Min Item Level roulette for dungeons, daily Faux Hollows for a random MINE Extreme, weekly Faux Hollows for a random MINE Savage floor.

It just seems so strange to avoid it when they've shown it is in their mind in interviews. It will now take an eternity for a new player to get enough Faux Hollows for all the rewards without buying them for hundreds of millions of gil, so it's already worth doing.