I think what may be confusing about expected outcome is the name. You don't actually expect to get 5 dollars out of this :) . You don't even expect to get, say, 5 million dollars after 1 million games, such would be rather unlikely. You do expect to get 5$ per game if you played infinitely many games, though, and if you are playing such games on small amounts of money you can choose the game to play based on expected outcome.