This is like my life. When I wake up there are people milling around my living room and I drift past them out the door to work. Then when I get back, they're still milling about and I drift past them to bed.
OK, so basically whoever goes 2nd and places the last piece wins the game. I haven't observed otherwise yet. It's because getting to be the one to pull the final chips in is a huge advantage. So ultimately this is just the prolonged outworking of a coin flip.