Pip Counting

Naccel 2—aN ACCELerated Pipcount
Part 1:  Introduction
Nack Ballard
January 2010
Naccel is an advanced system of pip counting first described by Nack Ballard in the September
2001 edition of Backgammon Today.  In 2010, Nack wrote a series of posts on the BGOnline Forum
describing a revised version of Naccel called Naccel 2.  These articles are taken from those posts.

Welcome to the renovated series of Naccel 2 posts. The diagrams are Naccel numbered, which by itself is a big improvement. Further, as a consequence, I have been able to improve the textual explanations as well.

This renovation would not have been possible without Matt Ryder's enthusiasm and html expertise. Before reading on, you might want to take a minute to check out Matt's Naccel diagram FAQ.

This Naccel 2 post #1 is in response to Lucky Jim's post, under an old "Kangaroo Count" thread and repeated below.

I have come across a pip-counting approach which Nack wrote about sometime ago—this looks very interesting to me. Click here:  aN ACCELerated Pipcount.

I wonder if Nack could let me know if he still uses this approach and if he would still advocate it?

Yes, I certainly do advocate it. I counted fastest when I was using Naccel.

Many years ago, I started experimenting with other pipcount systems (over thirty), counting pips various ways to relieve boredom while waiting for my opponents to move. (Hopefully clocks will put this problem behind us soon.) I skip around with counting systems now, as the mood strikes me.

I can explain Naccel much more simply than I did in my article that appeared in the quarterly magazine Backgammon Today (Sep., 2001). Indeed the approach is so modernized that I've adopted a suggestion made a few months ago (I forgot by whom) to call it "Naccel 2."


There are four Super-points, or "Supers," in Naccel, numbered 0, 1, 2 and 3 in black below, which also double as the Naccel 0pt, 6pt, 12pt and 18pt, as you will be able to deduce if you examine the sequence of white Naccel point-numbers labeling the diagrams.

If you are familiar with the traditional numbering system, you will also recognize the four Supers as the traditional 6pt, 12pt, 18pt and 24pt, respectively. Naccel point numbers are 6 smaller than traditional point numbers all the way around the board, as illustrated.

Hereafter, I will shorten the word "traditional" to "trad."

In the diagram below, I've placed a Blue checker on each of the Supers.

1O ' ' ' ' '1O ' ' ' ' '

 ' ' ' ' '1O ' ' ' ' '1O

The four Super-points

For counting purposes, you can, and should, ignore the checkers on the 0pt (trad 6pt). They count zero. The other three Supers can be counted just like the lower three points in a bearoff.

To get a feel for how easy it is, I've changed the point-numbering to trad(itional) just for this one diagram:

 ' ' ' ' ' ' ' ' ' ' ' '

2O1O2O ' ' ' ' ' ' ' ' '

Simple traditional bearoff

Using trad pipcount, I'll bet you can count this bearoff position quickly. There are two checkers on the 1-point (=2), one on the 2-point (=2), and two on the 3-point (=6), for a total of 10 pips.

This same trivial method used to count the 1-, 2- and 3-points in trad can be used to count the 1-, 2- and 3- Supers (Super-points) in Naccel. This is illustrated in the diagram below.

2O ' ' ' ' '1O ' ' ' ' '

 ' ' ' ' 'aO ' ' ' ' '2O

Count as you did before

And here we are. There are two checkers on Super1 (=2), one on Super2 (=2), and two on Super3 (=6), for a total of 10 super-pips, or more commonly "10 supes," or sometimes "10s" (pronounced "ten es"), or simply "10."

Note that you ignore the checkers on Super0 (trad 6pt) in exactly the same way you ignored the checkers in the bear-off tray in the previous diagram.

If you're not sure how the count of 10 was arrived at, or how the counting is similar to the traditional bearoff count of 10 pips in the previous diagram, please review.


