The bots
They hold every seat you don't
Seat one starts as a human and the other three start as bots. The button on each scoreboard card flips that seat between human and bot in the middle of a game, so handing a seat over and taking one back are the same action. A bot scores every legal placement of every block it holds, in all eight orientations: three points for each diagonal contact with its own colour, two for each square it puts on the rim of the board, one for each empty square diagonally beside it, and a fifth of a point for each step of average distance from its own corner. Ties break at random. Restarting puts seat one back to human.