Idea for Item Distribution Balance
If The current system stays I propose that each player gets a counter that gains points based on the number of items the opposing player has received (whether in play or on the side or on a player in the holding bay). A combined item counts for 2 and a single item is 1.
Once the counter gets to 10 the player gets a guaranteed random item and the counter returns to 0. Any points over 10 carry over i.e. 9/10 + 4 = 3/10.
This system would allow players with less items to catch up.