3.2 Diamond Midpoint Method

What the diamonds are for

The diamond markers along the rails are not decoration — they're a coordinate system for banks.

The Diamond Midpoint Method (a.k.a. the "addition system") uses simple cushion arithmetic to find the exact aim point on the opposite rail. Faster and more precise than mental mirroring.

Note on terminology: there are several diamond systems with confusable names — Plus System is a 3-cushion carom system (Walter Lindrum's). Corner-5 and Hopkins systems are 3-rail kick systems. This lesson covers the simplest case: 1-rail banks via midpoint arithmetic.

⏱ ~14 min · 4 drills · 1-rail banks become arithmetic

Diamond numbering

A standard 9-ft pool table has three diamonds + a side pocket + three diamonds along each long rail — 9 reference points labeled 0-8 (corners and side pocket included). The short rails have three diamonds between corners — 5 reference points labeled 0-4.

• Long rail: 0 (left corner) → 4 (side pocket) → 8 (right corner)
• Short rail: 0 (one corner) → 4 (other corner)
• Each interval = 1 diamond unit (abstract, not cm)

You don't actually count to 8 in real shots — you use relative positions (how many diamonds apart).

• Long rail = 9 points (0-8); short rail = 5 points (0-4)
• Spacing = 1 diamond unit
• All math uses relative positions

The midpoint formula

For a 1-rail bank — your start position rebounds off one cushion, ends at the target position:

Aim at = (start position + target position) / 2

Worked example:

• Start position aligns with long rail "2"
• Target aligns with long rail "6"
• (2 + 6) / 2 = 4 → aim at the opposite long rail's "4" (the side pocket)

This is the algebraic form of incident=rebound — the cushion midpoint is the geometric reflection point.

Scope: 1-rail banks only. 2-rail and 3-rail kicks need different systems (Hopkins's Corner-5, Bob Jewett's plus-system for kicks).

• 1-rail aim = midpoint of (start + target)
• Algebraic form of the incident=rebound law
• Accurate for moderate speed + center hit only; multi-rail needs other systems

Mirror vs Diamond

In practice: rough-aim with the mirror, fine-tune with the midpoint formula.

Drills below. The diamonds can be visualized — you don't need to count them.