Log Forge
$4? -- Action
Trash any number of cards from your hand. Gain a card with a cost equal to the product of the costs in coins of the trashed cards.
Would this be effective, and do I have it at the right price point?
There is no meaningful way to gain a Colony out of this, for example*. Three estates for a Province would be nice, but you can't trash Copper. It's kind of RBCI overall, and if all the price points were filled, it would be a bit crazy due to the exponential potential. (Generally, an empty product is regarded as 1, so you would get a Poor House if you trashed nothing)
Trashing a 2 and a 3 for a 6, or a 4 and a 2 for a province, isn't that amazing, and there just aren't enough numbers and things that factor in enough ways. The number of ways for things to cost something isn't great enough, and this is very bad at getting rid of 0-cost cards. If this card existed, the rest of the game and its costs would need to be balanced around it, such as with 0-costs cards being much more rare, and bigger composite numbers being relatively common, such as 10, 24, 30, 36, and 40.
It could also bump 0 up to 1 as a fix, but it has a hard time interacting with any $5 cards whatsoever, and the 2*3=6 interaction seems slow for what it does.
* - Cost lowering works, but yeah.