There's no formula and there's no pattern across all magic types.
Looking at the 1E DMG right now, potions run at about 60% XP:GP. Scrolls only use a formula, gp = xp x 3 for spells, gp = xp x 5 for protection-types (i.e., 33%, 20%). Rings, wands, and swords seem around 20%. Armor and misc. weapons are often around 10%. Misc. magic is all over the map, sometimes 5% or 10% to 20%.
Moreover, the OP was also asking for how to formulize the gold values for magic items, and there's definitely no such thing in 1E (except for spell scrolls).
Looking at the 1E DMG right now, potions run at about 60% XP:GP. Scrolls only use a formula, gp = xp x 3 for spells, gp = xp x 5 for protection-types (i.e., 33%, 20%). Rings, wands, and swords seem around 20%. Armor and misc. weapons are often around 10%. Misc. magic is all over the map, sometimes 5% or 10% to 20%.
Moreover, the OP was also asking for how to formulize the gold values for magic items, and there's definitely no such thing in 1E (except for spell scrolls).
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