Collection pieces

I love the game, but why does it take so long to get collection pieces? I understand that the pieces come up in random mystery chests, but is there a way to get the pieces to come up a bit more frequently - say once every 7-10 games or 15-20 mystery chests? I've been playing on the Fast Five special bingo level every day for the past week or so and have collected only one additional piece (I have a total of 3). I just hit five stars on the level tonight. At that point one would think that there would be about 15-20 pieces collected.