I don't know about anyone else, but on my boat we draw straws at the beginning of the trip. Actually, if you ever played 'pill pool' where you have a bottle with numbers representing the balls, we pick from there and #1 goes first, etc.
Seems to be the fairest way.
A run off with hook up counts as your turn, if you land the fish or not. Don't matter if it's a shark or blue fish or if the hook is pulled. If you start fighting a fish, that is your turn. A run off without a hook up, you keep your turn.