Now that you know where the Supers are and how they are counted, I'll begin to demonstrate the joys of the focal point that you have until now known only as the 6pt (six-point). This is the center of the Naccel universe, and it is both Super0, or "S0," and the Naccel 0pt, or "n0." If you take up Naccel, you'll never have to count the checkers on the trad 6pt (or "t6") again.

Let's have a look at that beautiful beast, in context.

 ' ' ' ' ' ' ' ' ' ' ' '

 ' ' '2O '4O '2O ' ' ' '

Count of zero

This is a common near-side formation that arises after an opening 42 is played. The stack of four checkers on the Naccel 0pt, n0 (trad 6pt, t6), count zero—they are invisible (or soon will be to your trained eye).

The two-checker point on the left (trad 4pt, but −2pt in Naccel) and the two-checker point on the right (trad 8pt, but the 2pt in Naccel) are equidistant from the (0-count) stack in the middle. They cancel each other out, thereby also yielding a count of zero. When you get used to seeing this formation (and many others like it), it will, in its entirety, vanish into thin air.

Now let's be bold and tackle a full fifteen checker position:

1O ' ' ' ' '2O ' ' ' ' '

 ' ' '2O2O4O2O2O ' ' ' '

Near side goes POOF

Here, the four checkers on the 0pt are invisible, and ... you guessed it: by cancellation, the four points reflected around the 0pt are also invisible. The entire near side goes POOF!

All that needs to be counted in this position are the three checkers on the far side of the board. The two checkers on S2 (Super2) count 2 × 2 = 4, and the one checker on S3 counts 3, for a total of 7. That is Blue's entire count.

"But 7 doesn't mean anything to me."

It does when you compare it to your opponent's similarly small count (and if you want to apply a race formula, Naccel has one). But we're getting ahead of ourselves. For now, do it the "hard" way: multiply by 6 and add 90—which in this case comes to 132.

That's enough for now. If this subject sparks enough reader interest, I'll follow up with post #2. Perhaps it would be most effective if someone interested in Naccel sends me a full board position (one s/he found difficult to count, or not, whatever), and I'll develop my explanations around that. In this way, readers can get a glimpse of the lightning counts they can ultimately achieve should they want to pursue Naccel 2 further.

Go on to Part 2.

Nack Ballard is a top international backgammon player.  He is a coauthor of Backgammon
and the inventor of Nackgammon and Nactation.  His website is www.nackbg.com.

Naccel 2 Series
Part 1: Introduction
  Supers • Poofs
Part 2: Symmetry
Six-Stacks • Six-Symmetry
Part 3: Mirrors and Triplets
Six-Syms • Mirrors • Triplets • Review • Tandems
Part 4: Reflections, Zags, and Wedges
Far-Side Reflections • Zag Mirrors • Wedges • Triplets • Pairs • Squad Poofs
Part 5: Primes and Hopping
Six-Primes • Hopping • Counting Habits
Part 6: Midpoint Combinations
Blocks • Zig Mirrors • Diag Mirrors • Diag Zig Mirrors • Midpoofs • Midgold • Midblock • Problem
Part 7: Diags and Mirrors
Hopping • Blot Diags • Truck • Mirror
Part 8: Combined Counts
Combined Counts • Midblot Formations • Problem • Zigging and Zagging
Part 9: Squad Variants
Pair • Split • Wide • Triplet • Layer • Wedge • Block • Triangle • Sock • Squad Poofs • Problem 1 • Problem 2
Part 10: Leftover Counts
Leftover Counts • Tweensyms • Midpoint Leftover Counts • Squad Poofs • Problem 1 • Nack 57 • Problem 2 • Problem 3
Part 11: Midblot Refinement
Midblot Counts • Revs • Leftover Counts • Problem 1 • Problem 2
Part 12: Motion Poofs
Chairs • Shift Poofs • Motion • Problem 1 • Problem 2 • Nack 57 • Handy Count

See: Other articles on pip counting
Other articles by Nack Ballard
Return to:  Backgammon Galore