System 4 (the gap method)
This system, based on distance, gives the arrival point of a shot played off one cushion, with no side spin. It gets its name from a simple rule: the total of gap + carry-over is always 4.
When to use it?
System 4 is used when you want to make your point by sending the ball off one cushion and back onto ball 3, after hitting ball 2 with a natural shot. It's especially useful when ball 3 isn't playable directly (it's on the other side, or the direct angle doesn't work): instead of guessing the arrival, you measure the gap and apply the rule of 4. Play it with no side spin, as a regular natural shot.
What the system gives you
A precision that changes everything: System 4 doesn't tell you where to aim. It tells you where your ball 1 is going to arrive on a shot played off one cushion, with no side spin. You start from the balls' position, and you come out with an arrival diamond.
1. The gap, between the two cushions
Run the cue between balls 1 and 2, and extend that line to both cushions. The gap is the number of diamonds separating the two points where the line reaches the cushions.
The blue line runs through the center of balls 1 and 2 and reaches both long cushions. We carry the top exit point down onto the bottom cushion: three diamonds between the two, so the gap is 3. The white line, meanwhile, is ball 1's actual path — it is played at half-ball, so it doesn't follow the blue line.
2. The carry-over: 4 − gap
A subtraction, always the same one:
carry-over = 4 − gap
The result can be negative, and that's normal: its sign is what gives the counting direction in the next step.
3. Carrying over from the right reference point
This is where the reference point changes depending on the measured gap:
- Gap under 0.5 diamond (the balls almost facing each other): count from the point where your ball 1 is going to hit the cushion after its contact with ball 2.
- Gap of 0.5 diamond or more (the most common case): count from the diamond directly above ball 2, on the long cushion opposite — not from the point where ball 1 eventually hits the cushion.
From this reference point, count the carry-over:
- positive carry-over → you count to the left;
- negative carry-over → you count to the right.
The number you get is the diamond on the bottom cushion that your ball 1 is heading toward. That's the arrival the system predicts.
Same position, gap 3: above the 0.5 threshold, so the red reference point is not ball 1's actual impact point, it's the diamond directly above ball 2. Carry-over +1 → one diamond to the left → ball 1 heads toward this yellow reference on the bottom cushion.
The calculation in 4 steps — gap under 0.5 (click)
Step 1. The blue line runs through the center of balls 1 and 2, extended to both long cushions.
Step 2. The gap is the number of diamonds between the two exit points. Here, they land in exactly the same spot: gap = 0, the clearest case of this mode.
Step 3. Natural shot, at half-ball. Ball 2 leaves along the line of centers. The red point, meanwhile, is the carry-over reference: here the gap (0) is under 0.5, so it's the point where ball 1 actually hits the cushion after its contact with ball 2 — not the diamond above ball 2.
Step 4. Carry-over = 4 − 0 = +4: four diamonds to the left from this reference point. Ball 1 heads toward this diamond on the bottom cushion.
The calculation in 4 steps — gap of 0.5 or more (click)
Step 1. The blue line runs through the center of balls 1 and 2, extended to both long cushions.
Step 2. The gap is the number of diamonds between the two exit points: here 2 diamonds.
Step 3. Natural shot, at half-ball. Ball 2 leaves along the line of centers. The red point, meanwhile, is the carry-over reference: here the gap (2) is ≥ 0.5, so it's the diamond right above ball 2, on the cushion opposite — not ball 1's actual impact point.
Step 4. Carry-over = 4 − 2 = +2: two diamonds to the left from this reference point. Ball 1 heads toward this diamond on the bottom cushion.
The 4 steps in detail
1. Run the cue between the balls
Place the cue between ball 1 and ball 2, and extend that line to both cushions. These two exit points are what serve as reference points — not the actual path your ball will take, which will be quite different after the collision.
2. Count the gap between the cushions
The gap is the number of diamonds between the two points where your line touches the cushions. Carry one of the two over to the opposite cushion if that helps you count.
3. Carry over 4 − gap from the right reference point
Calculate 4 − gap. The reference point to count from depends on the gap: below 0.5, it's the point where your ball 1 hits the cushion after its contact with ball 2; from 0.5 up, it's the diamond directly above ball 2, on the cushion opposite. From that reference point, count the carry-over: to the left if the carry-over is positive, to the right if it's negative. The number you get is the diamond on the bottom cushion that your ball 1 is heading toward.
| Measured gap | Carry-over (4 − gap) | Counting direction |
|---|---|---|
| 1 diamond | +3 | 3 diamonds to the left |
| 2 diamonds | +2 | 2 diamonds to the left |
| 3 diamonds | +1 | 1 diamond to the left |
| 4 diamonds | 0 | the arrival is the impact point itself |
| 5 diamonds | −1 | 1 diamond to the right |
| 6 diamonds | −2 | 2 diamonds to the right |
| 7 diamonds and above | −3 and beyond | the arrival falls off the cushion: no usable reference left |
And beyond a gap of 4? The rule doesn't change one bit: you always do 4 − gap. The result simply turns negative, and a negative carry-over is counted to the right instead of to the left. Gap 5 → carry-over −1: ball 1 heads toward a diamond one further than the reference. Gap 6 → carry-over −2: two diamonds further, and so on.
