I’ve been thinking about the hit point method explicitly stated in Swords & Wizardry White Box, the “re-roll all hit dice” method:
Hit points are re-rolled each time a Player Character advances in level—however, if the re-roll results in a character having fewer hit points for their new level than their previous level, ignore the re-roll and retain the prior amount.
This is obviously different than the “standard” method of simply rolling an HD and adding it to a PC’s previous total at each level advancement, but I’m thinking of using it in my Labyrinth Lord game. I’ve got a few posts on this topic planned for the next few days, but I lucked out when a discussion of this erupted on the Swords & Wizardry board. I encourage you to check it out, starting about here for the in-depth analysis and this thread for an excellent summary.
During the discussion, Random ran one million (!) simulations of the various totals at various levels and posted the results. Using his numbers, I put together a couple of charts to display the curves at 5th and 7th levels for fighters:
The number on the bottom is the hit point total, the number on the left is the number of times that result came up out of 1,000,000. Keep in mind that S&W WB uses d6 hit dice for fighters. Click the images for a better look.
As you can see, the re-roll method has a slightly sharper curve to the bell and tops out a little higher than the standard method, but not by a whole lot. Random’s simulations showed an average difference of less than 1.88 hit points at 10th level, something I don’t find significant enough to spend any time worrying about.
I like the idea that a “bad” HD roll, say a roll of 1 when advancing from 5th to 6th level, can be “made up” at the next level. The cost, of course, is the fact that hit points may not increase at all if earlier rolls were particularly good. As for narrowing the bell, drawing most characters toward the mean, I don’t see that as a problem, though those who are convinced they can beat the odds and get nearly max hit points each level won’t like it.