For the innumerate English majors, shoot in alphabetically-ordered pairs.
We see a new game go by maybe once a month. There is usually no point, by which I mean the "new" game is substantially like some other common game and it doesn't give the player anything novel. If you're going to invent a game, at least be inventive. The new game should require strategy and shots that are different from what is already played.
If you're looking for something "new" to expand your horizons, try the following if you have not already played them:
Snooker
Golf
Pink ball
English Billiards
3-Cushion
Straight rail
Artistic billiard shots
Partners rotation (15 balls with the 1-5-8-10 12-15 being special)
One pocket
Straight pool
Standard rotation
Cowboy
Loop, Irish pool, In-offs
Bank pool
Blackball
Russian Pyramid
Honolulu
Cutthroat
And any good inventor would have already done his homework and played all of those.
I did design a pretty cool game a few years back. You may find it interesting...
Two players, a full rack of 15 balls. Lag for the break.
Player A shoots first. The objective is to pocket a ball, any ball. Then it's Player B's turn. Player B must pocket a ball or at least make 1st contact with a ball that mathematical factors into the ball Player A pocketed. If a factored ball is pocketed then B gets a point. If a factored ball is not at least hit first, player A gets ball in hand.
When a ball is pocketed that has no factors, like a prime number, or a composite number of which all the factored balls have already been pocketed. The player that pockets that ball shoots again. The opposing player only gets to shoot if the ball pocketed has a factor left on the table.
Examples: Player A shoots the 6 ball and gets a point for it. It is now player B's shot, and B must either pocket or legally hit any factor of 6. So he can shoot the 1, 2, or 3 (the 1-ball can be used for a factor with any ball).
Let's say B pockets the 2. Now player A must hit or pocket the 1, seeing that it's the only factor available for a 2. Let's say she pockets it. Score is now 2-1 with player A ahead. But there is no factor for 1, so player A gets to shoot again. Now she pockets the 3, a prime number, and with the 1 off the table, she gets to shoot again. Score is 3-1. She pockets the 10. Score is now 4-1. Since the 5 is still on the table, player B gets a chance to pocket the 5. He at least better make a legal hit on it. He can play a safe also, but player A will be free to shoot any ball now.
The game can be played to 25 points or 50 points or whatever. A player can get on roll after the 1 ball is off the table. They can shoot as many prime balls or factorless balls thay can shoot and player B will not have a chance at the table until player A misses, fouls, or pockets a ball that has a factor left on table.
There is quite a bit of strategy here. But also the players must really pay attention. If A pockets a ball thinking there are no factors for that ball, let's say it's the 14, and then shoots again regardless of the fact that the 7ball is still on the table, player B can call a foul and get ball in hand.