, wherein at least one of the second groups includes Y-Z number of said unisymbol display reels, where Z is less than Y. 43. The method of claim 40, which includes at least one group having X-W number of said unisymbol display reels, where W is less than X and at least one group having Y-Z number of said unisymbol display reels, where Z is less than Y. 44. The method of claim 43, wherein the W number of unisymbol display reels is different from the Z number of unisymbol display reels. 45. The method of claim 40, wherein the unisymbol display reels in each of said plurality of first groups have the same number of each symbol. 46. The method of claim 45, wherein each payline is associated with a same number of unisymbol display reels from the same group. 47. The method of claim 40, wherein the unisymbol display reels in each of said plurality of second groups have the same number of each symbol. 48. The method of claim 47, wherein each payline is associated with a same number of unisymbol display reels from the same group. 49. The method of claim 40, which is provided through a data network. 50. The method of claim 49, wherein the data network is an internet. 51. A method of operating a gaming device, said method comprising: displaying a plurality of unisymbol display reels arranged in a matrix of rows and columns, where at least one unisymbol display reel has a different number of at least one symbol than another one of said unisymbol display reels, and where (a) at least one column of the unisymbol display reels has a different number of the unisymbol display reels than another of the columns, or (b) at least one row of the unisymbol display reels has a different number of the unisymbol display reels than another of the rows; and providing a plurality of paylines associated with said unisymbol display reels in said columns and rows, wherein each payline is associated with the same number of each of the unisymbol display reels having different numbers of at least one symbol such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 52. The method of claim 51, wherein at least one column of unisymbol display reels includes at least one symbol that is different from at least one symbol on the unisymbol display reels of at least one other column. 53. The method of claim 51, wherein at least one row of unisymbol display reels includes at least one symbol that is different from at least one symbol on the unisymbol display reels of at least one other row. 54. The method of claim 51, wherein the columns and rows are positioned orthogonally with respect to one another. 55. The method of claim 51, which is provided through a data network. 56. The method of claim 55, wherein the data network is an internet. 57. A gaming device comprising: a plurality of symbols; a plurality of unisymbol display reels, each unisymbol display reel configured to generate one of said plurality of symbols; a probability of generating one of said symbols associated with each unisymbol display reel, wherein at least one of said unisymbol display reels has a different probability of generating at least one symbol than another one of said unisymbol display reels; said unisymbol display reels configured such that: (a) X number of said unisymbol display reels are displayable in each of a plurality of columns, where X is at least one, and (b) Y number of said unisymbol display reels are displayable in each of a plurality of rows, where Y is at least one; and a plurality of paylines associated with said unisymbol display reels in said rows and columns, wherein each payline is associated with the same number of each of the unisymbol display reels having the different probabilities such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 58. The gaming device of claim 57, which includes a set of symbols displayable by each unisymbol display reel, wherein at least one of said sets of symbols is different than the sets of symbols displayable by the other unisymbol display reels. 59. The gaming device of claim 57, wherein at least one column includes X-W number of said unisymbol display reels, where W is less than X. 60. The gaming device of claim 57, wherein at least one row includes Y-Z number of said unisymbol display reels, where Z is less than Y. 61. The method of claim 57, which includes at least one column having X-W number of said unisymbol display reels, where W is less than X and at least one row having Y-Z number of said unisymbol display reels, where Z is less than Y. 62. The method of claim 61, wherein the number of unisymbol display reels is different from the Z number of unisymbol display reels. 63. The gaming device of claim 57, wherein the unisymbol display reels in each of said plurality of columns have the same probability of generating symbols. 64. The gaming device of claim 63, wherein each payline is associated with one unisymbol display reel from each column. 65. The gaming device of claim 57, wherein the unisymbol display reels in each of said plurality of rows have the same probability of generating said symbols. 66. The gaming device of claim 65, wherein each payline is associated with one unisymbol display reel from each row. 67. The gaming device of claim 57, which is provided through a data network. 68. The gaming device of claim 67, wherein the data network is an internet. 