One by-product of this rule is you can build tables without the fixed hit points at any stage of a character’s advancement. This is especially true if constructing a white box style class that always uses d6 for hit points.
I discovered this while translating the Kyssai race from Matt’s Pars Fortuna to Ruins & Ronin.. They have up to 9 d6+1 hit dice (the average is the same as a d8 or the same as the post-Greyhawk fighter) and then a constant +2 at levels 10+. While it would be easy to write a chart that started at 1+1 and ended at 9+9 at 9th level I decided I wanted to roll the maximum d6 (given we’re re-rolling each time) and have the average be within 0.5 hit points.
This leads to the following chart:
No, levels 10-12 are not wrong. I concluded given we’re re-rolling why not continue re-rolling instead of using just a flat amount. Sure, it means at higher level you’ll head even higher in hit points if you roll better and over time (given you can’t fall) characters will approach the max hit points (69 max versus 92 at level 15) I don’t think this will necessarily break down that badly as the increased randomness also risks you being at 17 instead of 24. Even if you didn’t continue after the fixed level the change from narrow range fighter dice (1d6+1 might average the same a d8 fighter but it’s on a 2-7 range, not 1-8) provides a more interesting process if you’re using the re-roll rule. Then again, the WB fighter is 1 dice per level except at level 1 where he gets a +1. Perhaps the conversion should just be which average matches up to the Core version.