The best and worst it can roll
Pick an item type and a loot tier and read the floor and the ceiling of every number on it — straight out of the server's own mutation tables. Then set an awakened tier and see what the same item looks like when it drops in a dungeon copy that deep.
What it can roll
The tier scales the item, not the roll
A personal dungeon copy at tier N rolls its loot from exactly the retail treasure profile — same tier, same quality, same tables. Nothing about the dice changes. What changes is the item afterwards: once the roll is finished, every number in the list below is multiplied by 1 + N × 2%, and the piece is stamped (Awakened N). So the tier never turns a common roll into a rare one; it takes whatever you rolled and makes it that much stronger. A bad roll in a deep copy is still a bad roll, just a bigger one. The growth is linear and uncapped — ten awakenings is +20%, fifty is +100% — while the monsters in those copies grow at 5% a tier, so gear improves forever and the dungeon improves faster.
Whole numbers grow outright: damage, elemental damage bonus, armour level, and the damage / crit / healing / resistance ratings. Modifiers grow only in the part above 1.00, so a 1.20 attack modifier at +20% is 1.24, not 1.44, and anything sitting at or below 1.00 is left exactly where it is: damage modifier, elemental damage modifier, attack, melee defense, magic defense and mana conversion. Everything else on the item — spells, cantrips, workmanship, wield requirements, gear ratings, burden, speed, value — is untouched. Rows that grow are marked with an arrow in the table above.
Reading the small print
A range is what the tables allow, not what you should expect. Most of these are heavily weighted — the top row of a tier 8 damage table is worth two per cent of rolls — so the maximum is a lottery ticket, not a target. Where one number is decided by an earlier roll, the note column says so: on a weapon the damage and the skill it demands come out of the same row, so the hardest-hitting blade always carries the steepest requirement.
Built by ops/build-loot-ranges.py straight from the ACE mutation scripts and chance tables in the published server source, so the page cannot drift from what the server rolls without the build failing first.