Opening Rolls

 Nactating a whole game

 From: Nack Ballard Address: nack2000@sbcglobal.net Date: 19 January 2011 Subject: Nactation: match annotation study Forum: BGonline.org Forums

```THE QUIZ

Nactation is primarily intended for early game use. However, Stick's
including Bill Riles's comment got me thinking.

I googled "Backgammon Annotated Matches" and clicked on the first link. The
first three games were longer than I wanted for this purpose, so I went to
Game 4 (http://www.bkgm.com/matches/woba-4.html). It is the fourth game of
a 1994 FIBS match between Kit Woolsey and Jeremy Bagai, the current score
being 2-4, played to 9 points.

Start by looking at the diagram of the opening position (on the page that
you've left open at the Game 4 link), where a 21 has been rolled and guess
what opening "21S" means. You are allowed to use your knowledge of
backgammon to deduce what I probably mean, and even if you don't understand
the letter/symbol at all you are allowed to guess what the player played.
Always make some guess.

To the right of 21S (first line), type a space followed by the move that
you think was played using traditional notation.  Then scroll to the next
diagram, look at the position and guess what the moves is, and so on.

21S
41S
22m
41P
33P
43H
31@
21L
52T
21@
53A
53R
63R
42P
53N
31\$
52D
11N
11P
54D
32C
55I
Cub
Tak
11F
64H
Fan
422
41C
63H
Fan
Rcb
Pas

I used assumption in a very few cases. There are two or three plays that I
would nactate differently for advanced interpreters (or for a computer
program, to get 0% ambiguity by strict usage, but the rest I'd do the same
way.
```

 Nack Ballard  writes: ```ANSWER AND RESULTS This began as a brief report but has expanded into a full-blown Annactated Game (with a summary of the study findings at the end). 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X O | | O X | | X O | | O X | | O | | O X | | O | | X | | O | | X | | | | | O to play "21S" | X | | O | | X | | O | | X | | X O | | O X | | X O | | O X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 100% success: All nine respondents got this 21S play right. Another acceptable way to nactate this play is 21Z, though 21S is the popular form. S stands for Split, which in Nactation means Split with the one number and come down with the other. Z (which resembles the letter S in the mirror) stands for reverse split, and has a similar meaning. The difference is that S splits with the larger or only number, and Z splits with the smaller number. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X O | | O O X | | X O | | O X | | O | | O X | | O | | X | | O | | X | | | | | X to play "41S" | X | | | | X | | O | | X | | X O | | X | | X O | | O O X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success: All respondents translated 41S correctly. Also permissible is 41Z. It is a mistake to use B here, which means 24/20 8/7. Likewise, in the previous left-hand position, 21B would be 24/22 8/7. For non-doublets, B means to split with one number and move within the outer board with the other number. (The efficient B/S/Z division of labor will be demonstrated in the tutorial update.) 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O | | O O X | | O | | O X | | O | | O X | | O | | X | | O | | | | | | | O to play "22m" | X | | | | X | | O | | X | | X O | | X | | X O | | O O X | | X X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 44% success: Only four of nine respondents guessed 24/22, 13/11, 6/4(2) correctly. Petter figured out 22m purely on Nactation but commented that he found it odd that someone would make that play. It seems that two wrong-answer respondents (Stein and Daniel) reasoned out 22m with the help of the tutorial afterwards. Four out of the five wrong answers were close, getting the 13/11, 6/4(2) part right but guessing 23/21 (instead of 24/22) for the last deuce. The fifth was 13/11(2), 6/4(2). In determining capital and lower case, use the hit/most/6 rule. That is, first apply the hit convention (hit if you can), then the most points convention (make the play that makes or retains the most points), and finally the 6pt convention (which mainly comes down to which point owned or blot/spare destination is closest to the 6pt). 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O O | | O O X | | O O | | O O X | | O | | O X | | | | X | | | | | | | | | X to play "41S" | X | | | | X | | | | X | | X O | | X | | X O | | O O X | | X X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success for 41P: Making the 5pt is obviously the best play in any case. Golden mentioned that the 5pt is closer to the 6pt than the 9pt is, and therefore the 5pt gets the capital P. However, there is a "dedication" clause in the definition of P that is not in the current tutorial, which is that the entire play is dedicated to making a point. (An entering portion of the move is waived.) In other words, a play that makes the 9pt in the diagrammed position is not in the P family (P, p, etc.). However, if you back up a midpoint spare to a vacant 14pt, then 41p means 14/9. (Or if you put one of Blue's back checkers on the bar, the 5pt can no longer be made, and 41P means Bar/24 13/9.) Other choices for this 9/5 6/5 play are "A" and "5." 