69. A gaming device comprising: a plurality of symbols; a plurality of unisymbol display reels, each unisymbol display reel configured to generate one of said plurality of symbols, wherein at least one of said unisymbol display reels has a different probability of generating a symbol than does another one of said unisymbol display reels; said plurality of unisymbol display reels configured such that X number of said unisymbol display reels are displayable in each of a plurality of first groups, where X is at least one, and such that Y number of said unisymbol display reels are displayable in each of a plurality of second groups, where Y is at least one; and a plurality of paylines, wherein each payline is associated with one of each of the unisymbol display reels having the different probabilities such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 70. The gaming device of claim 69, which includes a set of symbols displayable by each unisymbol display reel, wherein at least one of said sets of symbols is different than the sets of symbols displayable by the other unisymbol display reels. 71. The gaming device of claim 69, wherein at least one of the first groups includes X-W number of said unisymbol display reels, where W is less than X. 72. The gaming device of claim 69, wherein at least one of the second groups includes Y-Z number of said unisymbol display reels, where Z is less than Y. 73. The method of claim 69, which includes at least one group having X-W number of said unisymbol display reels wherein W is less than X and at least one group having Y-Z number of said unisymbol display reels, where Z is less than Y. 74. The method of claim 73, wherein the W number of unisymbol display reels is different from the Z number of unisymbol display reels. 75. The gaming device of claim 69, wherein the unisymbol display reels in each of said plurality of first groups have the same probability of generating at least one symbol. 76. The gaming device of claim 75, wherein each payline is associated with a same number of unisymbol display reels from the same group. 77. The gaming device of claim 69, wherein the unisymbol display reels in each of said plurality of second groups have the same probability of generating at least one symbol. 78. The gaming device of claim 77, wherein each payline is associated with a same number of unisymbol display reels from the same group. 79. The gaming device of claim 69, which is provided through a data network. 80. The gaming device of claim 79, wherein the data network is an internet. 81. A gaming device comprising: a plurality of unisymbol display reels arranged and displayable in a matrix of rows and columns, wherein at least one unisymbol display reel has a different probability of generating a symbol than does another one of said unisymbol display reels, and wherein (a) at least one column of the unisymbol display reels has a different number of the unisymbol display reels than does another of the columns of the unisymbol display reels, (b) or at least one row of the unisymbol display reels has a different number of the unisymbol display reels than does another of the rows of the unisymbol display reels; and a plurality of paylines, wherein each payline is associated with the same number of each of the unisymbol display reels having the different probabilities such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 82. The gaming device of claim 81, wherein each column of unisymbol display reels includes a set of symbols that is different from the sets of symbols of the other columns. 83. The gaming device of claim 81, wherein each row of unisymbol display reels includes a set of symbols that is different from symbol sets of other rows. 84. The gaming device of claim 81, wherein the columns and rows are positioned orthogonally with respect to one another. 85. The gaming device of claim 81, which is provided through a data network. 86. The gaming device of claim 85, wherein the data network is an internet. 87. A gaming device comprising: a plurality of symbols; a plurality of unisymbol display reels, each unisymbol display reel configured to generate one of said plurality of symbols; a number of each of said plurality of symbols associated with each unisymbol display reel, wherein at least one of said unisymbol display reels has a different number of at least one symbol than another one of said unisymbol display reels; said plurality of unisymbol display reels configured such that X number of said unisymbol displayable reels are displayed in each of a plurality of columns, where X is at least one, and such that Y number of said unisymbol display reels are displayable in each of a plurality of rows, where Y is at least one; and a plurality of paylines associated with said unisymbol display reels in said rows and columns, wherein each payline is associated with the same number of each of the unisymbol display reels having different numbers of at least one symbol such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 88. The gaming device of claim 87, which includes a set of symbols displayable by each unisymbol display reel, wherein at least one of said sets of symbols is different than the sets of symbols displayable by the other unisymbol display reels. 