Incantatrix, Persist and Extend

Agreed. "Doubling" a spell effects in D20 don't expand geometrically. Think of every spell effect as having a "x1" multiplier already in place. Things that double it add one to that multiplier, rather than actually doubling it.

Important point: This special multiplication only applies to game-specific values. Real-world values like weight, distance, and time are multiplied normally. If you could doubly-Extend a spell (which, as has already been noted, you can't) it would multiply normally for a x4 duration because time is a real-world value.
 

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Well, now we're venturing into "How much wood would a wood-chuck chuck..." territory. How something would be done, while noting that it really can't.

The simple guideline is that "doubling" things in D20 adds the base amount to the total, rather than adding the current amount to the total. Since there are so very few things that can do multiple double-up effects, the theoretical disclaimers add smoke to the fire, but very little light.
 

Well, now we're venturing into "How much wood would a wood-chuck chuck..." territory. How something would be done, while noting that it really can't.

The simple guideline is that "doubling" things in D20 adds the base amount to the total, rather than adding the current amount to the total. Since there are so very few things that can do multiple double-up effects, the theoretical disclaimers add smoke to the fire, but very little light.

For reference:

SRD said:
Sometimes a rule makes you multiply a number or a die roll. As long as you’re applying a single multiplier, multiply the number normally. When two or more multipliers apply to any abstract value (such as a modifier or a die roll), however, combine them into a single multiple, with each extra multiple adding 1 less than its value to the first multiple. Thus, a double (×2) and a double (×2) applied to the same number results in a triple (×3, because 2 + 1 = 3).

When applying multipliers to real-world values (such as weight or distance), normal rules of math apply instead. A creature whose size doubles (thus multiplying its weight by 8) and then is turned to stone (which would multiply its weight by a factor of roughly 3) now weighs about 24 times normal, not 10 times normal. Similarly, a blinded creature attempting to negotiate difficult terrain would count each square as 4 squares (doubling the cost twice, for a total multiplier of ×4), rather than as 3 squares (adding 100% twice).
 


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