Games played on an N × N+1 grid
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It's a little-known fact that the 19×19 Go board is not square, but rectangular: the grid is slightly elongated along the axis between the players so that it will appear square when viewed from each player's foreshortened perspective.

However, in this GeekList I'm looking for games in which the actual grid size is one off from being square.
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1. Board Game: Odd or Even [Average Rating:8.00 Unranked]
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6x7 with some cells deleted
 
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2. Board Game: Commander Chess [Average Rating:8.00 Unranked]
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11x12
 
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3. Board Game: Sum On [Average Rating:7.78 Unranked]
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8x9
 
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4. Board Game: Murus Gallicus [Average Rating:7.67 Overall Rank:7006]
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7x8
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5. Board Game: Essentia [Average Rating:7.56 Unranked]
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8x9
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6. Board Game: Click-Chek [Average Rating:7.50 Unranked]
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7. Board Game: Tamerlane Chess [Average Rating:7.50 Unranked]
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10x11
 
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8. Board Game: Alerya [Average Rating:7.44 Unranked]
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8x9
 
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9. Board Game: Escrete [Average Rating:7.36 Overall Rank:10463]
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5x6
 
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10. Board Game: Changgi [Average Rating:7.28 Overall Rank:6125]
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9x10
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11. Board Game: Bee-Siege [Average Rating:7.25 Unranked]
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12. Board Game: Stealth [Average Rating:7.20 Unranked]
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8x9
 
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13. Board Game: Xiangqi [Average Rating:7.14 Overall Rank:1188]
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9x10
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14. Board Game: Alien City [Average Rating:7.13 Overall Rank:6711]
Clark Rodeffer
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Ann Arbor
Michigan
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4x5 tiles
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15. Board Game: Camp [Average Rating:7.06 Unranked]
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5x6
 
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16. Board Game: Yōkaï no Mori [Average Rating:7.02 Unranked] [Average Rating:7.02 Unranked]
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Georgia
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Contains two games:
Dōbutsu Shōgi - 3x4 grid
Goro-Goro Dōbutsu Shōgi - 5x6 grid
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17. Board Game: Dirge: Carnage in Crimson [Average Rating:7.02 Overall Rank:9981]
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6x7
 
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18. Board Game: Goro-Goro Dōbutsu Shōgi [Average Rating:7.01 Overall Rank:9727]
Martijn Althuizen
(Martinus)
Netherlands
Helmond
Noord Brabant
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Played on a 5 by 6 board.
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19. Board Game: Logol [Average Rating:7.00 Unranked]
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5x6
 
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20. Board Game: Fāngqí [Average Rating:7.00 Unranked]
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7x8
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21. Board Game: Drop-Xianqi [Average Rating:7.00 Unranked]
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22. Board Game: Mirrorwing [Average Rating:7.00 Unranked]
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23. Board Game: Wali [Average Rating:7.00 Unranked]
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24. Board Game: Vilbergen [Average Rating:7.00 Unranked]
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25. Board Game: Simultaneous Captain's Mistress [Average Rating:7.00 Unranked]
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