For a USBC certified event, the ball must meet a set of criteria, which is usually up to a 3 ounce difference in top weight and 1 ounce for thumb, left and right side weight. Drilling holes for fingers and thumbs usually compensates for this when drilled in the standard location. Usually a ball without holes will not meet this requirement and need to have either finger holes or a counterweight hole drilled to bring the ball back to legal specs.
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The USBC (United States Bowling Congress) allows up to six holes to be legally drilled into a bowling ball: one for each finger being used to grip the ball, plus one additional one (colloquially known as the 'weight hole') to change the ball's center of gravity -- which affects how soon and by how much the ball will start to hook.
The vast majority of bowlers, however, grip the ball with only two or three fingers; a very few might use a fourth (usually the little finger, or pinky). Therefore, finding a ball legally drilled with five or six holes is extremely rare.