The paddle move is a bit of slight of hand that magicians use any time they want to do magic involving a paddle. This comes up more often than you might think.
For example, let's say a magician has a paddle on which is drawn a hat and wants to make the drawing of a rabbit appear in the hat. With the paddle move, it's as easy as pie and completely undetectable to the eye!
Here's how it works. The magician holds the paddle with the hat using the pointer middle and ring fingers and thumb. Secretly, the magician also holds a second paddle -- this one with the picture of a rabbit in the hat -- with the pinky and base of ring and pointer fingers, using the curve of the crook of the base of the thumb as a rest. When it's time to do the move, the magician pretends to turn the paddle over, but really pushes with the base of the thumb, swinging the hidden paddle up at the same time the first paddle is dropped between the fingers by deft motion of the index and swung down, switching the paddles' positions. With a few hours of practice, this can be done smoothly and undetectably.
Both sides of the paddle with the rabbit can now be freely shown. The rabbit can be vanished by repeating the paddle move and swapping in the original paddle, or perhaps a new paddle (one with a coyote eating the rabbit, for example) can be swapped in from a stack of paddles held hidden in the hand atop the first hidden paddle.
Note: Unless you have very large hands, the paddle move generally won't work with large paddles and/or oars.