“A statue that increases luck by 2.” —In-game description, New Mystery of the Emblem
The Goddess Icon (女神の像 Megami no zō) is a Stat booster that recurs across the Fire Emblem Series. When used, the Goddess Icon permanently raises its user's Luck by a set number of points that varies from game to game.
In Thracia 776, the Goddess Icon is substituted by the Luck Ring (ラックスリング Lakkusu ringu), where it permanently boosts its user's Luck by 2 when used.
In the localised versions of the Tellius Series, the Goddess Icon is renamed to the Ashera Icon, in recognition of the fact that the affairs of the continent of Tellius are overseen by the goddess Ashera.
In TearRing Saga: Utna Heroes Saga, the Goddess Icon's equivalent takes the form of a potion that is simply known as the Luck Plus (LUK プラス LUK Purasu), where it permanently raises its user's Luck by 2.
The Goddess Icon is usually inferior to any other Stat Boosting item in any given Fire Emblem game and generally won't grant your units a very noticeable change in battle performance. Nevertheless, they are still stat boosting items and as such are extremely useful. Goddess Icons are best used on units with poor luck and not enough defense to trivialize Critical hits. This can drastically reduce the risk of an unfortunate enemy critical hit, forcing a player to restart the chapter.
Goddess Icons can also be useful when given to units with high luck stats, as players will occasionally need to deal with enemies that have massive critical rates. For example, in The Sacred Stones, Pablo, has a 15% chance of landing a critical hit in Hard Mode, but will find himself unable to critical Seth or Innes at all, should one of them be given the Goddess Icon that Tethys starts off with.
In Three Houses, the Luck stat is used in calculations for both Hit and Avoid for magic attacks, but not for physical attacks. It is also used to calculate critical hit rate. As such, mages with shaky hitrates (or units who might have to take hits from mages) can benefit more from Goddess Icons than other units.
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The concept of the Goddess Icon being used as a means to boost one's Luck could possibly be a reference to the goddess Fortuna, who is the Roman personification of fortune and luck. The official artwork portrayal of the Goddess Icon further reinforces this fact, where it is depicted as a bust fashioned in the likeness of a Roman goddess.
The Luck Ring, as it appears in the fourth series of the TCG.
The Goddess Icon, as it appears in the fifth series of the TCG.
Official artwork of the Luck Ring from the TCG.
Artwork of the Luck Plus from TearRing Saga: Utna Heroes Saga.