Lengths Of Lengths Of Lengths Game

This game is for any plural number of players.

There are a predetermined number of rounds. Each player plays the same number of rounds as the offense player.

In a round: A list is made of 0's and 1's, starting at empty-set. The players take turns each appending either a 0 or a 1 to the end (right side) of the list. The total number of digits in the round's list is n, where n is a predetermined number that is a multiple of the number of players.
(n is the same for all rounds.)

After the list of 0's or 1's is made, we determine the score.

We now form a series of lists.

(*) If the new list consists entirely of 1's, then the offense player gets the number of 1's added to his/her score. And the round is over. (If the round is over, then go to **.)

If there is at least one number not equal to 1 in the latest list: Below the last list made, write a new list consisting, in order, of the lengths of the runs of similarly-valued numbers from the previous list.

Go to (*).

(**) Change who is the offense player. Start a new round.

After all rounds have been played, the player with the largest score wins.

Sample round: n = 25:

1010110011101000111001011

1,1,1,1,2,2,3,1,1,3,3,2,1,1,2

4, 2,1,2,2,1,2,1

1,1,1,2,1,1,1

3,1,3

1,1,1

Offense gets 3 points.


Thanks,
Leroy Quet