Noah
This great game is hard to learn for many people but is casual after. Strategy is required but I'm rating the game luck based because the game heavily depends on the starting planet. Expansions abound
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Race for the Galaxy
Good game for parties but lots of laughs but really depends on the group. It is a very casual game.
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Apples to Apples
It is a card game that is less luck based due to the drafting mechanic.Without the leaders expansion there is a little more luck but is predominantly skill based. Great quick game.
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7 Wonders
Great game. It is a cooperative game. The group plays against an enemy that is controlled by cards. Lots of dice are rolled. There still is a lot of strategy as well. The rules take a while to learn.
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Arkham Horror
this is a good deck building game. the game's races feel more balanced then the original. It rewards going a single race more so then the original. The trophy mechanic is a fun addition to the game.
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Ascension: Storm of Souls
This game is great to add with another different ascension game The 2 player game that you can play is ok The other Ascension games are better alone but this makes the first one's races feel complete
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Ascension: Return of the Fallen
I find this game a little more on the luck side. This is because every turn you draw a piece at random. and it decides you move great game for 2-3 people. Once you get more I recommend other games.
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Carcassonne
This is one of the best economic games ever made. It is not for people who are just getting into board games. It has almost no luck. It does take a lot of time.
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Agricola
A deck building game made from mtg pros it shows. It is a little more casual then the average game. It is luck based and even more then 2 people. Strategy always plays a part in deck building games.
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Ascension: Chronicle of the Godslayer