Three-cushion diamond systems
Every diamond system in 3C Arena, explained: what each one is for, its formula, how to read the numbers on the rails and how to play the shot. Practise any of them on a real-physics table, free in your browser.
Lessons
Coach-reviewed systems, with guided lessons, practice and scored challenges in the game.
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50 System
Aim = Start - Arrival + correctionRead a long-short-long route with the corner-50 scales.
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50 System · 4th Rail
Aim = Start - Arrival + correctionThe 50 System with the second ball waiting near the 4th rail: the cue ball takes three cushions and is met on its way to the fourth.
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50 System · 5th Rail
Aim = Start - Arrival + correctionThe 50 System with the second ball waiting near the 5th rail: the cue ball takes four cushions and is met on its way to the fifth.
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Short–Long–Short
Aim = Start - 1.5 x Arrival + table correctionTuzul without side spin.
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Short–Long–Long
Aim = Arrival - Start + table correctionPlus system: departure 2 to 5 on the long rail.
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Reverse System
Aim = Start + Arrival - Adjustment + table correctionCounter-English, long-long-short.
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Bank Long–Long–Short
Aim = Start + Finish + table correctionBank shot, no side spin: the cue ball takes the far long rail, the near long rail and then the short rail before either ball.
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Bank Long–Short–Long
Aim = Start − Finish + table correctionBank shot, no side spin: far long rail, short rail, then back to the near long rail before either ball.
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Bank Short–Long–Short
Aim = Start − Finish + table correctionBank shot, no side spin: the near short rail, the far long rail, then the other short rail before either ball.
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Distance Equals Aim
Aim = Finish − Start (distance) + table correctionBank shot off the short rail with running side: short rail, far long rail, then the near long rail before either ball.
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Long–Short–Long 024
Effect = Finish + Aim + Start − Space + table correctionSolved for side spin.
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Reverse Short–Long–Short
Effect = (Start + Aim + Finish) ÷ 5 + table correctionBank shot with reverse side, solved for side spin.
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Long–Long–Short (Effect)
Effect = Finish + Aim − Start + table correctionSolved for side spin.
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Original Position
Effect = 2 × (Start − Aim) − 1 + table correctionHalf-table return.
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Kobayashi
Effect = (Distance + 2) − Offset + table correctionThe KOBA "plus two" variant, as a video lesson teaches it: the side to play is the distance between the object balls, plus two, minus the cue ball's offset from the first one, all in long-rail diamonds.
System Library
Systems from published sources, checked in the game's physics but not reviewed by a coach.
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No Side · 1.5 Numbering
Aim = Start − Arrival + table correctionLong-short-long without side.
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Plus · Extended, No Side
Aim = Arrival − Start + table correctionThe Plus system played without side: high tip, level cue, soft stroke.
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Plus · Starts 20 to 60
Aim = Arrival − Start + table correctionThe Plus system on the source's scale: start on the long rail behind the cue ball, aim at the short rail, arrive back on the near long rail.
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Mirror · One-Cushion Kick
Aim = (Red out × Cue along + Cue out × Red along) ÷ (Cue out + Red out) + table correctionEqual distance: reflect the red in the cushion and aim where the line from the cue ball to that image crosses it.
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2/3 · Rescaled
Aim = Start − Arrival + table correctionThe Turkish 2/3 system in its rescaled form: long-short-long without side, the start 5 a diamond, the aim 10 and the arrival 7.5.
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Bernie · No Side
Aim = Start − Arrival + table correctionShort-long-short without side: start on the long rail, aim at the short rail from its middle, arrive on the far short rail.
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Maximum Plus
Aim = Start − Arrival + table correctionThree tips of running side into the far corner: start on the long rail near the corner, aim at the short rail just below the far corner, arrive back on the start rail.
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Conti · Long-Short-Long
Aim = Start − Arrival + table correctionLong-short-long with plenty of running side: start rail minus third rail gives the first rail.
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Sid · Two Banks
Aim = Start × Arrival + table correctionTwo cushions before the red: across the table to the short rail, back along the long rail, onto the red there.
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2/3 · Full Scale
Aim = Start − Arrival + table correctionLong-short-long without side, three tips of follow.
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Plus 2 · Starts 5 to 15
Aim = Arrival − Start + table correctionThe Plus system for starts below 20: one attack scale from the far corner, four tips of running side, a soft stroke.
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Plus 4 · Distance × 4
Aim = 4 × (Arrival − Start) + table correctionThe Plus system counted in diamonds: the distance along the near long rail from where the cue ball's line starts to where it must arrive, times four, is the attack on the short rail.
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Easy Seven
Aim = Start × Arrival + table correctionShort-long-short without side, worked by multiplying: the start on the long rail times the arrival on the far short rail gives the aim on the near short rail.
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Florida Backup
Aim = Start − K × Arrival + table correctionFour cushions before either ball: long, short, short, long.
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Double Rail · 17
Aim = 17 − (Start + Arrival) + table correctionMaximum side into the short rail by the corner, along the long rail and back to the same short rail: the double rail.
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Ball System
Thickness + Tips = Ball value + Arrival + table correctionSide-around, red first: the baseline the cue ball meets the red on, plus where it must reach the third cushion, is the total to play — thickness in eighths plus tips of side.