I just invented a new brain/core exercise, new use for an exercise ball.
Prop a fully inflated exercise ball up in an office chair. Find a baseball-sized dog squeaky ball. Throw it at the exercise ball with your right hand, it will rebound very quickly and randomly. Catch the ball with your left hand. throw the ball again with your left hand and catch with the right. Repeat for 30 minutes.
I discovered it by accident when I threw a ball to my dog and hit the exercise ball. It is very challenging and fun. By the end of the first 30 minutes I could throw and catch the ball 100% of the time. It works the core muscles in the chest and abdomen, your arms, your wrists, your neck, your legs and the randomness of the ball is amazing for hand-eye coordination. I assume it's going to be very good for ambidextrous-ness. As I got better, the rhythm of the bouncing became very soothing and meditative. Nifty!
It's very important that the ball has a high contrast pattern on it so you can see the spin, a soccer ball pattern works well. It seems to help my eye and brain pin-point the ball's location better. Oh and find the spot on the exercise ball that gives the best rebound and draw a target with a sharpie to aim at. It helps a lot.
Have fun!