Originally posted by The_Contemplator
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Take several different decks of cards. Makes they're uniquely identifiable, as we're going to use them to represent ancestors. If you're only going to the grandparents 4 decks will suffice. (It's an oversimplification, but not too far from the point.
Take 2 of the decks, split them in half, then take two of those halves, and shuffle them together. That's one of your parents.
Now repeat that with the other two decks, that's your other parent.
Now split those two decks in half, and now combine two of those respective "half-decks" from each parent together. That's you. Now go back through that deck and look at the distribution of cards from each of those 4 source decks. It isn't going to be as evenly divided as the statistics claim it should be.

On average it should split 25% 4 ways(52 cards in a "standard deck", or 13 cards per "ancestor deck" when split 4 ways), if you run it across enough iterations. But in practice, it's another matter. (Doing siblings in that example would get messy as you would need to reconstitute the deck(so "you" no longer exist) and require repeating the example again for that specific (representation of a) person, but it could be done)
In any case, it's a decent demonstration as to why Autosomal DNA results can come back with seemingly strange results in some cases.
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