My friend Troy is a total board game nut, and every year on his birthday he holds "TroyCon", which is a 12-hour orgy of board games. I got into three games myself today:
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Shogun, which casts you as rival warlords in feudal Japan. There are ten phases to each turn, always the same actions but always in a different order, and the last five phases are hidden to start, so you really don't know what's coming when. The combat mechanice is really neat -- you drop colored cubes representing your armies into a tower with all kinds of crazy cut-outs inside that can trap your pieces. So you might drop nine cubes in and have only three come out, and later drop four in and have the six that got trapped before come out as well. It really adds a dynamic feeling to the combat rather than rolling dice or just using numbers. Throw in revolting peasants and a bid process for turn order and it's a really fun, unpredictable game.
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Smallworld is a very simple fantasy-based conquest game. To capture a province, you simply move in tokens equal to two plus any enemy tokens already there. Where the twist comes in is every player is a classic race -- orks, trolls, giants, halflings, etc. -- combined with some sort of characteristic with an in-game benefit. You also have the option of putting your race into decline, where you basically abandon that race and pick a new one. When and how you do so can give you quite an advantage. It's quick, easy game that feels ideal for introducing younger players to these kind of games.
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Agricola, the game that ended Puerto Rico's five-year run as the top-rated game at Board Game Geek. This is definitely not for beginners -- the sheer number of pieces and cards is overwhelming to begin with. Players compete to build farms, and game actions can only be taken once per turn, so you have to really carefully consider not only what you want to do but what your opponent might be building towards. The goal is to score as many victory points by not only improving your farm, but by diversifying what you produce, since you lose victory points for empty spaces on your farm and for every item you don't grow. Took us a while to get the feel for it but it was worth it.
What I love about all these games is that there's no one way to win. There are plenty of different strategies and ways to snatch victory from the jaws of defeat.