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Recently I discovered that you can reforge the shield of cthulhu and was wondering what the best modifier is. Does anybody have the answer?

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While it will depend on your difficulty, equipment, and what you intend to do, Warding (+4 defense) and Menacing (+4% damage) are popular modifiers for all accessories that can be reforged.

In terms of what the game considers best, based on the effect of the modifier on the item's price, there's a 5-way tie:

  • Warding (+4 Defense)
  • Lucky (+4% Critical Strike Chance)
  • Menacing (+4% Damage)
  • Quick (+4% Movement Speed)
  • Violent (+4% Melee Speed)

There also exists a +20 Maximum Mana modifier, Arcane, that is considered by the game to be lower value, but it is the best (and only) Maximum Mana modifier.

https://terraria.gamepedia.com/Modifiers

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As stated in another answer, the best DPS modifiers are menacing and lucky. Whichever one is better depends on your other modifiers. If you have more damage modifier than crit modifier, lucky is better. If you have more crit modifier than damage modifier, menacing is better. The goal here is to balance the two stats as much as possible, which will optimize DPS. An important caveat here is that minions cannot crit, which should be considered if going for a summoner build.

At some point, damage becomes less important than dodging shots, so in general I would say the best modifier is quick (consider the Dungeon Guardian and Empress of Light battles, for example).

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