Keeping Score

A game of snooker is usually a series of frames. When a game starts, the players decide, usually by a coin toss, who will play first. The player who plays first keeps his score on the top counter and maintains that position throughout the game.
You do NOT flip-flop the scoreboard after every frame 'to keep track of who broke-off last'. Use a chalk board for that. Too many frames are ruined by players getting confused over who is scoring on top.

When your opponent is at the table, count out his break as he makes it. Wait until the balls on the table have stopped moving, and all balls pocketed have been re spotted if necessary, and then let him and the observers know what his break is so far.
This way, there is no argument about the score when the break comes to an end.