Start by deciding what the cue ball should hit first. On a ball-first shot, contact thickness on the object ball is part of the aim. On a cushion-first shot, the first cushion target is the immediate aim. Both can produce a legal three-cushion carom.
Map the tip position before predicting the route
Squirt, swerve and cushion response still depend on cue, speed, cloth and delivery.
Separate the first target from the scoring condition
The cue ball must contact both object balls and make at least three cushion contacts before contacting the second object ball, without a foul. The cushion contacts may occur before or after the first object-ball contact. They need not be three different sides.
For ball-first play, choose the first object ball and the intended thickness. Then trace the cue ball’s departure toward the cushions. For cushion-first play, choose the initial cushion contact and check that the later ball contacts fit the scoring sequence.
Choose a reference that matches the route
A half-ball reference concerns ball-contact geometry. Corner-5 and Plus concern particular cushion-route diagrams with their own scales and stroke assumptions. They are tools for different questions, not interchangeable names for one formula.
Keep the complete chart beside the calculation. Identify departure, first-cushion aim and the specified arrival. If an object-ball collision changes the cue-ball path before the chart’s starting leg, you cannot simply insert the original cue-ball location into the rail-only calculation.
Compare two candidates before committing
For each candidate, name the first target, the intended cushion sequence and where a moving object ball could create a kiss. Reject a route whose first leg is obstructed, even if its arithmetic looks easy.
Next ask which input you can reproduce. A clear contact at moderate speed may suit you better than a very thin contact with extreme spin; this is a choice to test in that position, not a universal ranking of shots. Change aim, speed or spin one at a time when comparing.
Measure where your prediction first fails
Record the predicted first contact, actual first contact, third-cushion arrival and final carom separately. If the first contact differs, correct alignment or thickness before compensating at the final rail. If it matches but the later path shifts, compare speed, spin and cushion response.
In 3ball, save the position and use replay for the comparison. A computed path is a model result; use real-table repetitions to establish your own reliable reference. Keep successful and unsuccessful attempts so that one lucky point does not become a rule.