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Naccel race formula
Posted By: Nack Ballard In Response To: Naccel race formula (Andreas)
Date: Tuesday, 26 January 2010, at 2:37 a.m.
Exercise for me: Ballard/Grandell match in MBG.
I recommend that you practice your Naccel pipcounts by looking at positions in books that show pipcounts, if you have any. (Cover with your hands, then confirm by multiplying your Naccel count by 6 and adding 90.) Here is a short list of pipcount-display books:
Jerry Grandell, His most important matches (Ortega/Kleinman)
New Ideas in Backgammon (Woolsey/Heinrich)
Classic Backgammon Revisited (Bagai)
Backgammon Problems (Corbett)There may be others. There are exactly three errors in New Ideas...; see if you can find them. I don't know/remember about errors in the other books. If you don't have any of these, you can always use a bot or go to an online backgammon server and make use of the pipcount button.
Compared to traditional cluster counting the big POOF makes a great step forward for easier pipcounting.
Agreed. In my experience in experimentations, I have found cluster counting is faster if you change the 0pt to the 5pt (or even the 10pt). It can be further improved by creating Supers on the bearoff tray, 5pt, 10pt, 15pt, 20pt and roof, and counting by 5's (the superpips/supes), though at that point it has morphed into something else and I no longer call it "cluster counting." These six Supers come in three-vertically aligned pairs, so it actually has a visual advantage for straight mirrors (though other symmetries fall short of Naccel). Compared to Naccel, you have to shift and count a bit more in this decimal-catered version because the stack on t6 and starting back checkers aren't on Supers, and the midpoint is 2 ahead or 3 behind a Super (worst location).
In short, the 0pt on t5 (or t10) and integration of supes are definitely speed improvements over cluster counting. However, if one wishes to make such a leap, I think it makes more sense to learn Naccel and fully exploit board geometry.
In Naccel we get something like: Black: Nb/Cb; White: Nw/Cw for the super counts and the corrections.
I assume "b" and "w" are for blue/black and white. I suppose by "N" you mean something like Naccel supes and by "C" you mean Corrections. That's one way to count in Naccel -- working your way systematically around the board and keeping separate supe and baby-pip counts -- but it's a bit pedestrian. IMO, shifting to large-scale formations using board symmetries (aided by repeatable quadrant patterns) is considerably faster. If, OTOH, you were just speaking in abstract theory, then yes that's the general idea.
Nack wrote: "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."
Andreas: I hope I did not miss it here: The next step would be of course to omit the "hard way" over the calculation via the traditional pipcount and the use a traditional race formula for racing D/T decisions. ...and instead to use the Naccel count direct for the D/T decions.
So I would be happy to hear something about "Narde" (Nack's advanced racing double equation :)
If we use an acronym, I think I prefer "Nerf" (Naccel's efficient racing formula).
I was going to wait to impart the the Naccel race formula, but since you asked, the minimal pip lead needed to double is:
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If the leader's count is positive, divide by 2 and add 7.
If the leader's count is negative, add 8.Minimal redouble: Add 1 to the above double point.
Marginal pass: Add 4 to the double point.
-----------------------------------------------------------When I refer to the leader's count, I mean in supes. Always round fractional supes UP (meaning to the more positive or less negative integer).
Below are two examples. They assume a straight race, and the player on roll is listed first (he leads).
Example A: 3(1) to 4(4). [Difference of 9 pips.]
Round leader's 3(1) up to 4, div by 2 = 2, add 7 gives you a 9-pip minimal double point. The actual difference (between 3(1) and 4(4)) is 9 pips. So it's on the number -- a minimal double but 1 pip shy of a redouble.
Example B: -2(-1) to -1. [Difference of 7 pips.]
Round leader's -2(-1) up to -2, add 8 gives you a 6-pip minimal double point. The actual difference is 7, so that qualifies as a minimal redouble.
Traditional equivalents: Example A = 109 to 118. Example B = 77 to 84. Use whatever formula you use to determine cube action. Do you get the same answers?
In a computer crash years ago, I lost the notes to the sophisticated version of my formula, but the simple one outlined above should serve well. I invite anyone who would like to help to please test examples (even create parallel tables, whatever) and report back any weak spots (or tell me you found none).
I'll tell you what little I know or remember about straight race formulae. Using the leader's decimal total and lead, one can follow:
Robertie: 8% = marg. double; 9% = marg. rdbl; 12% = bord. T/P.
Weaver: Dif > 10%-2 = Double (add 1 for rdbl); Dif > 10% + 2 = Pass.
Trice: Subtract 5, div 7, round down = bord T/P; Init dbl 4 pips less or init rdbl 3 pips less.The Robertie formula is at its best when leader is at 100, and works pretty well between 80 and 120. I'm guessing that the Weaver formula is not as quite as accurate on average within that range, but it holds up better outside the range, and it's easier to use. The Trice formula is only intended for use below 70 pips or so, where I've been told it's very strong.
I'm interested in any corrections/modifications to the above and any other race formulae people can tell me about.
My goal with the Naccel formula (if negative add 8, or if positive div 2 add 7) was to keep it simple and as much as possible agree with Trice below 70, and one or both of Robertie and Weaver above 70. Below 40 or so and above 140 or so I don't care much about.
That said, I will use whatever information offered me to modify the above formula (if that seems indicated) while keeping it simple, and to rebuild a sophisticated formula for those who want dead-on accuracy.
Thanks in advance for any help.
Nack
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