In my experience (which is purely anecdotal), it seems like I have the best luck getting the lucky-emoji items when I switch back to the lucky emoji after playing with a different emoji. If I use the same lucky emoji over and over, the item doesn't seem to drop, but if I switch away for a game or two and then come back, the item seems more likely to appear. So, I used Cinderella for several games, but couldn't get the last two brooms. I switched to Gus, played a game, and then switched back to Cinderella. Both items dropped in the next two games.