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1 3 6...
Jim Cote
United States
Maine
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The series 1 3 6 10 15 etc is formed using a simple aritmetic sequence adding the next number to the previous: 1 1+2 1+2+3 1+2+3+4 etc. This series is used in some games for scoring/etc based on some count of items. Feel free to add your own.
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1. Board Game: Coloretto [Average Rating:6.98 Overall Rank:438]
Jim Cote
United States
Maine
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Your score is PLUS based on the number of cards in 3 of your colors and MINUS in the other colors. The picture shows the value used based on the number of cards in each color.
 
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2. Board Game: Oltre Mare [Average Rating:6.69 Overall Rank:1038]
Jim Cote
United States
Maine
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The sequence 1/3/6 is used for distribution of ducati, increase of pirate cards, market action drawing of goods, harbor bonus, and prestige bonus.
 
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3. Board Game: Saint Petersburg [Average Rating:7.34 Overall Rank:189]
Jim Cote
United States
Maine
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The VP bonus at the end of the game is based on the number of unique nobles a player has. The chart (which goes up to 55 with 10+ nobles) can be seen clearly by viewing the full-sized version of this image.
 
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4. Board Game: Goa [Average Rating:7.65 Overall Rank:90]
Dave Peters
United States
Belmont
California
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Powers:Coleridge:Milton: Faith...must be, if anything, a clear-eyed recognition of the patterns and tendencies, to be found in every piece of the world's fabric, which are the lineaments of God.
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That's Tim Powers' fictional Samuel Coleridge "quoting" John Milton in _The Anubis Gates_.
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The vast majority of Goa's scoring is based on triangular number sequences.
 
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5. Board Game: Hare & Tortoise [Average Rating:6.66 Overall Rank:973]
Richard Irving
United States
Salinas
California
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The carrot costs increase in the triangular pattern--you go as far as you like it's just going to cost you.
 
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6. Board Game: Hare & Tortoise [Average Rating:6.66 Overall Rank:973]
Richard Irving
United States
Salinas
California
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The carrot costs increase in the triangular pattern--you go as far as you like it's just going to cost you.
 
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7. Board Game: Amun-Re [Average Rating:7.37 Overall Rank:221]
Barak Engel
United States
Oakland
CA
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And the Geek shall Inherit the Earth
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I am the unholy trinity: Agnostic, Atheist, and Skeptic.
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The province cards have the same mechanic - until that funky "28" enters the picture.
 
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8. Board Game: Entdecker: Exploring New Horizons [Average Rating:6.57 Overall Rank:1397]
Brent Werness
United States
Unspecified
Unspecified
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The game has three units that you can buy, the scout, the fort, and the settlement. Respectivly these three units cost 1,3,6 gold pieces (indicated on the upper right hand corner of the board).
 
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9. Board Game: Ticket to Ride [Average Rating:7.48 Overall Rank:109] [Average Rating:7.48 Unranked]
Thomas Franke
Germany
Nuremberg
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Ticket to ride does this with a slight twist as can be seen on the left: It shifts the sequence by one position by giving the second train placed only one additional point and then has to fiddle a bit to get back on track:
1 train: 1
2 trains: 2 (+1)
3 trains: 4 (+2)
4 trains: 7 (+3)
5 trains: 10 (+3) should be 11
6 trains: 15 (+5)
and of course the infamous Petrograd tunnel in TtRE
7 trains: 21 (+6)

Would the sequence 1-2-4-7-11-16-22 perhaps have unbalanced the game?
 
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10. Board Game: Iglu Iglu [Average Rating:5.99 Overall Rank:7346]
Fran F G
Spain
Barcelona
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Café Race is a race game set in a business office. The players take the role of office workers going upstairs to the first floor to get a cup of coffee who then improvise a race while they are going back downstairs… with a cup full of coffee.
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Someone you trust is one of us. Fnord. - Ich bin ein Spielfreak, aber ich spiele sehr selten
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This little know game by Bruno Faidutti uses triangular numbers in the hardcore gamers variant.
 
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11. Board Game: Industrial Waste [Average Rating:6.75 Overall Rank:1229]
Jenna Rivet
United States
Glen Ellyn
Illinois
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The victory points for factory upgrades are 1 3 6 10 15.
 
