Walk into any Vietnamese billiard hall and you will hear coaches calling out numbers in a pattern: năm mươi trừ ba mươi bằng hai mươi — fifty minus thirty equals twenty. What looks like arithmetic is actually a complete aiming framework called bộ nút số (literally the number-button set). It assigns a numeric value to every diamond position on the table and gives each shot a three-number identity. Once you understand the logic, you can read Vietnamese coaching videos, practice with Vietnamese partners, and add a proven regional system to your repertoire.
What Is Bộ Nút Số?
The term breaks into three words: bộ (set or system), nút (button or dot — the inlaid diamonds on the rail), and số (number). Together, bộ nút số means the numbered-diamond system. Vietnamese players use it as the umbrella name for any approach that assigns fixed values to rail positions and derives a shot formula from those values.
The dominant variant is called bộ 50 (the fifty-set), named after its reference anchor: the corner of the table closest to the player, called góc dậu, is assigned the value 50. All other diamond positions derive their numbers from that anchor, running outward in both directions along each rail. The word dậu carries a connotation of readiness or alertness — the corner where you plant yourself to play — and it anchors the whole counting grid.
This is the Vietnamese equivalent of what English-speaking players call the Diamond System. The underlying geometry is identical — proportional rail positions, angle of reflection physics — but the labeling convention, the reference corner, and the spin vocabulary differ. Understanding both lets you translate freely between coaching traditions.
NGẮN-DÀI-NGẮN: The Short-Long-Short Framework
Before you touch a number, Vietnamese coaches insist you identify the cushion sequence your shot will travel. The two primary sequences are:
- NGẮN-DÀI-NGẮN (short-long-short, often abbreviated N-D-N): the cue ball strikes a short rail first, crosses to a long rail, then arrives at the opposite short rail on its way to the target ball.
- DÀI-NGẮN-DÀI (long-short-long, abbreviated D-N-D): the cue ball strikes a long rail first, bounces to a short rail, then continues to the far long rail.
Vietnamese teachers draw this distinction before introducing any number because the same diamond position carries a different value depending on which type of rail it sits on, and the formula changes between the two sequences. The words themselves are descriptive: ngắn means short, dài means long. Saying NGẮN-DÀI-NGẮN out loud as you plan the shot is a mnemonic that locks in the path.
The NGẮN-DÀI-NGẮN path is particularly common when the cue ball sits near a short rail — a situation called thế bi góc (corner position) or thế bi sườn (side position). It is the bread-and-butter route for many Vietnamese-style scoring shots and the one most thoroughly covered by the bộ nút số literature.
How the Numbers Are Assigned
Each rail type uses a different scale, which is the key insight newcomers often miss. Here is the standard bộ 50 grid:
Short rails (băng ngắn)
The short rail where the cue ball starts (first contact) is counted in units of 10, running from 40 at the near long-rail edge down to 0 at the far corner. There are four diamonds on a standard short rail, so the values are 40, 30, 20, 10, and 0 (corner). The góc dậu reference corner sits at 0 on the departure rail.
The target short rail (third contact, where the ball should arrive) uses a compressed scale: units of 5, running from 20 down to 0. Each diamond on the arrival short rail is worth 5 points rather than 10. This compression reflects the physical reality that a ball arriving at a short rail after two prior reflections spans a shorter range of possible landing zones.
Long rails (băng dài)
The long rail (second contact, the middle of the N-D-N path) is counted in units of 2, from roughly 0 to 8 across four diamonds. In the bộ 50 context for the D-N-D path, the long rail where the cue ball departs can scale from 0 to 100 with the góc dậu corner fixed at 50.
The master formula
For the standard bộ 50 on a D-N-D path:
Điểm trúng = Điểm đầu − Điểm đánh
(Arrival point = Departure point − Aim point)
Where điểm đầu is the cue ball's starting position value, điểm đánh is the value of the first-rail contact point you choose, and điểm trúng is the value of the diamond where the cue ball will land after completing the path. If you want the ball to arrive at diamond 30, and your cue ball starts at 70, you aim at the long-rail point valued at 40. The subtraction is the shot.
For NGẮN-DÀI-NGẮN paths, the formula adjusts to account for the different rail-scale ratios, and a multiplier of 1.5 enters when the cue ball starts on the short rail rather than the long rail. Vietnamese coaches teach this as a separate set of reference tables rather than a single equation, because the scale mismatch makes a universal formula unwieldy in practice.
Want to practice your angles on a virtual table before drilling them in person? The diamond calculator lets you map aim points using the Corner-5 framework — a useful cross-reference while you learn the Vietnamese number grid.