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O | | O O X | | O | | O X | | O | | O X | | O | | X | | O | | | | | | | O to play "33P" | X | | | | X | | O | | X | | X O | | X | | X O | | O O X | | X X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 100% success for 33P. (I'm including Maik, who said he definitely would have answered 11/5(2) if he had been looking at the right diagram!) This is an interesting case. I conjectured, based on the current level of reader understanding, that respondents would see that the 5pt is both the strongest point and closest to the 6pt and 11/5(2) is the standout play, and would therefore choose to interpret P in that way. By contrast, I felt uncertain how they would interpret p. Golden alone considered the hit/most/6 rule but concluded that given the high caliber of Kit and Jeremy's backgammon I likely applied assumption anyway. Thus, my speculation paid off. Nevertheless, the correct strict-usage Nactation is 33p (lower case). Following the hit/most/6 rule, P = 8/2*(2) and p = 11/5(2). To be clear, if pointing on the 2pt had been the best play or if the tutorial update were already published (either one), I would have chosen to nactate 11/5(2) correctly as 33p. The greater the nactator's or reader's skill level at backgammon, the more one should be willing to use assumption. On the other hand, the greater the nactator's or reader's knowledge of Nactation, the less one tends to resort to assumption. At first, that may seem paradoxical. This position helps demonstrate the simplification value of P's "dedication" clause. As Golden points out, there are six possible points that can be made. However, White cannot use up the entire roll to make the 1pt, 3pt or 10pt. That limits the P family to the 2pt, 5pt and 7pt, which match up to P, p and P, respectively. (This is one of the relatively few times when the capital letter does not represent the best play.) In support of 11/5(2) Havard (to my pleasant surprise) evoked the previously unpublished dedication clause in saying, "Several ways to make the 5pt, but just one way to 'only' make the point and [do] nothing else." Without the dedication clause, more P plays would exist, each requiring a tie-break procedure for the leftover portion(s). I imagine that nobody will be happier learning of the dedication clause than poor Golden. The non- dedicated point-making plays have other letters to handle them. Another way to nactate 11/5(2) is "o." Capital O is 13/10 11/8 8/5(2). [If this doesn't sound to you like the right way to apply the 6pt convention, read the analysis to Blue's 11N play.] 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O O O | | O X | | O O O | | O X | | O | | O X | | | | X | | | | | | | | | X to play "43H" | | | | | X | | | | X | | X O | | X X | | X O | | O O X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 78% success. One respondent guessed 13/10 6/2* because he was under the impression that H hits on the deepest point. It's the opposite: H hits on the highest point (almost always the better place to hit). The other wrong respondent guessed 6/2* 8/5, evidently unaware of both the highest point convention (hit on highest point) and the down default. The latter is explained in the current tutorial, the former not, but both have been used and/or explained in several bgonline posts. Another excellent option is 43N (referring to the Near side, where half of the play is to or within the outer board, and the other half is within the inner board). Another choice is 3, and yet another is 9, with the other half of the play assumed. However, using a numeral here seems like assumption for its own sake, given that H and N are both fine choices that require no assumption. As Daniel and Golden point out, 6/3* 6/2* would be nactated with K, meaning Kill (hit twice). 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O O O | | O X | | O O O | | O X | | O | | O X | | | | | | | | | | | | | O to play "31@" | | O | | | | | | | X | | X O | | X X | | X O | | O X X X | | X X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 100% success: Two respondents said they didn't know what @ means, but one of them (Daniel) guessed correctly and said, "... 'At' means 'Anchor' was an easy enough guess for an English speaker." I'm not sure if the remaining respondents all knew @ means anchor (noting that it is not yet in the tutorial), or if some felt that Bar/22* 23/22 play is a "next" anyway, but @ has appeared in many posts. @ is the most straightforward Nactation for this play. You can use P (Point) if you prefer; just verify that there is no other point that can be made (because almost any other point is closer to the 6pt). For example, if White's 8pt spare were instead a blot on her 10pt, P would be Bar/24 13/10, and Bar/22 23/22 would be relegated to p (or still @ of course). You can also use U (Up). Applying the hit/most/6 rule, U = Bar/22* 23/22, V = Bar/22*/21, and u = Bar/24/21 (no hit). For those who might not know, U/V is a double-sized family (U, V, u, v...). 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O O O | | O X | | O O O | | O X | | O | | O X | | | | | | | X | | | | | | X to play "21L" | | | | | | | | | X | | X O | | X X | | X O | | O O X X | | X X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. All respondents seemed to know the meaning of L (which is in the current tutorial) save two, one of whom guessed the word "Lift" correctly anyway. Golden is right in his observation that there is a choice of blots to Lift: the one on the 9pt, and the one on the 24pt that can be lifted to the safety of the 23pt (after entering with Bar/23). As the 8pt destination is closer to the 6pt, 9/8 earns the capital L. Another fine choice for this play is "8." I tend to prefer a letter (to a numeral) because it is more distinct from the dice roll, though the 8 in 218 is clear in any case (of course) because it is the third number in the character string (and there is no 8 on the dice). You may also use B, if you and your readers know the 6pt convention wrinkle (explained later, in the notes to Blue's 11N play). 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O O O | | O X | | X O O O | | O X | | O | | O X | | | | | | | | | | | | | O to play "52T" | | | | | | | X | | X | | X O | | O X X | | X O | | O X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 100% success, including one respondent who didn't know the meaning of T (which is sTack or Tower, take your pick), and another that forgot. There are two points onto which one can create or add to a stack (a point with four or more checkers): the 8pt and the 6pt. By the hit/most/6 rule, 13/6 gets the capital T (while 13/8 6/4 gets the lower case t). Alternatively for this 13/6 play you can use O: playing into and out of the Outer board. