Complexity is Simple.

Throw 2 jacks.

The white jack is designated "evil" and the wooden jack is "good". The player closest to the good jack increases the magnitude of his score by 1 (or a bit more to keep the score integral) for each ball closest to that jack.

This player also choses the direction of rotation of the opponent's score. The player with balls closest to the evil jack must multiply his score by (1+i)^n or (1-i)^n where n is the number of evil balls. The player closest to the good jack choses which of (1+i) or (1-i) is used.

The winner is the first player to have a pure real score 13 or greater. If a player gets a pure real score -13 or less, he loses. (imaginary component must be zero).

Winner: Rob (+48) to Simon (-20i).

Bocce in the Complex Field

Rules:

1. Any player with a score of 10 loses immediately.
2. Kicked balls count double.
3. Two jack shall be thrown. One is positive and the other negative. A score of -10 wins and -13 or less loses.
4. If a player has balls closest to both jacks then the opponent's score is multiplied by i (square root of -1). Scores add or subtract from the radius. Only real numbers can win or lose.
5. If both players win on the same go, then a concave polygon is drawn around each player's bocces and the player whose bocces define the smallest area wins.
   

Winner: Simon (13), Rob (9 i).

The two jack rule was very interesting and the complex number rule was just wierd. Future use of this rule will require more thought so that escape from imaginary numbers involves some level of skill.

The Tree

29 June 2006,

As we were feeling brain challenged, the first extra rule was to ban adding further rules. Hence, we played something not entirely unlike Bocce on a beautiful winter's day looking out over the Sydney Harbour Bridge and the Opera House.

Score: Rob (a.k.a The Bounce Master) 13, Simon 5

Return of the Budgie

Rules for 2 June 2006.

1. Any player who harms a budgie loses the game instantly.
2. Any player who fails to talk like a pirate at some stage each end is penalised with the yellow card.
3. If a player plays a worthy shot, then the opponent may award a promotion. The ranks are chess pieces in order of worth. The starting rank is Pawn. The value of the Knight and Bishop depend on how open the field is. If the field is open, the Bishop is worth more.
   
4. If a player reaches a score of exactly 10 points, they lose.
5. The closest ball is treated as the second closest ball, and the second closest ball is treated as the closest ball.
6. The 3rd closest ball is treated as a ball of the opponent.
7. Both feet must be off the ground at the moment of bocce release.
8. The bocce must first hit the ground further away from the thrower than the jack, if it hits closer then that bocce is ignored.
9. If any rule is broken, then one point is deducted and the player is demoted one rank.

Results:
Simon 7, Rob 4 when time ran out.
Simon was ranked Bishop and Rob was ranked Pawn with one yellow card.

Location: The Sheep of Solitude

Updated Initial Rules (24 May 2006)

Initial Rules as at 24 May 2006.

1. Choose initial thrower of the jack by coin, start an end as normal with normal bocce rules (first to 13 etc.),
2. While playing an end, the player who threw the jack proposes a new rule / amendment. This is debated with possible amendments by the end of the end. More than one rule can be added per end, but a minimum of one per end must be added.
3. The new rule is voted on, and imposed immediately. If the vote is split, then a coin decides. If the proposer wins a coin toss, then the rule is accepted and the proposer gets an extra point. If the proposer loses the toss, then rule is not accepted and the proposer loses a point.
4. Go to step 2.

Winning: by score or by paradox.

• The winner is the first to 13.
• If the rules are changed so that further play is impossible, or if the legality of a move cannot be determined with finality, or if a move appears equally legal and illegal, then the first player unable to complete a turn is the winner. This rule takes precedence over every other rule determining the winner.

The first Nomic Bocce match.

Rules for today:

1. All balls that don't hit a "sheep" are not counted, but remain on the field
2. If 4 points are scored, then players swap scores before adding the 4 points to the winner of the end.
3. All balls must move "left" at some point before stopping. If it doesn't then the ball becomes the other player's.
4. If a ball is in shaddow at the time of scoring, then it counts double.
5. The lower stripes of the 4 balls must go left and the higher 2 bocces must go right.
6. The player with more points must throw the boche while facing the opposite direction in any manner.
7. The "bounce off a sheep" rule was repealed.
   

Simon won 13-3 (due to a 9 point end with some non right bouncing shadow balls), then Rob won 3-2 when time ran out.

Note: The "sheep" are part of the art installation that Rob and I have named "The Sheep of Solitude". This is a collection of ruins from old buildings lying on the grass as an artwork near government house in the botanic gardens of Sydney.

The inaugural base ruleset

The initial ruleset of the first ever Nomic Bocce game is as follows:

1. Choose initial thrower of the jack by coin, start an end as normal,
2. While playing an end, the player who threw the jack proposes a new rule / amendment. This is debated with possible amendments by the end of the end.
3. The new rule is voted on, and imposed for the next end. If the vote is split, then a coin decides. If the proposer wins a coin toss, then the rule is accepted and the proposer gets an extra point. If the proposer loses the toss, then rule is not accepted and the proposer loses a point.
4. Go to step 2.

Nomic related links:
"Nomic." Wikipedia, The Free Encyclopedia.
The original ruleset by Peter Suber.
Nomic.net