I wanted to submit a card, but put off thinking about it till today. So I didn't think about it much, and it turned out silly. oh well.
Hogwash
If your Hogwash Mat is empty, +1 Card, +1 Action.
Reveal the top card of your deck. Trash it, discard it, or put it back. If you trashed it, play a card from your Hogwash mat. If there is still at least one card on your Hogwash mat, +$3.
-
When any player gains an action card, you may set this aside. If you do, put a copy of the gained card from the supply onto your Hogwash mat and play this at the start of your next turn.
(I originally called it Gee Wiz, but then I noticed we were on H.)
This can't gain, though, which is one of the criteria.
And as for a generalization of my card:
Generalized Epsilon:
You may play an Action card from your hand. If you do, trash it, then gain an Action card costing exactly $X more than it, playing it.
Cost: $5/$6
Note that the original version should also be able to only gain Actions, which I accidentally left out.