Games played on an N × N+2 grid
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My list of games played on an N × N+1 grid was successful enough (we eventually collected over 100 such games) but I keep finding more games which don't quite fit.

So here's a companion list for the near misses. 4×6, 6×8, 7×9, 21×23 ... add them if you've got 'em.
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1. Board Game: Chesscalation [Average Rating:8.40 Unranked]
Board Game: Chesscalation
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5x7
 
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2. Board Game: Hong [Average Rating:8.12 Unranked]
Board Game: Hong
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7x9
 
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3. Board Game: Helios [Average Rating:8.00 Unranked]
Board Game: Helios
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20x22
 
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4. Board Game: Pickit [Average Rating:8.00 Unranked]
Board Game: Pickit
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3x1
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5. Board Game: Kasta [Average Rating:8.00 Unranked]
Board Game: Kasta
Rey Alicea
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10x8 abstract strategy dice game.
 
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6. Board Game: Le Shogi [Average Rating:8.00 Unranked]
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4x6
 
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7. Board Game: Sovrano [Average Rating:7.78 Unranked]
Board Game: Sovrano
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7x9
 
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8. Board Game: Color Guard [Average Rating:7.50 Unranked]
Board Game: Color Guard
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9. Board Game: Treefort Nations [Average Rating:7.50 Unranked]
Board Game: Treefort Nations
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14x16
 
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10. Board Game: Chivalry [Average Rating:7.50 Unranked]
Board Game: Chivalry
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14x16 with corners rounded off. Or perhaps it's better to see it as 14x14 with cut corners and with goal squares added on two opposite sides.
 
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11. Board Game: Mountain Pass Chess [Average Rating:7.50 Unranked]
Board Game: Mountain Pass Chess
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5x7
 
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12. Board Game: Shing Shang [Average Rating:7.43 Unranked]
Board Game: Shing Shang
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8x10
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13. Board Game: Star Fleet Scramble [Average Rating:7.39 Unranked]
Board Game: Star Fleet Scramble
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5x7
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14. Board Game: Acquire [Average Rating:7.34 Overall Rank:259]
Board Game: Acquire
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Schmidt Spiele edition is 10x12.
 
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15. Board Game: Ordo [Average Rating:7.34 Overall Rank:7399]
Board Game: Ordo
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8x10
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16. Board Game: Shattered Olympus [Average Rating:7.33 Unranked]
Board Game: Shattered Olympus
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17. Board Game: Fishery [Average Rating:7.30 Unranked]
Board Game: Fishery
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18. Board Game: Myriath [Average Rating:7.25 Unranked]
Board Game: Myriath
Martijn Althuizen
Netherlands
Helmond
Noord Brabant
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The 3 player game is played on a 9 by 11 grid.

Note: 2 player game is 9 by 9, 4 player game is 9 by 13.
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19. Board Game: Barragoon [Average Rating:7.23 Overall Rank:5717]
Board Game: Barragoon
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7x9
 
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20. Board Game: Flash Point: Fire Rescue [Average Rating:7.21 Overall Rank:329]
Board Game: Flash Point: Fire Rescue
Phil Sauer
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Willow Street
Pennsylvania
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6 x 8
 
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21. Board Game: Epaminondas [Average Rating:7.20 Overall Rank:5916]
Board Game: Epaminondas
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12x14
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22. Board Game: Schatzsucher [Average Rating:7.17 Unranked]
Board Game: Schatzsucher
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23. Board Game: Alien City [Average Rating:7.11 Overall Rank:7420]
Board Game: Alien City
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8x10
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24. Board Game: Melting Chess [Average Rating:7.02 Unranked]
Board Game: Melting Chess
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25. Board Game: Dubble Kross [Average Rating:7.00 Unranked]
Board Game: Dubble Kross
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11x13
 
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