Rerolling lets you change the random parts of an item: its affix, its quality and its traits. Head to Oyun, the Mystical's Rerolling Cauldron in the Tavern to reroll an item.
Pick the item from your inventory, tick the parts you want to reroll, and press the Reroll button. Anything you don't tick stays the same. Each part has a Table button that shows everything it could roll into.
The price is based on the item's Item Power. The higher the IP, the more silver it costs.
Affix: 30 silver per IP
Each quality +: about 5.6 silver per IP
Each trait rank: about 5.6 silver per IP
Every item's page also lists its exact price.
You can put an item in the fuel slot to make a reroll cheaper or free. The fuel item is used up.
Duplicate: Another copy of the same item. The whole reroll is free, and it can upgrade the item's quality.
Roll Scroll: 20% off everything (40% for +, 60% for ++). See Roll Scrolls.
Reroll Items: A discount on the affix only. See Reroll for the full list.
Affix: Rolls a new affix. It will never give you the same affix again. HATED affixes can only roll if a HATED character uses a duplicate.
Quality: Changes what a + boosts. A duplicate can also add a +; see Upgrading Quality.
Traits: Each trait rank can be rerolled on its own. Pinned traits can't be rerolled.
Roll Scrolls drop from dungeon enemies and bosses, into your soulbound bag. Harder dungeons drop scrolls that work on stronger items:
Intermediate Roll Scroll: items up to 39 IP
Experienced Roll Scroll: items up to 49 IP
Advanced Roll Scroll: items up to 59 IP
Expert Roll Scroll: items up to 69 IP
Endgame Roll Scroll: items up to 79 IP
A scroll's quality decides its discount: plain scrolls take 20% off, + scrolls 40% and ++ scrolls 60%.
Most scrolls also have an affix, like Clear Might. When you use the scroll to reroll an affix, it makes some affixes more likely. The first word decides how big the bonus is:
The second word decides which affixes it favours:
A scroll never changes how often each tier rolls, only which affix you get within that tier.