Is the carom angle the largest with a half-ball hit?

Close, but not precisely. See the bottom of TP 3.3. The maximum carom angle (33.75°) actually occurs at a cut angle of about 28°, which corresponds to a 0.53 ball-hit fraction. These numbers are close to 30° and a 1/2-ball hit, but not exact.

The 30° rule angle template is useful to visualize better approximations for the CB angle over a range of shots.

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