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12. Board Game: Dominoes [Average Rating:5.43 Overall Rank:13152]
Jeff Luck
United States
Sandy
Utah
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Dominoes use triangular numbers too, but not in scoring. A double-6 set has 28 domninoes, a double-9 has 51, a double-12 has 91 dominoes.

To figure the count for double-x, use (x+1)(x+2)/2. For example, a double-5 would be 6*7/2 or 21. This is one off from basic triangular numbers computation by 1 because of the zero's. A double-0 set would contain 1, a double-1 would have 3, a double-2 - 6....

Triangular numbers are called that because you can arrange a basic triangle with that many items. That's why a bowling alley has 10 pins rather than 8 or 11. The basic pool table 8-ball arangement is of 15 balls - because 15 balls form a triangle.
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13. Board Game: Tiles [Average Rating:5.94 Unranked]
Valdir Jorge
Canada
Montreal
Quebec
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Tiles by BoneGames uses the same scoring mechanism. See the right side of the picture.
 
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14. Board Game: Civilization [Average Rating:7.53 Overall Rank:179]
Luke Morris
England
Faversham
Kent
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When collecting the goods cards and trading them, multiples of the same cards increase the value.
For example, Salt is worth 3.
One salt card = 3.
Two salt cards = 3+3 then multiplied by the fact you've got two cards = 12.
Three salt cards = (3+3+3)x3 = 27
Four salt cards = (3+3+3+3)x4 = 48
And so on...
 
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15. Board Game: Snake Pit [Average Rating:6.14 Overall Rank:7945]
Mauro Di Marco
Italy
Firenze
Unspecified
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Snake Pit uses this succession whenever a complete snake is scored.
 
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16. Board Game: Rat Hot [Average Rating:6.33 Overall Rank:2311]
Mauro Di Marco
Italy
Firenze
Unspecified
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Groups of the same goods score with the 1-3-6-10... succession in Dschunke das Legespiel
 
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17. Board Game: Go West! [Average Rating:5.81 Overall Rank:4960]
Doug Hoylman
United States
Chevy Chase
Maryland
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I was thinking about doing the same list. The only one I have that wasn't on here is "Go West". The scoring costs are the triangular numbers for the first five, but the sixth (which it's hard to imagine ever gets used) costs 16 instead of 21.
 
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18. Board Game: Numba Duel [Average Rating:3.00 Unranked]
Scott A. Reed
United States
Lawrence
Kansas
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Rokkin' Old Skool....

Scoring in this one is the triangular number scheme.
 
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19. Board Game: Ponte del Diavolo [Average Rating:6.56 Overall Rank:1904]
David Molnar
United States
Ridgewood
New Jersey
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Jim, I know you've played this one!
An island by itself is worth one point; two islands connected by a bridge are worth 3; three connected islands are worth 6, etc.
 
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20. Board Game: Hacienda [Average Rating:6.97 Overall Rank:604]
Quinn Swanger
United States
Holly Springs
North Carolina
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I haven't played this myself (though I would like to soon), but Hacienda clearly fulfills the requirement for this list as "points for connected markets" uses this sequence, as shown in the rules listed on Yucata: http://www.yucata.de/default.aspx?PageID=6&name=HaziendaRule...
 
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21. Board Game: Cabale [Average Rating:6.21 Overall Rank:5749]
Quinn Swanger
United States
Holly Springs
North Carolina
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Looking at this board, Cabale obviously qualifies. Note however that the center blokades (on the non-bolded lines) were likely played in error because of an unfortunate omission in the English rules translation (what I heard anyway). I just got the game and it looks very intriguing.
 
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22. Board Game: Intrigue [Average Rating:6.37 Overall Rank:1654]
Quinn Swanger
United States
Holly Springs
North Carolina
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You score 1, 3, 6, or 10 thousand ducats depending on what salary area your scholar is hired at within your opponents palaces. A highly regarded, cut-throat negotiation (and to some extent, hand managment) game.
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23. Board Game: Qwixx [Average Rating:6.92 Overall Rank:638]
Quinn Swanger
United States
Holly Springs
North Carolina
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Scoring for the number of crossed out die rolls in each of 4 color rows uses this sequence.
 
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24. Board Game: Dominant Species [Average Rating:7.87 Overall Rank:44]
Quinn Swanger
United States
Holly Springs
North Carolina
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The "Bonus" Points table uses this sequence, but the points here are actually quite integral to much of the scoring rather than just being extra.
 
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