In hobby gaming, the distinction between European (Euro) and American style games relates as much to the players as to the games themselves. But, insofar as different types of personalities are drawn to different types of experiences, the difference between Euro and American gaming revolves primarily around the role of chance. American games require you to do the best with what is given to you, while Euro games provide players, collectively, with near complete control over their destiny.
In American games, players never really know what they are going to get, or what the final outcome will be. In the presence of chance, there is an incentive to accurately hedge your bet and determine contingency plans within a greater regime of discerning strategies and employing counter-strategies. These games only remain intellectually stimulating as long as there is enough choices per game to mitigate chance and develop coherent plans even if the exact details are susceptible to variance.
In Euro games, on the other hand, the range of possible actions is always known from the outset. Players are often presented with near complete information about the game state and a set of choices constrained only by the previous actions of the other players and the desire to act instrumentally to win. Rarely in Euro games are players challenged with unexpected or unanticipated events, or asked to build their success upon an unknown set of variables. The challenge of the game rather emerges from the complexity of possible game states which arise as a consequence of the decisions of other players to maximize their personal gains. But, like chess, the outcome remains deductively complete.
As long as the outcome is entirely determined by the choices of the players, players are rewarded for familiarity with the rules, meta-game analysis of optimal play, recognition of inevitable outcomes and ultimately thinking one step farther than their competitors. If uncertainty is introduced, however, then players are forced to guess what other people are trying to do, recognize patterns of behavior and remain flexible enough to cope with bad luck and adapt to other players decisions.
