Variant Channeling half die rolls

Question

The following is an excerpt from the PRD section on Variant Channeling (found here on Paizo's site (emphasis is mine):

When using positive energy to heal, affected creatures gain only half the normal amount of healing but also receive a specific beneficial effect.
...
Some variant channeling abilities are enhanced when used on particular creature types. Such channeling increases the normal healing or damage from channeled energy by 50% for that creature type, rather than the default half healing or damage for the alternative channeling. For example, a 7th-level cleric normally heals 4d6 points of damage with channeled positive energy; with the Nature alternative channeling, that cleric instead heals only half that amount (2d6) when channeling, but heals animals and fey an additional +50% over the unhalved value (4d6 + 50%).

I can not find any other reference in the core rules that talks about dividing dice-based abilities this way. Is this an error in the example (should it be 4d6, rolled and divided by 2?), or is there another reference on how this division is done?
If this is a standard way of dividing, how would you divide an odd number of dice?

I'm siding towards "error" because there is a lot of inconsistent wording in this whole section that leaves certain things open to GM interpretation. i.e. does the base damage inherit the properties of, i.e., fire? It even explicitly says as part of _or_ instead of in the text which means there's no official answer.

Answer 1

I would like to start by noting that this question has also been discussed on the paizo messageboard, without a definite answer unfortunately.

That being said, there is no official answer to this question, and I can give only a recommendation on how to handle it, based on the fairness of the math involved.

There are three (and a half) readily available possibilities to go about this. Ideally, what you want is something that will not alter the statistics of the roll too much. The mean and standard deviation of the complete roll should ideally equal half the mean and deviation of Xd6 (see here for X=5)

• 1d3 has a mean of 2, with all values equally distributed. The mean is matched rather well, However, the deviation of (X/2)d6+1d3 is quite large.
• 1d6/2 (round down as is usual in PF), has a mean of 1.5, with 0 and 3 being half as probable as 1 or 2. Again, the mean is alright, but the deviation for X=5 is even larger in this case.
• 1d6/2 (min 1) has a mean of 10/6 = 1.667, with 1 being thrice as probable as 3.
• Xd6/2 will actually yield a probability distribution similar to the distribution of Xd6.

From a probability standpoint, the last solution seems best, and is consistent with the way +50% is calculated as well. However, it directly contradicts RAW, as you would roll 4d6/2 instead of 2d6 on level 7. If you want to stay RAW, I would suggest using 1d3 instead of 1d6/2 for a half d6, because it does not break the symmetry of the bell curve.