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Naccel 2 -- post #1

Posted By: Nack Ballard
Date: Friday, 8 January 2010, at 7:46 a.m.

In Response To: Kangaroo count - Quick question for Nack (Lucky Jim)

This is in response to Lucky Jim's post, under the old "Kangaroo Count" thread and repeated below.

Lucky Jim said:

I have come across an approach which Nack wrote about sometime ago - this looks very interesting to me.

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 by someone (forgot who) to call it "Naccel 2."

It will be tough to do Naccel 2 justice without properly labeled diagrams, but I'll make a go of it.


There are four Super-points, or "Supers," in Naccel, numbered 0, 1, 2 and 3. These are the traditional 6pt, 12pt, 18pt and 24pt, respectively. In the diagram below, I've placed a Blue checker on each of the Supers.


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

 ' ' ' ' '1O ' ' ' ' '1O
The four Super-points

You can, and should, always ignore the checkers on the 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 ...


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

2O1O2O ' ' ' ' ' ' ' ' '
Simple traditional bearoff

Using traditional 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 traditional notation 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 the 1-Super (2), one on the 2-Super (2), and two on the 3-Super (6), for a total of 10 super-pips, or "10 supes," or sometimes abbreviated "10s" (pronounced "ten es").

Note that you ignore the checkers on the 0-Super (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 explain the joys of the 6-point (as it is traditionally known). This is the center of the Naccel universe. It is the Naccel 0-super. It is also the Naccel 0-point, or "N0" (N zero). If you take up Naccel 2, you'll never have to count the checkers on the traditional 6pt again.

Let's have a look at that beautiful beast.


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

 ' ' '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 N0 (trad. 6-point) count ZERO -- they are invisible (or soon will be to your trained eye).

The two-checker point on the left (trad. 4pt) and the two-checker point on the right (trad. 8pt) are equidistant from N0. They cancel each other out. When you get used to seeing this formation (and many others like it), it will 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 N0 are invisible, and... you guessed it: the four points reflected around N0 are also invisible. The entire near side goes POOF!

All that needs to be counted in this position are the three checkers on the other side of the board. The two checkers on S2 (i.e., the 2-Super, the trad. 18pt) count 2 x 2 = 4, and the one checker on S3 counts 3, for a total of 7. That is your 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. If not, we'll put this to rest at post #1, no problem.

Perhaps it would be most effective if someone (only someone actually interested in Naccel, please!) sends me a full board position (perhaps one 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.

Nack

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