89. The gaming device of claim 87, wherein at least one column includes X-W number of said unisymbol display reels, where W is less than X. 90. The gaming device of claim 87, wherein at least one row includes Y-Z number of said unisymbol display reels, where Z is less than Y. 91. The method of claim 87, which includes at least one column having X-W number of said unisymbol display reels wherein W is less than X and at least one row having Y-Z number of said unisymbol display reels, where Z is less than Y. 92. The method of claim 91, wherein the W number of unisymbol display reels is different from the Z number of unisymbol display reels. 93. The gaming device of claim 87, wherein the unisymbol display reels in each of said plurality of columns have the same number of each symbol. 94. The gaming device of claim 93, wherein each payline is associated with one unisymbol display reel from each column. 95. The gaming device of claim 87, wherein the unisymbol display reels in each of said plurality of rows have the same number of each symbol. 96. The gaming device of claim 95, wherein each payline is associated with one unisymbol display reel from each row. 97. The gaming device of claim 87, which is provided through a data network. 98. The gaming device of claim 97, wherein the data network is an internet. 99. A gaming device comprising: a plurality of symbols; a plurality of unisymbol display reels, each unisymbol display reel configured to generate one of said plurality of symbols; a number of each of said plurality of symbols associated with each unisymbol display reel, wherein at least one of said unisymbol display reels has a different number of at least one symbol than another one of said unisymbol display reels; said plurality of unisymbol display reels configured such that X number of said unisymbol display reels are displayable in each of a plurality of first groups, where X is at least one, and such that Y number of said unisymbol display reels are displayable in each of a plurality of second groups, where Y is at least one; and a plurality of paylines, wherein each payline is associated with the same number of each of the unisymbol display reels having different numbers of at least one symbol such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 100. The gaming device of claim 99, which includes a set of symbols displayable by each unisymbol display reel, wherein at least one of said sets of symbols is different than the sets of symbols displayable by the other unisymbol display reels. 101. The gaming device of claim 99, wherein at least one of the first groups includes X-W number of said unisymbol display reels, where W is less than X. 102. The gaming device of claim 99, wherein at least one of the second groups includes Y-Z number of said unisymbol display reels, where Z is less than Y. 103. The method of claim 99, which includes at least one column having X-W number of said unisymbol display reels wherein W is less than X and at least one row having Y-Z number of said unisymbol display reels, where Z is less than Y. 104. The method of claim 103, wherein the W number of unisymbol display reels is different from the Z number of unisymbol display reels. 105. The gaming device of claim 99, wherein the unisymbol display reels in each of said plurality of first groups have the same number of each symbol. 106. The gaming device of claim 105, wherein each payline is associated with a same number of unisymbol display reels from the same group. 107. The gaming device of claim 99, wherein the unisymbol display reels in each of said plurality of second groups have the same symbols or same probability of generating said symbols. 108. The gaming device of claim 107, wherein each payline is associated with a same number of unisymbol display reels from the same group. 109. The gaming device of claim 99, which is provided through a data network. 110. The gaming device of claim 109, wherein the data network is an internet. 111. A gaming device comprising: a plurality of unisymbol display reels arranged and configured in a matrix of rows and columns, wherein at least one unisymbol display reel has a different number of at least one symbol than another one of said unisymbol display reels, and wherein at least one column of the unisymbol display reels has a different number of the unisymbol display reels than does another of the columns or at least one row of the unisymbol display reels has a different number of the unisymbol display reels than does another of the rows; and a plurality of paylines, wherein each payline is associated with the same number of each of the unisymbol display reels having different numbers of at least one symbol such that at least one winning combination of said symbols has an equal or substantially equal likelihood of occurring on two different paylines. 112. The gaming device of claim 111, wherein at least one column of unisymbol display reels includes at least one symbol that is different from at least one symbol on the unisymbol display reels of at least one other column. 113. The gaming device of claim 111, wherein at least one row of unisymbol display reels includes at least one symbol that is different from at least one symbol included on the unisymbol display reels of at least one other row. 114. The gaming device of claim 111, wherein the columns and rows are positioned orthogonally with respect to one another. 115. The gaming device of claim 111 which is provided through a data network. 116. The gaming device of claim 115 wherein the data network is an internet.