Naccel 2 -- post #3
Posted By: Nack Ballard In Response To: Naccel 2 -- post #3 (Matt Ryder)
Date: Tuesday, 12 January 2010, at 5:44 p.m.
In Response To: Naccel 2 -- post #3 (Matt Ryder)
I remember the concept of 'squads' from the first iteration of Naccel. So far most of your lessons have centred around principles of symmetry and mirroring. Forgive me for pushing greedily ahead, but I for one am keen to learn these squads, as I find memorizing a set of reference patterns invaluable in improving my counting speed (it reduces all the frenetic mental shifting to a minimum). The more reference squads the better, I say.
My concern is that too much squadding will scare off Naccel learners. The board-symmetry counts are more important anyway. However, I'll give you a peek ahead if you're willing to set these up on a board:
Two basic squads have already shown up: the stack (six-stack) and the triplet (three-stack on an even-numbered point, formerly called duck). The other basic one is the "pair," which is  -- two checkers on the center point of a field (a field being any quadrant minus its Super).
The other single-squad patterns are the "block"  and the "sock" .
The triplet has two shift variants: the wedge  and the layer . And the pair has two variants: the split  and the wide . The block has one variant: the triangle .
The number of stack variants (in this case also called six-syms) depends on where the stack is in the field. If it's , there is no variant. When it is , the variants are the top hat , the three-prime , and odds . Note that the top hat is also a triplet + layer, the three-prime is also a double layer or a block + pair, and odds is also a pair + triangle.
Note, too, that all squads have a "partner," and the partner being applied depends upon which Super is closer. For example, the wedge is  counted one direction but  the other. (If distinguishing, call them the little wedge and the big wedge.) The symmetrical squads (pair, split, wide) self-partner.
(a) See how many shift variants (six-syms) you can find for the  stack;
(b) Identify for each which basic squads can be combined to achieve the same formation;
(c) For all the squads, list ways that shifting to the Supers (that flank a five-point field) can reduce the size of the squad or make it disappear;
(d) Count all formations forwards to S0 and backwards to S1; list the partner notations and counts for each.
(e) If you know the (global) count for a squad in one quadrant field, how can you most easily determine its count in another quadrant?
Report back your discoveries for (a), (b), (c), (d) and (e).
That should quench your thirst for a while :)
I'll just say for others reading, I don't recommend that you memorize squads beyond the very basic ones, but playing with them can be fun and will increase your aptitude for Naccel counting.
Is there any useful way to combine knowledge of traditional clusters (such as a closed board = 42 pips) with Naccel squads? Or are they mutually exclusive systems?
To convert known trad formation counts, you can divide by 6 and subtract the number of checkers in the formation. So, a closed board is 42/6 - 12 = -5 in Naccel. But it is easy to learn and remember that a closed board is -5, or to treat it as two six-syms of -4 and -1, or sum the end points for any six-prime -- in this case 0 and -5, so I don't recommend getting caught up in such conversions.
Your closed-board example does demonstrate one of the advantages of using a 6-based (or 3-based) system, though. Natural formations that arise due to board geometry are multiples of 6 pips (= 1 supe) and not multiples of 5 or 10 pips (unless they are also multiples of 30).
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