Thanks everyone for submitting reports about this matter. One of the developers and I ran an extensive series of integration tests (sample size in the millions) over the last couple of weeks, and results were within expected parameters. We also combed through user data gleaned from reports and determined that the overall drop rate was consistent with our integration test findings across all rooms.
One thing that is important to consider about Collectibles is they only appear inside Mystery Chests (or Mystery Envelopes in CLUE). They don't come from Bingos or daubs. It's possible to play a bunch of cards, Bingo them all, and get no Collectibles because the number of Mystery Chests earned was low. Since the drop rate is for the room is static, the more Mystery Chests you open, the more Collectibles you will receive
on average.
One fairly advanced (and riskier) strategy is to make the most of your cards and boosts by intentionally delaying Bingos until the game is about to end. If you Bingo a card after 4 balls are called, and the game ended 30 calls later, you essentially gave up 30 opportunities to daub additional numbers on that card. If you Bingoed that card before daubing its Mystery Chest, then you missed out on that opportunity to collect that Mystery Chest (and ultimately, a chance at a Collectible). This is even more true when activating a Mystery Chest boost, which adds more Chests to all your cards. Of course, the risk here is obvious: the longer you delay your Bingos, the faster you have to be to claim them before all remaining Bingos are called... but often, it's worth it.