Flipping Bits/Squares

This game is for any plural number of players.

You need a blank piece of paper and a pen/pencil.

A predetermined number of rounds are played.

Start each round by making a row of n squares, where n is at least 7 or more if there are 2 players; n is larger if there are more players.
Fill in every other square.

Take turns.

On a turn a player can change any ONE square from filled in to not filled in, or vice versa.
Make a new row of squares to reflect the move.

A move may not lead to a pattern of how the squares are filled that has already existed in the round.
If all patterns achievable by changing one square (flipping one bit) lead to patterns that have already existed in the round, then a player flips two bits. If all patterns achievable by flipping two bits also lead to patterns that already occurred in the round, then flip three bits; etc.
A player MUST move with the fewest number of bits flipped as possible that will lead to a new pattern for the round.

As soon as a player achieves with their move a pattern with exactly one bit/square a different color (either filled or not filled) than the rest of the row, then that player gets {the number of squares from the left side of the row that is this unique square's position} added to his/her score.

The round is then over.
(So, one player scores each round.)

Play a predetermined number of rounds, adding up each player's scores.

The player with the largest grand total wins.


Example round: (n = 7)

(*)( )(*)( )(*)( )(*): start
(*)( )( )( )(*)( )(*): player 1
(*)( )( )( )(*)( )( ): player 2
(*)( )( )(*)(*)( )( ): player 1
(*)(*)( )(*)(*)( )( ): player 2
(*)(*)( )(*)(*)( )(*): player 1
(*)(*)(*)(*)(*)( )(*): player 2
Player 2 gets 6 points, since the blank square is the 6th square from the left.

(I wonder what the funnest n is for any given number of players, especially for 2 players.)

Thanks,
Leroy Quet