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Nactation and Zare's position

Posted By: Nack Ballard
Date: Friday, 2 December 2011, at 12:43 a.m.

In Response To: Nactation: S/Z rehash, etc. (Timothy Chow)

Good backgammon strategy is complicated, and if you build it into your notation, then your notation is inevitably going to be complicated.

Granted, to an extent. There is a tradeoff between (a) the learning curve and (b) ease of use once you're over the hump.

What I claim to have seen clearly is that this kind of philosophy is inevitably going to lead to the equivalent of spaghetti code if you carry out consistently to the bitter end, and come up with a way to nactate all 2226 legal ways to play snake eyes in Zare's position.

Indeed, I can already -- the current system can handle it! However, I wouldn't bother with such a tedious procedure, nor would I suggest anyone else bother. The relatively recent and expanded goal of Nactation is only to be able to nactate (or interpret, or record, or electronically store, or display compactly, whatever) entire games/matches that are played in practice. Zare's position (diagrammed below) is a puzzle/contest contrivance.


1O1O1X1O1O1X1O1O1X1O1O1X

1X1X1O1X1O1O1X1O1O1X1O1O

Zare's max-move position


It is hard to imagine that a position with remotely this many legal plays would arise in practice, but okay, we'll suppose it did. As any other play is at least a whopper, the only move I should need to nactate is 8/7*/6 5/4*/3, which is I. That was way too easy. Next.

It is no accident that the best play produces the top member of its family (the underlined I family), even in a position of extreme fabrication and 2226 legal choices. The carefully designed hit/most/6 rule makes properly executed Nactation user-friendly, because one seldom needs to dig through and account for random plays only to end up using italics or worse for the strong/obvious play actually made.

For someone inexperienced in Nactation, a natural inquiry might be: Wouldn't it be easier if, say, the only rule used to govern families is that the play with the closest checker destination to the 6pt is highest ranked? Easier to learn, yes, but much harder to implement in practice (the part you have to do over and over and over).

For a concrete example, let's contemplate the much more normal type of position below:


2O2X '2X2O4X2X2X2X ' ' '

 '2O2O2O2O3O ' ' ' ' ' '

How do you nactate 6/2?


Blue has 11 to play. Now, how do we communicate 6/2, the clearly best play, to a computer program?

All four aces must be played in the inner board, so we know the move will be nactated with a member of the "I" (Inside) family. However, if the only rule we apply is closest-destination-to-6pt, then 6/5(3) 5/4 is the highest-ranked play. We then have to carefully figure out and count 19 more double-ace plays before we get to 6/2, which is the 20th-ranked play; what a nightmare!

By contrast, with the fully equipped hit/most/6 rule, we apply the most-points convention (so don't break any points) and the first part of the 6pt convention (keep owned points closest to the 6pt). It is trivial to see that 6/2 is nactated "I" -- it sits squarely atop the "I" family.

Nack

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