TL;DR: The Diamond System is a numerical method for calculating three-cushion billiards routes using the diamond markings on the rails. The simplest formula: starting diamond + target diamond = first-cushion contact diamond. Once you've memorised the basic count, you can solve 60–70% of routine three-cushion positions in 5 seconds without trial-and-error.
Step 1: Counting diamonds
Each long rail has 7 diamond markers (some tables have 5; count yours). Number them 1, 2, 3, 4, 5, 6, 7 starting from your end.
For the first cushion contact on a long rail, count both rails as a continuous number line: short rail diamonds are valued differently. The standard Korean system valuation:
Long rail (your side): 1 2 3 4 5 6 7
Short rail far end: 8 9 10
Long rail (opposite): 11 12 13 14 15 16 17
Short rail near end: 18 19 20
Long rail (back to you): 21 22 23 24 25 26 27These numbers represent positions a ball at the head spot would travel to with neutral english.
Step 2: Finding your starting position
Locate where your cue ball will exit the first cushion. A cue ball at "diamond 5" on the long rail equals 5.
Step 3: Identifying the target
Find the position on the third cushion where your cue ball needs to arrive to complete the carom on the second object ball. This is your arrival number.
Step 4: The formula
first cushion contact = starting position − arrival position
If starting = 5 and arrival = 2, then contact = 5 − 2 = 3 (i.e., you aim at diamond 3 on the first cushion).
Visualisation
Open the position in 3ball — the simulator overlays the diamond numbers and the calculated route in real time.
Open 3ball →Step 5: Real-world adjustments
The math is exact in a vacuum. Real tables shift it:
- Slow stroke: add +1 (use Plus 2 system: add +2 for very slow)
- Heavy running english: subtract −1
- Heavy reverse english: add +2
- Heated table: subtract −0.5 (heating speeds the cloth)
- Higher humidity: add +0.5
Pros internalise these as "feel" but new players benefit from a checklist taped to the wall during practice.
Step 6: Common mistakes
- Counting the wrong rail. The first-cushion contact diamond must be on the long rail your cue ball is heading toward, not the rail it just left.
- Forgetting english. A textbook diamond solution with neutral english fails on tables with sticky cushions; add ½ tip running english as default.
- Pace mismatch. Diamond predictions assume medium pace; firmer strokes "open up" cushion angles by ~10%.
- Half-ball calculation. The diamond system assumes a full-ball contact on the first object ball; thin cuts deviate the cue-ball trajectory.
Step 7: Plus 2, Korean, half-ball variants
Plus 2 system
Adds a fixed +2 diamonds to the contact-cushion calculation when you intentionally hit the cue ball softly. Designed by European 3-cushion players in the 1970s. Original: contact = start − arrival. Plus 2: contact = (start − arrival) + 2.
Korean (5-and-half) system
Developed by Korean pros in the 1980s as a Diamond System variant. Cushion values are divided by 5 for higher precision. Best in fast tempo play; learning curve is steeper than European Plus 2 but yields tighter control on system shots. Cho Jae-Ho and Kang Dong-Koong both rely on it primarily.
Half-ball reference method
Aim at the half-ball point — the cue tip strikes the side of the object ball such that the line through the contact point passes through the centre of the cue ball when extended. This produces a known cushion-bounce angle (~30°), used as a calibration reference for system-shot estimation.
Step 8: When to ignore the system
System-only play caps at ~1.2 average. The top players blend system with intuition built from thousands of hours. Use the system as a sanity check, not a crutch.
Cases where intuition wins:
- Very tight angles (< 15°) where small system errors compound
- Positions with kiss potential — the system doesn't predict mid-flight collisions
- Massé and jump shots (the system assumes flat-table behaviour)
Practise in 3ball: the simulator overlays diamond numbers as you set up shots. Toggle the Diamond Helper panel to see real-time predictions, then compare with the AI Solver's full simulation.