The normal bardic knowledge bonus is +1 per 2 levels. The catfolk FCB adds .5 to that bonus amount each time you take it. This is all one bonus, so you add up everything and then only round down when you are done. You end up getting +1 each and every level.
For the human cleric, although the two bonuses stack just fine. They are entirely separate though and technically should be rounded before being applied so each will round down for odd levels. Combining before rounding wouldn't be game breaking, but as far as the rules go it is +2 for every two levels.
Basically, before you take a number and 'put' it anywhere else (in this case adding it to your other skill modifiers) you have to round it down.
A bard adds half his class level (minimum 1) to all Knowledge skill checks and may make all Knowledge skill checks untrained.
Add +½ to the bard's bardic knowledge bonus.
so each level you're adding 2 halves which is a whole.
You get 1 per level.
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+1 per 2 levels
and
+½ to the bard's bardic knowledge bonus
When combined, at 1st level you would add 0 from the first and 0 from the second.
At 2nd level you would add 1 from the first and 1 from the second.
So if they are paired up, it is +2 every 2 levels and +0 on the off levels.
James, you're missinterpreting the text.
A bard adds half his class level (minimum 1) to all Knowledge skill checks and may make all Knowledge skill checks untrained.
You're not adding +1 per 2 levels. You're adding .5 per level. Now since we round down it equals the bonus only increasing every 2 levels.
But now we have the FCB of "Add +½ to the bard's bardic knowledge bonus." available each level.
Normally going from lv 2 to lv3 would take me from a +2 to a +2.5 which rounds down to 2, but with this FCB it's taking me to a +3, which stays as a +3. Then from 3 to 4 I'd normally only get a +.5 taking me to 3.5, but then the FCB comes in again and increases it back to a full number, 4.
The .5's are coming from two different sources, so I'm pretty sure that James is correct in rounding down before adding them.
Chess, I copied the OP sentence.
Hasn't their been an answer for FCB stating they don't add anything until they add whole numbers?
Nope, as far as I could see there is no FAQ relating to this issue.
There is however, this:
Finally, some of these alternate favored class benefits only add +1/2, +1/3, +1/4, or +1/6 to a roll (rather than +1) each time the benefit is selected; when applying this result to the die roll, round down (minimum 0). For example, a dwarf with Rogue as his favored class adds +1/2 to his trap sense ability regarding stone traps each time he selects the alternate Rogue favored class benefit; though this means the net effect is +0 after selecting it once (because +1/2 rounds down to +0), after 20 levels this benefit gives the dwarf a +10 bonus to his trap sense (in addition to the base value from being a 20th-level Rogue).
see it's not adding to a die roll, it's adding to the bardic knowledge that goes up .5 every level.
I feel this is similar to the Wild Caller Summoner that adds 1/4 his level to evo pool and the FCB that adds 1/4 to the evo pool. Everyone I've seen says it equates to adding 1/2 every level. Which is what I feel happens with bardic performance going to 1 every level.
But it seems people think that the bard has 2 separate bonuses that add to a +2 every two levels, applied to the summoner means that it gets +2 every 4.