Why is my sister related to me only 50%?

Think about it in terms of particular mutations causing altruistic behavior, and the conditions under which they spread. Also, remember that when a mutation that causes altruistic behavior towards some group first arises, it is rare.

Say that I spontaneously mutated in conception to be altruistic towards siblings (via the mechanism of liking agemates I grow up with in sufficiently close contact). Then half of my children carry the dominant mutation and help each other, so that even though the mutants help non-mutant siblings, a large enough fraction of aid goes to other mutant siblings that the gene becomes more frequent in the population.

On the other hand, imagine a new mutation causes altruism towards some broad group, like tall people. My mutant children will spend most of the resulting altruism on tall strangers who lack the gene.

When competing with members of your own species, what is relevant is the genes that actually change from one member of your species to the next. So the fact that you share the vast majority of genes isn't what matters.

You share 50% of the variable genes.

Here's my first stab:

The ancestral environment had little if any interracial couples producing kids. (The old rape-the-neighboring-tribe's women thing still didn't involve vastly different races on the scale of chinese/causasian.) Therefore, kin selection pressures did not perceptably benefit from distinguishing between "siblings from interracial parents" vs. "siblings from more closely-related parents" -- all parents were the latter type.

So it doesn't seem like there would be room for a more fine-grained relative-gene-similarity detector to develop: most of the benefit from helping your kin in the ancestral environment is from the fact of that kinship, and further deviations from the simple percentage-genes-shared calculations (due to the relative relatedness of parents you mention) would just be very weak noise.

A side note: AFAIK, it isn't known whether siblings are really 50% identical. They are slightly more than 50% identical with regard to gene expression, because of gene imprinting on the sex chromosomes. It's possible there's some weird mechanism that causes an imbalance or bias in recombination. Perhaps we haven't sequenced enough siblings to know.

But I obviously share more than half my genes with my sister because my parents are not unrelated.

You're also fairly closely related to a carrot too, for what it is worth. At least as compared to a totally random string of DNA or something that doesn't even store its genotype with amino acids.

There is an impressive name for 'the amount of the novelty of the genetic heritage that can be particularly associated with you' measure but unfortunately it has slipped my mind again.

The standard story when dealing with inclusive fitness in evolutionary arguments is that my sibling's life is worth half of mine and my cousin's life is worth a quarter of mine.

...if your expected reproductive output happens to be the same. Otherwise you would be well advised to multiply by that.

Should I expect my kids to like each other less than I like my sister, because they are less closely related?

Possibly a little, if they actually are less closely related. The idea that kin-cooperation is based partly on percieved cues of physical resemblance started here. Your offfspring may have other cues about their relatedness to go on, though.

Because it works something like this, in a grossly oversimplified explanation:

Human genes are organized on 23 chromosomes, 2 complete sets of them, so 46 in all, with 50% being redundant. Your DNA is fragmented in 46 stripes of neatly ordered DNA.

Information on these two sets of chromosomes aren't identical, just redundant: On one set could for example be the information to make fair hair, on the other the information for brown hair, with the carrier of those genes getting brownish hair.

If a human produces gametes (cells used for reproduction, sperm and eggs), each gamete will get half of the set of chromosomes.

So, to oversimplify even more, your daddy will put one of its two sets of chromosomes into his sperm, yielding sperms with each half of his whole set of chromosomes. For the sake of clarity, lets call the sets of sperms he can produce D1 and D2. Mommy will do the same, just getting M1 and M2.

If they procreate, the embryo will get chromosomes from 2 randomly chosen gametes, which can be M1 or M2, and D1 and D2.

That leads to following possible genotype-mixtures: M1D1 M2D1 M1D2 M2D1

The outcome is completely random, so you would have a chance to get a sibling with identical genes 25%, with half of your genes 50% and with none of your genes also 25%. Which gets to an average of 50% of identical genes per sibling.

Evolution works with huge numbers and enormous timescales, so it is save to assume that this statistic works out true and is safe enough to bet on.

Less simplified, each the chromosomes which is put into a gamete is randomly chosen. So, each gamete gets 23 completely randomly chosen chromosomes from the whole set of 46 chromosomes. (Keyword here is meiosis, biologogenes for "making gametes"). And, to complicate matters further, in one step of the meiosis the DNA-strands which make up the chromosomes are broken randomly (but at the correct places) and joined. (This process is called crossover.)

So, the body does it's best to make the genetic makeup of any gamete to a very randomly chosen set of all genes in the body. (That's because the body does not know and isn't able to find out which of his genes make him fit in an evolutionary sense. So, randomness is the best chance. Again, that's very simplified.)

That boils down to the fact, that siblings share approximately 50% of their genes, give or take a few.

If you want to know that a bit better, read Dawkins "The selfish gene" (no atheism in there, just good old biology). Really good book, which clarifies many things regarding evolution and genetics with just traces of chemistry.

Or, if you want to know it really good, read a book about genetics, I would recommend the tome "Genes IX" by Benjamin Lewin or similar.) (Serious biologenes and chemistry there, though.)

Hope that helped.