eBay Guides has a collection of tips to boost your chances of grabbing a prize in a claw machine game. From the Guide:
Three Pronged Claws:
This type of claw usually handles small stuffed animals and small collectable basketballs. This type of claw is somewhat similar to the four pronged claw, but instead of having two of the prongs positioned above the arms, you have a choice of the prongs going around the left or right arm. Have the claw at an angle so that it covers the whole chest area of a stuffed animal; this is the best way to get things out of three pronged machines. To get a small collectible basketball, try and make sure a ball is not being surrounded by any other basketballs. For this might rotate the claw on its way down and might miss your basketball target. If this is inevitable, try and make it straight down as much as possible. For best results, aim the center of the prongs in the radius center of the basketball. This technique draws a 60 to 70 percent chance of grabbing a basketball, but it is very difficult to center the claw in the middle of the basketball.