Bottomless chest pieces are a nightmare. But I can show you how, out of mining 700 blocks, you can get 10 chest pieces, opposed to the usual ratio of one or two.
Step 1: What do piece do you want?
• Left piece can be found in Terra (That's your starting world)
• Middle piece can be found in Seth (low chance) or Magmar (high chance)
• Right piece can only be found in Abla, making it the most rare chest peice.
Step 2: What blocks do I mine? IMPORTANT!
• For left pieces, only mine sand blocks in Terra. NOT in Seth! Two Antanium shovels should do the trick.
• For middle pieces, only mine rough red dirt FROM Magmar. Yes, that's right. Mine up the dirt from Magmar, get the hell outta there and set it down again in Terra. You can now mine this at your leisure, and still collect middle chest pieces
• For right pieces, have faith. I have found no block in alba which gives out right pieces openly, so my current ratio is 2 right to 600 blocks of dirt :,( . If you have tips, please share them!
Step 3: Crafting!
This is for the people who haven't got the craft note, just use the tinker's table and have the Left, Middle and Right pieces across it in order.
PRO TIP!
If you have a lucky amulet or a four leaf clover, equip it to your special item bar. Double the chest pieces and way more random junk!