My cousin compared it to monopoly, but I think it's far closer to Careers.
Essentially though it plays exactly like the show. Find a crew, find a job, keep flying. It has some budget balancing involved (not much), some specialization/customization elements (mostly from buying certain upgrades or picking up crew with a very special ability), but mostly it's about building up a large crew and finding jobs that pay well enough to keep flying.
The nifty thing is that the game has a bunch of cards that determine the game's actual story. So you have all these missions here and there (pretty much everything in the game references the show BTW, and possibly the movie though I haven't noticed any movie references yet) that send you flying around the 'Verse. As you do missions for certain people, you become "solid" with them and they start doing more business with you (buying any cargo or contraband you might have). But the game's actual story is one giant mission which you pick at the beginning of the game and it's a race for all the players to try to complete it. This is a much more difficult series of missions that requires that your ship have a few improvements, a large, well-equipped crew, possibly a well-balanced crew, and that you are quick enough you can beat the other players to it.
The game also sometimes forces you to deal with things like bad luck, your Firefly falling apart and needing repairs, getting wanted by the law, reaver attacks, etc. It's interestingly balanced with the show in that, for instance, all the nice stuff is in Osiris (a core planet) so if you REALLY want the best ship upgrades, spiffy laser weapons, hovercrafts, or companions, you have to hit Osiris to find them. Go to the border planets, stuff there is functional but less pretty and less awesome, though less expensive.
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Basically long story short - it plays JUST like the TV show does.
One of the missions is entitled "Niska's Vacation" which is the only one I've played all the way through. I'm honestly unhappy with this mission, it seems highly imbalanced. Gameplay takes a long time on that one but it seems this particular one has a runaway winner.
The other story cards seem much better balanced. Niska's Vacation requires a very large crew that's good at fighting and there doesn't really seem to be enough of these guys (and not enough equipment either) to allow everyone the opportunity to even start the story. So I'm doubtful I'd play that one again anytime soon, but I'll have to give the other ones a go.
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Still...I find this game to be HIGHLY enjoyable, if just for the fact that you get to do exactly what they do in the show and the gameplay itself is loads of fun and worth playing on account of that alone. Plus the map makes me think I could use it for future Firefly Tabletop RPG's.
~Robert