@Graviton - I was feeling like that for a few days too, then spent a few diamonds to make it "slide in safe to home plate". The variability of getting few starting paws and then no additional paws - is maddening. I understand it's part of the game, but it's actually deeper than that, too.
I found 2 consistent "trends" that presented often in the minigame play design:
Paws seem to come in burst @ move 20 or so... in other words
you get a bunch at the top, and the very end of your playing time. They're tantalizing, but you can't get them captured in your regular cycle UNLESS you spend wildlife coins to get 10 more moves. Not a good idea unless you can see a perfect path to drop enough of them to justify that double expenditure.
The column the paw you want is in is
BLOCKED at the bottom by a color not present in EITHER COLUMN (left or right), so you have to buy something - a hammer or tool, to break it free.
2 consistent themes controlled by the overall design, and it what makes this one of my least favorite game types.
Unlike St. Paddy's day - which people typically don't like at first due to it's seemingly overt complexity, but the players controls the event progress and success (for the most part) vs having random events NEVER under his/her control - happen.