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My family won't speak to me anymore. I had a DNA test to explore the wonders of my heritage, and the authorities wound up corralling a bunch of them on cold cases for rape, murder and grand theft.
You get 23 of your 46 chromosomes genes from each parent, and they each got half from their parents, etc. So let's count your chromosomes going back in the generations:
46 (you)
23 (from a parent)
11.5 (from a grandparent)
5.75 (from great grandparent)
2.875 (from gg grandparent)
1.4375 (from ggg grandparent)
0.71875 (from gggg grandparent)
0.359375 (from ggggg grandparent)
Now we have arrived at the point where your average inheritance is less than 0.5, but chromosomes are transmitted in whole units. You either get that one or you don't (ignoring the "crossover" effect which I won't go into). So on average you did not get even one chromosome from any given ggggg grandparent, of which you have 128. So you're probably unrelated to your own ancestor! Sure, you got your chromosomes from some of them, just from not all of them.
Now for siblings: When an egg or sperm is created, it gets a random selection of 23 chromosomes from the 46 that you have. Each chromosome has a 50/50 chance of being included in the egg or sperm. So the 46 that you end up with could be the exact opposite of the 46 that your sibling ended up with. It's really super unlikely (2^46) but possible. You'd have the same parents, but absolutely nothing in common genetically. Conversely, you could have every single chromosome in common, so you'd be an identical twin to your sibling, just born at a different time.