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Since the Sword of Planes appears to exist transcendently on multiple planes, can a wielder avoid the 20% miss chance when striking something on the Prime Material Plane? Essentially a player could pay the 22,315 gp for a +1 sword to avoid a 20% miss chance (plus higher bonuses against situational creatures.)
Nope. It doesn't exist on multiple planes at once, it just works extra well on other planes or against creatures from other planes.
Nowhere it the description does it even remotely mention functioning as though it was in multiple planes at the same time.
For the enhancement bonus alone, it would work as you described:
Sword is on material, used by native of material vs material creature:
flat +1
Sword is on ethereal, used by native of material vs material creature:
+3/2 round down=+1
However, any other modifiers would also be halved.
Where are you getting any of this halving from?
The Sword of the Planes doesn't get halved for anything. Its bonuses just gets better under certain conditions.
Incorporeal and ethereal are different things.
Incorporeal says:
An incorporeal creature has no physical body. It can be harmed only by other incorporeal creatures, magic weapons or creatures that strike as magic weapons, and spells, spell-like abilities, or supernatural abilities. It is immune to all nonmagical attack forms. Even when hit by spells or magic weapons, it takes only half damage from a corporeal source (except for channel energy). Although it is not a magical attack, holy water can affect incorporeal undead. Corporeal spells and effects that do not cause damage only have a 50% chance of affecting an incorporeal creature. Force spells and effects, such as from a magic missile, affect an incorporeal creature normally.
Blink makes you ethereal (sort of), which actually gives you a 50% miss chance not half damage.
Edit: Just noticed that blink gives you the incorporeal quality as well as the ethereal quality....never noticed that before. And it's weird.
Because outside of that entry in the Blink spell ethereal and incorporeal are treated as different qualities.
In any even though, you don't round the enhancement modifier on the sword itself. It's enhancement is it's enhancement, though the damage will be reduced because of incorporeal. Damage is the only thing that gets halved. The other effect is the miss chance. Aside from this, I'm not sure where you're getting rounding the enhancement bonus.
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Since the Sword of Planes appears to exist transcendently on multiple planes, can a wielder avoid the 20% miss chance when striking something on the Prime Material Plane? Essentially a player could pay the 22,315 gp for a +1 sword to avoid a 20% miss chance (plus higher bonuses against situational creatures.)
No.. because the Sword doesn't work the way you describe it as such... it's simply a form of variable enchancement bonuses.
In any even though, you don't round the enhancement modifier on the sword itself. It's enhancement is it's enhancement, though the damage will be reduced because of incorporeal. Damage is the only thing that gets halved. The other effect is the miss chance. Aside from this, I'm not sure where you're getting rounding the enhancement bonus.That was the result of (a+b)/2=a/2+b/2. I agree that we'd be looking at floor((a+b)/2). Though, if incorporeal does not imply ethereal, where are incorporeal creatures?
I still don't understand why you're doing any math with the enhancement bonuses. It is only 1 particular value based on either what you are attacking or what plane you are on. Nothing else changes that, and enhancement bonuses don't stack so you just take the best.
The Sword of Plane works like this:
(Normal) On the material plane or attacking a creature of the material plane +1
On the elemental planes, or attacking a creature of those planes +2
On the astral or ethereal planes, or attacking a creature of those planes +3
On any other plane, or attacking a creature of any other plane +4
There is no math to be done here with the enhancement bonus. The only math that is done is halving the total damage of your attack. So there is no point in doing any math since we don't know how much damage a character is doing normally since we don't even have a character.
As for the other part, all incorporeal creatures are ethereal. Not all ethereal creatures are incorporeal. That's what I was referring to.
In any even though, you don't round the enhancement modifier on the sword itself. It's enhancement is it's enhancement, though the damage will be reduced because of incorporeal. Damage is the only thing that gets halved. The other effect is the miss chance. Aside from this, I'm not sure where you're getting rounding the enhancement bonus.That was the result of (a+b)/2=a/2+b/2. I agree that we'd be looking at floor((a+b)/2). Though, if incorporeal does not imply ethereal, where are incorporeal creatures?I still don't understand why you're doing any math with the enhancement bonuses. It is only 1 particular value based on either what you are attacking or what plane you are on. Nothing else changes that, and enhancement bonuses don't stack so you just take the best.
The Sword of Plane works like this:
(Normal) On the material plane or attacking a creature of the material plane +1
On the elemental planes, or attacking a creature of those planes +2
On the astral or ethereal planes, or attacking a creature of those planes +3
On any other plane, or attacking a creature of any other plane +4There is no math to be done here with the enhancement bonus. The only math that is done is halving the total damage of your attack. So there is no point in doing any math since we don't know how much damage a character is doing normally since we don't even have a character.
As for the other part, all incorporeal creatures are ethereal. Not all ethereal creatures are incorporeal. That's what I was referring to.
As for that last part, I think you're mixed up. You can become incorporeal without being ethereal (gaseous form, for instance), but I'm not aware of any way to be ethereal without being incorporeal