Diamond System Pool — One-Rail Bank Shot Drills
1-rail banks via cushion arithmetic
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.
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
| Method | Speed | Precision | Best for |
|---|---|---|---|
| Mental mirror | ★★★ | ★★ | Quick estimation, 1-rail |
| Diamond midpoint | ★★ | ★★★ | Precise 1-rail aim |
| Multi-rail systems | ★ | ★★★ | 2-3 rail kicks (out of scope) |
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.
Drill 1/4 · Mirror review
1-rail bank using the mirror method (no diamonds needed). Warmup from Lesson 3.1.
Drill 2/4 · Midpoint formula
1-rail bank using the midpoint formula: (start + target) / 2 = aim. Mentally label the start and target with diamond positions, then compute.
Drill 3/4 · Long-distance 1-rail
Long-distance 1-rail bank. Start and target are far apart — the midpoint formula still works. Soft speed + center hit.
Drill 4/4 · Open bank challenge
Pick your method: mirror or midpoint. Both can solve this — choose whichever feels faster.