OK so here is my idea for an invention that can be used in a new game called...Random Rotation. Though I thought this up myself, I have no doubt many before me have thought of this.
Basically, Random Rotation works exactly the same as all your other rotation games (eg. 9-ball) except that the order in which the balls become the object ball is randomly chosen immediately AFTER the break shot. The 1-ball is always the first ball in rotation and is racked in its normal spot. The game winning ball (eg. 9-ball) is always the last ball in rotation and is racked in its normal spot. All other balls can be placed however the person racking chooses.
After breaking the rack, a pea bottle with all the other balls in it is shaken and poured out (see picture). The order of those balls determines the order of the rotation.
This would not change the essence of the rotation game at all, and it would totally remove any possibility of an advantage by pattern racking.