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As we follow the rules of creating magic itens we can recreate the Ring of Invisibility in perfetion:
Use-activated or continuous
Spell level × caster level × 2,000 gp
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Invisibility
Sorcerer/Wizard 2
Duration: 1 min/lvl
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Spell level 2 x caster level 3 x 2.000 gp x 2 (as Invisibility has 1min/lvl duration) = 20.000 gp.
But what if I decide to make a ring of permanent Vanish spell?
Use-activated or continuous
Spell level × caster level × 2,000 gp
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Vanish
http://paizo.com/pathfinderRPG/prd/advanced/spells/vanish.html
Sorcerer/Wizard 1
Duration: 1 round/lvl
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Spell level 1 x caster level 1 x 2.000 gp x 4 (as Vanish has 1 round/lvl duration) = 8.000 gp
A cheaper ring with (in theory) with same effects (permanent invisibility while not attacking).
Thoughts?

Mojorat |
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you are not supposed to use the creation rules to create cheaper versions of existing items. when you create an item its price is supposed to be compared to those existing items.
What this esentially means int he case of your ring of vanish is it costs... exactly the same as a ring of inisibility because their effect on the game is identical.

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you are not supposed to use the creation rules to create cheaper versions of existing items. when you create an item its price is supposed to be compared to those existing items.
What this esentially means int he case of your ring of vanish is it costs... exactly the same as a ring of inisibility because their effect on the game is identical.
Got you, I rolled an 1 in Perception, could you help me in my "Ask 20"?

Orfamay Quest |
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The spell you'd be looking to base it on is "greater invisibility," so it would be appropriately more expensive.
But given how pants-wettingly broken the item is, a game master would be well within her rights simply to say "no, you can't have it." Custom item are not priced or allowed by rule, but by GM fiat.

Lifat |
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I think we have all covered the fact that the rules are guide lines and when creating custom magic items you should ALWAYS refer to your GM and let him decide.
The interesting part of this thread was this:
The 20k price for the regular Ring of Invisibility is use-activated, and each use lasts for 3 minutes.
The duration of your Ring of Vanish is only 1 round.
QFT!
My response: Sure you can spend 8k on a ring that grants you 1 round of invisibility every time you use a standard action on it.So even GM fiat aside the item created by OP is not that powerful.
For rules info:
Caster Level (CL): The next item in a notational entry gives the caster level of the item, indicating its relative power. The caster level determines the item's saving throw bonus, as well as range or other level-dependent aspects of the powers of the item (if variable). It also determines the level that must be contended with should the item come under the effect of a dispel magic spell or similar situation.
Unless stated otherwise, activating a use-activated magic item is either a standard action or not an action at all and does not provoke attacks of opportunity, unless the use involves performing an action that provokes an attack of opportunity in itself. If the use of the item takes time before a magical effect occurs, then use activation is a standard action. If the item's activation is subsumed in its use and takes no extra time use, activation is not an action at all.
By activating this simple silver ring, the wearer can benefit from invisibility, as the spell.

Lifat |
<.<
>.>
...what's "QFT"?
Hehehehe... Quoted for truth. The rest of the thread was just so much about "Maybe, but the GM shouldn't allow it", whereas you went right ahead and said that the guidelines meant that the ring could have it's uses but was nowhere near as good as it sounds. (Because of the necessity of activating it once per round)

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Well, I asked for something and learned another thing complety diferenty. And that was amazing.
Plot twist: Actually, I´m the GM, trying to figure it out where was the flaw behind the player idea of "cheap" Ring of Invisibility. Understood now the "as the spell" on the description of the ring turns the table. But I still struggling in Zhayne's "a lot" to calculate such a permanent thing.
Understand about the Guidelines of the Custom Magic Itens. Let´s say I´m trying to alow it, if it was fair. If you don't be bored by my basic answers, I have another question to make:
If we have to remember a thing: the [2] entry of the table says:
² If a continuous item has an effect based on a spell with a duration measured in rounds, multiply the cost by 4. If the duration of the spell is 1 minute/level, multiply the cost by 2, and if the duration is 10 minutes/level, multiply the cost by 1.5. If the spell has a 24-hour duration or greater, divide the cost in half.
Well, so the Ring of Invisibility without the Permanent effect as it as in the Magic Item index should be calculated by this way:
Magic Level 2 * Caster Level 3 * 1,800 gp (comand word)= 10,800 gp. Plus a GM factor that turn it 20,000 by a 1.85 (plus 85%) to justify 'unlimitless' uses per day and materials to make.
Let's keep this factor to calculate all the others variants.
Magic Level 2 * Caster Level 3 * 2,000 gp * 2 = 24,000 plus the 85% factor = 45,000 gp
Magic Level 4 * Caster Level 7 * 1,800 gp = 50,400 gp. Plus the 85% factor = 100,000 gp
Magic Level 4 * Caster Level 7 * 2,000 gp * 4= 224,000 gp. Plus the 85% factor = 415,000gp
Which is a Epic Item and not accessible by players so far.
Magic Level 1 * Caster Level 1 * 1,800 gp = 1,800 gp. Plus the 85% factor = 3,500 gp
Magic Level 1 * Caster Level 1 * 2,000gp * 4 = 8,000gp Plus 85% = 15,000gp
But by further readings, I find that Invisibility could only be made permanent on objects, that made a ring without the need to activate but the ring is invisible too, need the True Seeing spell to be found everytime. ;)
So I, as GM, won't alow the "Permanent" versions of those rings. Sorry long post. ;)

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Here's an useful advice thread about magic item pricing. It was originally intended for the RPGSS contest, but the advice applies to PF in general because the people who write items for magic item books follow the same principles:
Here's the most relevant part for this discussion:
7a) Your item includes the powers of an existing item, but has a lower price than that item.
If your item is similar to a belt of giant strength +2, but has a lower price, you've made a mistake. Likewise, if your item is a belt of giant strength +2 plus other abilities, and its price is less than the 4,000 gp for a regular belt of strength +2, you've priced it wrong--nobody would get the regular belt if they could get a better version at the same price. We've had several items each year that fail this simple test.