From the TBA rule book (v. 6.0):
RULE 603 DRILLING SPECIFICATIONS
Holes
The following limitations will govern the drilling of holes in the ball:
1. Holes or indentations, not to exceed five (5), for gripping purposes.
2. One hole for balance purposes not to exceed 1 1/4 inch in diameter.
3. No more than one (1) vent hole to each finger and/or thumb hole not to exceed 1/4 inch in diameter.
4. One mill hole for inspection purposes not to exceed 5/8 inch in diameter and 1/8 inch in depth.
Any hole drilled for gripping purposes will not be deemed to be a balance hole. However, when delivering a ball that
has a thumb hole drilled, the player must have his/her thumb in or over the thumb hole. It may not be 180 degrees away
from the thumb hole. If a bowler delivers a ball and did not have his/her thumb as defined, the ball will be deemed
illegal for that delivery and pins knocked down with that delivery will not be counted.
VERSION 6.0 – 11/3/05 34
Balance
The following tolerances will be permissible in the balance of a bowling ball used in accredited competition: Refer to
Rule 127 for the penalty for bowling with a ball that is found to be illegal.
1. 10 pounds or more:
(a) Not more than three (3) ounces difference between top half of the ball (finger hole side) and the bottom
half (side opposite the finger holes).
(b) Not more than one (1) ounce difference between the sides to the right and left of the finger holes or
between the sides in front and back of the finger holes.
(c) A ball drilled without a thumb hole may not have more than one (1) ounce difference between any two
halves of the ball.
(d) A ball drilled without any finger holes or indentations may not have more than one (1) ounce difference
between any two halves of the ball.
(e) A ball used without any hole or indentations may not have more than one (1) ounce difference between
any two halves of the ball.
2. Less than 10 pounds:
(a) Not more than one (1) ounce differences between the top half of the ball (finger hole side) and the bottom
half (side opposite the finger holes).
(b) Not more than 3/4 ounce difference between the sides to the right and left of the finger holes or between
the sides in front and back of the finger holes.
(c) A ball drilled without a thumb hole may not have more than 3/4 ounce difference between any two halves
of the ball.
(d) A ball drilled without any finger holes or indentations may not have more than 3/4 ounce difference
between any two halves of the ball.
(e) A ball used without any hole or indentations may not have more than 3/4 ounce difference between any
two halves of the ball.
Plugs and Designs
1. Plugs may be inserted for the purpose of redrilling the ball.
2. Designs may be embedded in the ball for guides, observation or identification purposes, provided such designs
are flush with the outer surface of the ball.
3. In all cases there will be no interior voids.
4. Plugs and designs must be made of material similar to, although not exactly the same as, the original material
out of which the ball was made, and will otherwise comply with all other specifications for a bowling ball.
5. No foreign material may be placed on the outer surface of the ball.
This was found on the TBA website
www.tenipn.org.au
The rule is pretty specific, basically, if you have 5 fingers and a thumb, one finger would not be able to be used in a gripping hole. I'm not sure if you can apply for an exemption, being as it is a special instance. it might be a good idea to contact someone from the TBA to get a proper ruling.
hope this helps.