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I have been reading over the falling rules in Pathfinder and one thing that is unclear to me is how falling damage works between 10ft intervals. Is it that everything up to the first 10ft takes 1d6 damage and then 10ft to 19ft11in takes 2d6? Or do you take no damage falling the first 9ft11in and then take 1d6 for 10ft to 19ft11in? Or is it something else like it is no damage for the first 4ft11in, then 1d6 for 5ft to 14ft11in. The last one makes the most sense to me, but is also least in line with normal mechanics.

Since players climb at 1/4 their movement speed, this seems pretty relevant since someone in heavy armor is probably only climbing at 5ft per round with big minuses to their check. This would make the difference for them between fumbling around for a long time to finally get up that 10ft ledge vs giving up trying before they kill themselves.

Not required information for an answer, but in case you are curious:

I need a RAW answer for this because I am using it for part of a simulation I am doing. I want to look at how dice rolling mechanics effects outcomes for common tasks in different scenarios. Right now I am running a "Climb or Death" scenario where the character climbs until they get to the top or dies of falling damage and seeing how various things effect the chances of them getting to the top. Currently, the character takes no falling damage until 10ft. Some of my simulations where the character moves very slowly (20ft per round movement so 5ft climb) and they need a high check to climb, the character is taking thousands of rounds to repeatedly get up high enough that they can finally fall to their death, even if they only have 10 hp. That seems odd, but maybe just because I have never played with anyone stubborn enough to try and climb 10ft 1000 times.

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There are solid arguments for either doing 10-19ft = 1d6 fall damage or 6-15 feet = 1d6 fall damage.

Note that in both cases, 10 and 15 would be on the same die count, so if you're abstracting to 5-foot increments these are functionally identical.

10-19ft:
The SRD says falling 10ft is 1d6 and falling 20ft is 2d6.
If you fall 15 feet, did you fall 10 feet? Yes.
Did you fall 20 feet? No.
Clearly you must use the 10 feet value, because the rules do not specify that you do anything for that extra 5 feet.d

6-15ft:
This requires a little bit of extrapolation, and as such is not strictly RAW. However, it offers support to the RAW definition provided above.
The ring of feather falling states that it activates automatically if the wearer falls more than 5 feet. Since the intention of a ring of feather falling is to prevent fall damage it would be pretty silly if a 5-foot fall caused damage, as the ring would not activate to protect you.
Since the ring specifies 5 feet and not 9 feet, it's logical to assume that's the maximum distance you can fall without taking damage.
With the SRD's specification of 1d6 per 10ft increment, you end up with a range of 6-15 = 1d6, 16-25 = 2d6, and so on.

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