Bộ Nút vs. Western Diamond Systems
If you already know the Plus-2 or Corner-5 systems taught in European and American coaching materials, you are closer to bộ nút than you think. The physics — proportional diamonds, specular reflection modulated by spin and speed — is universal. The differences are notational and pedagogical.
| Feature | Bộ Nút Số (Vietnamese) | Plus-2 / Corner-5 (Western) |
|---|---|---|
| Reference anchor | Góc dậu = 50 | Corner = 5 (Corner-5) or variable |
| Short-rail scale | 40-0 departure, 20-0 arrival | 0-4 diamonds (counted by position) |
| Cushion sequence name | N-D-N / D-N-D (Vietnamese) | Short-long-short / long-short-long |
| Spin labeling | Ép phê (1–4 levels) | English (tip fractions or clock positions) |
| Primary formula | Arrival = Departure − Aim | Aim = Origin − Destination (Plus-2 adds +2) |
The deeper coverage on how to read rail diamonds in either tradition is in our guide to reading diamonds. For a direct look at the Corner-5 calculation logic that maps most naturally onto bộ 50 arithmetic, see the Corner-5 system explained.
Ép Phê and Góc Dậu in Practice
Ép phê (literally press-effect, analogous to English or side spin) is the spin vocabulary of Vietnamese billiards. Rather than clock positions or tip fractions, Vietnamese coaches rate spin in integer levels:
- Không ép phê (zero spin, center ball) — the baseline for learning any new number set. The bộ 0-3-6 system, a NGẮN-DÀI-NGẮN variant, is explicitly designed for không ép phê play, making it ideal for beginners who want to isolate path geometry before adding spin.
- 1–2 ép phê — light running or check side, used on standard distance shots to keep the path on the calculated line.
- 3–4 ép phê — heavy side spin for extended routes, reverse angles, or correction when the cue ball sits far from the góc dậu reference corner.
The góc dậu corner (value 50 in bộ 50) is not merely a number — it is a physical anchor. When your cue ball sits near the góc dậu, the bộ 50 numbers are most accurate and require the least correction factor (sai số). As the cue ball moves away from that corner toward values above 60, experienced players add a positive correction of +3 to +13 to compensate for trajectory drift. Below 50, a negative correction of −1 to −6 applies. Vietnamese coaching materials publish these correction tables as part of the system, not as exceptions to it.
The bộ 0-3-6 sub-system names itself after the three diamond values on the target short rail that correspond to the most common NGẮN-DÀI-NGẮN arrivals when playing without spin: positions 0, 3, and 6 (in a compressed 0-to-6 scale). Coaches use this subset as a teaching scaffold — master arrivals at 0, 3, and 6 first, then interpolate the intermediate positions.
Understanding these systems also deepens your grasp of the broader aiming landscape. Our overview of three-cushion aiming systems places bộ nút alongside the Turkish Diamond and Korean 5-and-half systems so you can see where each excels.
Learning Drill: The N-D-N Reference Map
Vietnamese coaches typically introduce bộ nút through a fixed-position drill sequence rather than through formula memorization. Here is a condensed version you can use at any table:
- Set the cue ball at góc dậu (departure corner, value 0 on the short rail). Play a straight N-D-N shot without spin — center ball only. Observe where the ball arrives on the opposite short rail. That arrival point is your baseline value 0.
- Move the cue ball one diamond along the short rail (to value 10). Play the same center-ball N-D-N path. Note the new arrival. The arrival should shift by approximately one unit on the compressed arrival scale (about 5 points).
- Continue through all four departure diamonds (10, 20, 30, 40). After four shots you have a personal reference map of N-D-N arrivals for your specific table. Tables vary — this step calibrates the numbers to your cloth and cushion condition.
- Introduce ép phê. Repeat the sequence with 1 ép phê (light side spin). Notice how each arrival shifts. Repeat with 2 ép phê. You are building a spin-correction sense rather than memorizing tables.
- Play the bộ 0-3-6 reference shots. Aim to arrive exactly at the 0-position (corner), the 3-position (mid-rail), and the 6-position (near-rail diamond) of the target short rail without spin. These three targets cover the most common scoring opportunities in the N-D-N path and are the checkpoints Vietnamese coaches use to verify a student has internalized the system.
Once you can place the ball reliably at all three reference arrivals, the arithmetic of bộ nút số becomes physical intuition rather than mental calculation. That is the goal: not to compute shots at the table, but to have pre-computed reference images that let you recognize the correct aim point immediately.
Practice these paths in the simulator at 3ball.app/play — load the NGẮN-DÀI-NGẮN position set from the training library to drill the exact departure diamonds described above, then bring the numbers to the physical table.