This isn't an exception, it's the logical continuation of the same calculation. Gap 4 is the pivot point of this flip: at 4, the carry-over is 0, so the arrival coincides with the reference point itself — it's the easiest case to check at the table.
Past gap 6, the carry-over pushes the arrival beyond the last diamond: you'd need balls almost lined up on the diagonal to get there, and the system no longer gives a usable reference. In practice, the useful cases run from 1 to 6.
4. Place ball 3, and correct with side spin
The three previous steps gave you an arrival diamond, and with it the path your ball 1 is going to take.
- Is ball 3 on that path? You've got it: play your natural shot with no side spin, and the point falls.
- Is it off to the side? Count the gap, in diamonds, between the announced arrival and ball 3. Side spin is what will make up the difference.
Positive carry-over: 1 tip of side spin = 1 diamond of offset
Negative carry-over: 1 tip of side spin = ½ diamond of offset
The conversion depends on the sign of the carry-over calculated in step 3 — not on the direction ball 3 is offset. If the carry-over was positive (gap of 1 to 3), one tip shifts it by a full diamond, and that fraction scales: two diamonds call for 2 tips, a diamond and a half calls for 1.5 tips. If the carry-over was negative (gap of 5 or more), one tip only shifts it by a half diamond — you need twice as much for the same shift. The side to apply spin on is whichever shifts it in the right direction — normal side spin on one side, reverse side spin on the other.
| Ball 3 is… | Positive carry-over | Negative carry-over |
|---|---|---|
| on the announced arrival | nothing — no side spin | nothing — no side spin |
| 1 diamond off | 1 tip, on the side that catches up | 2 tips, on the side that catches up |
| 1 diamond and a half | 1.5 tips | 3 tips |
| 2 diamonds | 2 tips | 4 tips |
This is what makes the system usable in a match: you don't need the position to fall exactly right. You calculate the arrival with no side spin, you look at how far off you are, you check whether the carry-over from step 3 was positive or negative, and you convert the remaining gap into tips according to that sign.
This conversion gives you the principle. Handling the side spin itself — how much you really need depending on distance, power and the table's condition — will be the subject of a dedicated page.
⎙ Printable A4 sheet The table and two examples on one page, to keep near the table.
Six examples, from gap 1 to gap 6
Six positions, one per gap value. All have a gap of at least 1 diamond — well above the 0.5 threshold — so all six use the new reference point: the diamond above ball 2, not ball 1's actual impact point. The reference moves with ball 2 from one diagram to the next: it's no longer fixed the way it was with the old calculation.
In each drawing, the blue dotted line is the line run through the centers of balls 1 and 2, the one that gives the gap; the yellow dotted line is ball 2's starting point; the red point is the carry-over reference, and the white line connects ball 1 to the reference, then the reference to the arrival — a construction that shows where to count from, not the actual ball-by-ball path along the cushion.
Gap 1 diamond → carry-over +3
The balls are almost on the axis of the short cushions, and the 1-2 line is nearly perpendicular to the long cushions. Carry-over +3: three diamonds to the left from the reference. This is the gap where the old and new reference points are furthest apart from each other.
Gap 2 diamonds → carry-over +2
One notch more open. The reference has also moved — it follows ball 2, not a fixed point. Carry-over +2: two diamonds to the left from this reference.
Gap 3 diamonds → carry-over +1
One more notch. Carry-over +1: just a single diamond to count to the left from the reference. This is the gap from which the old and new reference points start noticeably converging.
Gap 4 diamonds → carry-over 0
Carry-over 0: the arrival coincides with the reference point itself, here the diamond above ball 2. This is the easiest case to check at the table — just measure directly where the ball comes back.
Gap 5 diamonds → carry-over −1
The carry-over turns negative and the counting direction flips: one diamond to the right from the reference (the diamond above ball 2), not from ball 1's actual impact point.
Gap 6 diamonds → carry-over −2
Two more notches out: carry-over −2, two diamonds to the right from the reference, all the way to the last playable diamond on that side.
📐 These 6 diagrams are built to stay consistent with the calculation: the white line leads exactly to the announced diamond. They show the trend — the smaller the gap, the bigger the adjustment, and it flips direction at gap 4. On a real table, the cushion and natural side spin shift the return a little: check it in practice.
Practicing System 4
A position drawn at random, to read from start to finish: the gap between the blue line's two exits, the carry-over, then the arrival diamond. Chain them together — that's how the calculation becomes automatic at the table.
The exercise deliberately stops at the arrival with no side spin. Choosing the side spin needs a method of its own, which will have its own page: the conversion presented above (1 diamond per tip if the carry-over is positive, half a diamond if it's negative) explains the principle, it isn't enough to practice it.
Carry-over calculator
—