Here's an overhead view of the game so far. It's the only time we see what they're trying to do.
I have no idea what it is.
Rei discards the 3 of Hearts, but I have no idea where she puts it.
We know that Ami discards a Joker and puts it next to the 8 of Clubs. No idea why this is where the card goes, nor the strategy for putting it there.
Usagi asks Rei to discard the 5 of Hearts, and Taiki knows Ami is waiting for a 5 of Clubs discard.
And then there's the players who pass on their turn.
I don't understand why some players are holding out for another player to discard a certain card. Maybe when we understand what the game is and how someone wins we'll understand why.