I got this idea from watching one of those automatic chess boards that moves your peice around for you.
Basically the entire "field" area is covered in a grid of magnets
say you want to redo that shot
you hit a button and it will move all the balls back to where they were before the
shot. can also be useful for doing the same shot over and over and you can program in famous shots or trick shots ( 2d trick shots)
the balls will move by turning on the magnet just in front of the ball and turning it off as it approaches and turning on the next closest magnet
the witch magnets turn on along with the speed and strength they turn on for are controlled via a computer.
because the balls have a metal exterior and a rfid ( coated with paint) when they roll over a magnet they produce a small charge that the computer can sense to keep track of the balls ( so it knows the 8 ball when left and the 9 ball when right)