I have a certain way I like to move my coin when I mark my score. If I am looking from the break, I like to move my coin to the left.
So, if I win the first game, I move my coin first to the left.
If I lose the first game, I *hope* my opponent moves their coin to the right.
When my boyfriend and I spar, since we both prefer to move the coin to the left, whoever wins first gets that luxury. :)
Something else I do - if my opponent wins the first game, and then they go rack (because it's their rack in alternate breaks), then I will move their coin for them, as I stand there to wait to break. Well, obviously, I move their coin to the right, because I like to move on the left, lol.
Only one time, that I can remember, did someone switch their coin to the other side. Normally, people leave it there.
If they moved my coin to the right for me first, I'd switch it to the other side.
So imagine my surprise during the Season Opener of the Omega Billiards Tour when I saw a player lose their first match, wait to break, and as their opponent was racking asked, "which way do you want your coin to go?"
So, either this person did not have a preference, OR they truly respected that their opponent won the first game and therefore deserved to choose which direction they wanted their coin to move.