The Heavyweights, a rare group of burners...
Salim Khoury
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I was searching for games and revisited the Vinhos site only to be reminded that so many consider this a really tough game, and, sure enough as of today it's "Avg. Game Weight" is 4.1.

This caused me to think about how rarely I see a 4+ weight for a non-wargame game and so I decided to do some digging (I like heavier games) and I think I figured out a way to filter out the games through an advanced search. I excluded the Subdomain "Wargames" and limited it to games with at least 50 ratings & 50 weight ratings with a weight range of 3.95-5. I expected a laundry list of games, instead there were only these 16 17 18 20 21 22 sorted here by weight...kind of a fun rare breed. Heaviest Designer: Jeroen Doumen, Heaviest Category: 18xx, Heaviest Publisher: Splotter Spellen.

I'm aware of the controversies around the BGG weight rating but this data certainly has some meaning, and it's shocking to me that with so many games in The Geek database only these proud few earn the prestigious title of The BGG Heavyweights.

Battle it out, ding, ding, ding.

Edits:

1) English, added Dominant Species, Indonesia, Go, & 18AL and clarified the filter method
1.30.14: Added Madeira
2.23.14 Added Android
1.3.15: Added Kanban: Automotive Revolution, added heaviest designer comment in header, & updated High Frontier to 4.2
3.13.15: Added Arkwright
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1. Board Game: Magic Realm [Average Rating:7.17 Overall Rank:1025]
Salim Khoury
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AGW 4.5 and current Heavyweight Champion of the Wooooorld!!!
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2. Board Game: Die Macher [Average Rating:7.63 Overall Rank:221]
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AGW 4.4
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3. Board Game: Antiquity [Average Rating:7.91 Overall Rank:197]
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AGW 4.3
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4. Board Game: The Republic of Rome [Average Rating:7.55 Overall Rank:383]
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AGW 4.3
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5. Board Game: 1856: Railroading in Upper Canada from 1856 [Average Rating:7.52 Overall Rank:957]
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AGW 4.3
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6. Board Game: Revolution: The Dutch Revolt 1568-1648 [Average Rating:7.33 Overall Rank:1432]
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AGW 4.3
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7. Board Game: 1861: The Railways of the Russian Empire [Average Rating:7.57 Overall Rank:1879]
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AGW 4.3
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8. Board Game: Kanban: Driver's Edition [Average Rating:7.82 Overall Rank:185]
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AGW: 4.2 and Vital Lacerda now has two games that make the list.
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9. Board Game: Madeira [Average Rating:7.64 Overall Rank:325]
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AGW 4.3 4.2

I haven't gotten my hands on this yet (en route), but, nonetheless a fairly new game has become a real heavyweight contender. What's Your Game? seems to be in the heavyweight business...

Edits: Updated it's weight (down .1) and edited the comments to reflect my purchase!
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10. Board Game: Twilight Imperium (Third Edition) [Average Rating:7.87 Overall Rank:53]
 
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AGW 4.2
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11. Board Game: Roads & Boats [Average Rating:7.72 Overall Rank:316]
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AGW 4.2
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12. Board Game: 1870: Railroading across the Trans Mississippi from 1870 [Average Rating:7.44 Overall Rank:1361] [Average Rating:7.44 Unranked]
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AGW 4.2
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13. Board Game: High Frontier [Average Rating:7.43 Overall Rank:878] [Average Rating:7.43 Unranked]
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AGW 4.1

1.3.15 Update: AGW 4.2
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14. Board Game: Through the Ages: A Story of Civilization [Average Rating:7.99 Overall Rank:35]
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AGW 4.1
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15. Board Game: Mage Knight Board Game [Average Rating:8.11 Overall Rank:24]
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AGW 4.1
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16. Board Game: 1830: Railways & Robber Barons [Average Rating:7.86 Overall Rank:174] [Average Rating:7.86 Unranked]
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AGW 4.1
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17. Board Game: Vinhos [Average Rating:7.49 Overall Rank:342]
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AGW 4.1
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18. Board Game: 1860: Railways on the Isle of Wight [Average Rating:7.95 Overall Rank:1454]
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AGW 4.1
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19. Board Game: Dominant Species [Average Rating:7.85 Overall Rank:49]
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AGW 4.0, added with improved filter of using lowest rating of 3.95
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20. Board Game: Go [Average Rating:7.65 Overall Rank:135]
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AGW 4.0, added with improved filter of using lowest rating of 3.95
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21. Board Game: Indonesia [Average Rating:7.84 Overall Rank:193]
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AGW 4.0, added with improved filter of using lowest rating of 3.95
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22. Board Game: 18AL [Average Rating:7.27 Overall Rank:1886]
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AGW 4.0, added with improved filter of using lowest rating of 3.95
 
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23. Board Game: Android [Average Rating:6.73 Overall Rank:1126]
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As of 2.23.14 AGW: 4.0

It seems Android has snuck in recently...
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24. Board Game: Arkwright [Average Rating:7.91 Overall Rank:548]
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Houston
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Welcome Arkwright, crashing onto the scene with an AGW of 4.4!
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