Cheapest mystic forge recipes?

Solution 1:

The simplest forge recipe would be 4 karma-purchased items => one random karma-purchased item.

Since the items in question are bought with karma, they can neither be sold nor disassembled, but you should be able to do this with some of the 70-karma accessories (or 280 karma total -- essentially one event at max level) from the starting zones.

Solution 2:

Since you're just asking about any cheap recipes for the sake of doing your dailies (i.e. you don't really care what you get out of it), you can throw pretty much any old trash that you'd normally sell or salvage into it. Just do your daily kills etc. and, at the end of your four other daily achievements, you should easily have enough items (you'll need 20, five groups of four) to throw into the Mystic Toilet.

Just use four pieces of armour (blue or even white will do) or four weapons of any level - experiment with it, you'll notice items that won't work being disabled as you put items in. No need to throw in items that could be useful or worth something (unless of course you do care what you get out of it, but that's not what you were asking). Four random blue pieces of armour, for instance, will likely get you another blue item, with a small chance of getting a green.

Simple and cheap - all it will cost is that you won't be able to sell or salvage those 20 items at the end of your dailies run.

Solution 3:

Credit to one of my friends for thinking of this:

You need to already have 1 Experience Booster, 1 Magic Find Booster, and 1 Karma Booster for this. You buy 5 Leather Bags for 32c each, then forge and open a Booster Multipack five times. This results in a total cost of only 1s 60c for the Mystic Forgesmith daily.