Euclid ball was created during my freshman year of college (2005-2006).  It started as a simple billiards variation, and grew to be much more complex.  It is named for Euclid of Alexandria, the great Greek Mathematician.  After reading the rules you will understand why.

EUCLID BALL

1. To start:

All fifteen balls are racked in the traditional triangle configuration. The 1 ball must be at the pinnacle of the triangle and the fifteen ball must be in the “eightball” position with the eight and the seven ball directly behind it.

2. Game Play:

Similar to nineball, all fifteen balls must be hit in sequential order, but can be sunk in any order (i.e. One to fifteen combos are valid).

Not hitting the next ball in sequential order results in a penalty of  '+ i' to the offending player's score.

Scratching the cue ball results in a penalty of '-e'(2.718281828) to the offending player's score and the next player receives ball in hand. A sunk ball paired with a scratch is spotted on the dot.

3. Keeping score

Each ball pocketed is worth the value specified in the table below.

Keep track of each player's score individually.  It is best to keep track of the numbers and mathematical constants separately, factoring their value at the end.

Two minus i's result in +1 to the players score. Similarly two plus i's result in -1.

*gopf = “Get out of Phi free” --see explanation in rule 4

4. Miscellaneous Rules

Sequencing: When a player pockets n consecutive balls(remaining on table) with no other balls in between, the player is awarded a bonus of the sum of the first n-1 Fibonacci numbers (starting with 1,2,3,5,8...etc.).

The Golden Ratio: If a ball is pocketed without hitting the object ball first, the offending player receives a penalty of '-Φ'(1.61833). The only way to eliminate this penalty is by pocketing a Fermat prime which will relinquish all -Φ's acquired up to that point. If a player has not received that penalty yet, he has one so called, “Get out of Phi free” card, which can be used at any point during the game to eliminate that penalty.

Epsilon: If a player pockets the 15 ball and scratches, his/her score is then multiplied by 'ε'(.1) and the 15 ball is spotted.