It seems like player two always gets the short end of things, from getting second choice to always being second to play. But a really sweet animated short published to Vimeo last month makes the argument that there's something very special about going second when your older sibling is the one up first. I won't say more than that except to say that you really ought to watch it — and that if you can relate to this at all, you'll probably get kind of emotional before it's over.
The short was made by Zachary Antell. He says the animation was mostly done through rotoscoping.