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I'm working on creating a character for Pathfinder, he is a gnomish wizard and the "Alternate Favored Class Bonus" says:

Select one arcane school power at 1st level that is normally usable a number of times per day equal to 3 + the wizard’s Intelligence modifier. The wizard adds +1/2 to the number of uses per day of that arcane school power.

When creating a Gnomish Wizard the favored class bonus says to add +1/2. I don't understand what it means to add +1/2 to the number of uses per day?

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What this means is that each level you take in Wizard, if it's your favored class, the power you would get from your Arcane School gets +1/2 uses.

In pathfinder things tend to round down, which means you will see that benefit if you take more than 1 level of Wizard in that favored class. From the Getting Started portion of the core book:

Rounding: Occasionally the rules ask you to round a result or value. Unless otherwise stated, always round down. For example, if you are asked to take half of 7, the result would be 3.

For instance, let's say you're a Wizard with a focus on the Abjuration Arcane School; the power "Protective Ward" would receive the aforementioned Favored Class bonus. If you take that bonus twice (by choosing to gain a second level in that class) you'll be able to use Protective Ward an additional One (1) more time per day. If you take that bonus four times, you'll get to use it an additional Two (2) more times per day.

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First, you need to know what a favored class is.

Instead of receiving an additional skill rank or hit point whenever they gain a level in a Favored Class, some races have the option of choosing from a number of other bonuses, depending upon their Favored Classes.

So, when you reach wizard level 2 you get 2 times 1/2 extra uses, which equals one extra use. At level 4 you get 2 extra uses, at level 6 in wizard you get 3 extra uses, and so on.

You don't get the skill rank or hitpoint bonus you'd otherwise get.

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