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I am playing a Tiefling Alchemist (level 2, favored class is also Alchemist), and I read about the Favored Class Bonus involving Additional Bomb Damage on this page:

Add +1/2 to the alchemist's bomb damage

So does this mean that if I chose this bonus two times (once for each level), any bomb I throw will have as damage 1d6+6?

1d6  (base bomb fire damage)
+4   (my INT modifier)
+2   (Favored Class Bonus Additional Bomb Damage)
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No, the +1/2 is meaning +0.5 damage. This means you need to take it twice in order to get any benefit because of how fractions work.

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No.

The favored class bonus increases your bomb damage by +0.5 for each level you take the bonus, So every other level that you take that specific bonus you'll gain 1 bomb damage. This damage stacks with any other bonuses you can get to bomb damage, including whatever intelligence bonus boost you get to the bombs, and any other bomb damage boosts you can find.

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