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If one chooses to play an elven wizard the favored class bonus is stated to be:

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 +½ to the number of uses per day of that arcane school power.

Would this mean that the elven wizard could select an arcane school power other than the one from his initial chosen class and gain both access to that power and the ability to use it 3 + INT + 1/2 times per day?

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I expect most GMs mandate that the elf wizard favored class bonus adds extra uses to an arcane school special ability that the elf wizard already possesses. This 2012 thread on the same topic cites Pathfinder designer Jason Bulhman's post that says that, essentially, You can't add something to nothing. That is, adding +½ to the number of uses of an ability a creature doesn't possess doesn't grant the creature the ability!

However, a strict legalist could argue that the elf wizard favored class bonus specifically 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, and that sentence does not limit the elf wizard only to special abilities he's already selected, therefore leaving open the option to select via the elf wizard favored class bonus a new, previously unpossessed arcane school special ability.

For example, an elf wizard that specializes in abjuration at level 1 gains the supernatural ability protective ward usable a number of times per day equal to 3 + his Intelligence modifier. At level 1, using the elf wizard favored class bonus, the same elf could select the universalist wizard supernatural ability hand of the apprentice. However, it would be up to the GM if the elf wizard were, at level 1, able to use the ability hand of the apprentice either a number of times per day equal to 3 + his Intelligence modifier or 0 times per day (i.e. ½ rounded down), this latter reading stemming from the GM reading the elf wizard favored class bonus number of uses specifically overriding the typical number of uses for the special ability.

Despite this second reading being possible in the very abstract, I wouldn't expect any GM to agree with it without substantial persuasion in the form of booze, cash, or pizza.

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No, it does not allow access to other powers, because these are not normally usable for someone with your character's specialization at all. All it does is to add one use every two levels.

Even if this would be possible to gain access to other powers, you would only add ½ to your initial use, that is, to 0. But that is really, really generous interpretation.

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    \$\begingroup\$ It would be good to note that the reason for the somewhat odd wording is for future-proofing of that trait; if a future arcane school granted more than one 1st level power, the wording ensures that only one can be selected. \$\endgroup\$ – LegendaryDude Feb 2 '17 at 18:28
  • \$\begingroup\$ The word normally in the elf wizard favored class bonus applies to how often the ability can be used—hence establishing to which special ability the favored class bonus can apply (for example, an abjurer can select protective ward but not resistance); that normally is not defining whether the ability can be used by the wizard at all. \$\endgroup\$ – Hey I Can Chan Feb 2 '17 at 18:58

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