BloodHenge wrote:

The situation Killjoy presented would result in someone who is 3/64-Elven. I'm not sure how you could wind up with a denominator that's not an exponent of two, even with a long and complicated family tree, although the numerator can certainly be larger than 1.

1/54th could be the approximate fraction, e.g. that 3/64ths is approximately 1/21st. 19/1024ths is approximately 1/54th. So if you had an Elf in your family six generations back, and aside from that person's ancestors you also had another Elf in your family eight generations back, and aside from his and the first guy's ancestors you had another Elf in your family ten generations back, you'd be approximately 1/54th Elf. Alternatively, since there probably weren't many if any whole Elves in the population, if 38 of your great-great-great-great-great-great-great-great-grandparents were half-Elves, you'd be approximately 1/54th Elf.

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Well, the fact that it's an approximation makes me feel better... but isn't 1500/33 ~= 45?

That, and why does he give a percentage of 1/[# of generations]? I think it'd be something like

[% of half-Elves in original populations]*[# of generations elapsed]^2/[# of generations elapsed]^2*2

to get the percentage of Elf blood in you. For every 2 half-Elves in your family n generations ago, you have 1/(n^2) Elf blood, so you have half as much Elf blood as the number of half-Elves in your ancestry n generations ago divided by the number of ancestors you had n generations ago, which is 2^n. Of course, now that I think about it this simplifies to

[% of half-Elves in original populations]/2

So the average Tsuirakuan has a percent of Elven blood equal to half of the percentage of the original Tsuirakuan population who were half-Elves, which seems pretty straightforward and obvious in hindsight.

So the question is, what percent of the original Tsuirakuan population were half-Elven? Divide that by 2 and you'll have the average amount of Elven blood in today's Tsuirakuan. Of course, this is presuming that all half-Elves were literally *half* Elven, and not just partial-Elves of some degree.