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O O O | | O X | | X O O O | | O X | | O | | O X | | O | | | | | | | | | | | X to play "21@" | | | | | | | X | | X | | X | | O X X | | X O | | O X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. In response to Golden's inquiry: Yes, @ is used for making or covering a new anchor (not for adding to an existing one). If you have two checkers already anchored on the 20pt plus a checker on the 23pt and roll 21, the move of 23/20 is simply an Up play. Be aware, too, that the definition of @ includes the dedication clause (like P does), though if it is only possible to anchor with part of the move and the rest of the move is obvious, you may combine @ with assumption. While neither U nor P is as common these days, you can certainly use either here instead of @. 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X X O O O | | O X | | X O O O | | O X | | O | | O X | | O | | | | | | | | | | | O to play "53A" | | | | | | | X | | X | | X | | O X X | | X O | | O X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 89% success. The one wrong respondent made up his own A word, causing him to abandon the midpoint with 13/10 13/8, but the rest remembered (with varying degrees of certainty) that A means Attack (except for Maik, who actually guessed Attack, which he said led him to the correct move). Sometimes the alternate word Aggress, or Amplify (board strength), or Augment (the inner board), might fit a particular position better, but the word Attack is the most dynamic and is just supposed to point you to the general area where attacking usually takes place, to help you remember what A means. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X X O O O | | O X | | X O O O | | O X | | O O | | O X | | | | | | | | | | | | | X to play "53R" | | | | | | | X | | X | | X | | O X X | | X O | | O X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. R (for Run) is one of the basic characters in Section 1, and the play of 23/15 is the only Running play. 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O X X | | X O O O | | O X | | O O | | X | | | | | | | | | | | | | O to play "63R" | | | | | | | X | | X | | X | | O X X | | X O | | O X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 100% success. Again, there is only one legal R (Running) play. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O X X | | X O O O | | O X | | O O | | X | | | | | | | | | | | | | X to play "42P" | | | | | | | X | | X | | X O | | X X | | X O | | O X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. Golden aptly explains: "P = Point. Could make 4pt or 11 pt here. Making the 4pt gets the capital as it's closer to the 6pt." 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O X X | | X O O O | | O X | | O O | | X | | | | | | | | | | | | | O to play "53N" | | | | | | | | | | | X O | | X X X | | X O | | O X X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 89% success. Six of nine respondents seemed to know exactly how to handle N. Two other respondents knew that N refers to somewhere on the Near side and guessed the obvious play. Maik alone entertains us with, "13/5 [*cough* had I actually looked at the position, it would have been clear that Jeremy had to hit, but when I'm not seeing K, H or X, I'm looking for quiet plays]." For N, one half of the move is played to or within the outer board. The other half is played only within the inner board. Applying the 6pt convention in isolation, N would be 13/8 5/2, but the hit and most points conventions both override, making 13/10* 6/1 the doubly clear interpretation. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O X | | O X O O O | | O X | | O | | X | | | | | | | | | | | | | X to play "31\$" | | | | | | | | | | | X | | X X X | | X O | | O X X X | | X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. The definition of \$ includes moving to a vacant point, which banishes nonsense interpretations with a point-breaking move portion of 6/5 or 4/3*. Generally speaking, the "natural" slotting play is intuitively obvious. However, for reference, the full priority rules for slotting are listed below. (1) Slot 5pt or 4pt (2) Most Points (3) Unstack the taller point (4) Order of preference for slotted point: 5pt, 4pt, then 7pt, 3pt, 2pt, 1pt You may also nactate the diagrammed play B or 7. 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O X | | O X O O O | | O X | | X O | | X | | | | | | | | | | | | | O to play "52D" | | | | | | | | | | | | | X X X | | X O | | O X X X | | X X O | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 100% success. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O O X | | O X O O O | | O X | | X O | | O X | | | | | | | | | | | | | X to play "11N" | | | | | | | | | | | | | X X X | | X | | O X X X | | X X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 33% success. David got this play right, presumably because I've shared the 6pt convention wrinkle with him (and until now nobody else). Storm guessed it right by combining assumption with selective use of the 6pt convention (definitely not what I had in mind). Daniel acknowledges that he guessed right only because he chose the play that he thought is best, finishing his comments with, "Aren't there several N plays?" [Answer: The four N-family plays that include 4/3*(2) are at the top of the hierarchy. There are 4*6 = 24 additional N-family plays (all of which are comically bad) when you include other ways to play two aces in the inner board.] Any play that includes 7/6 cannot be N, as any N move is composed of two aces on the left and two aces on the right, without crossing the bar. Stein subsequently realized that his 13/12 8/7 8/6 guess was wrong for that reason. 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O O X | | O X O O O | | O X | | X O | | O | | | | | | | | | | | | | O to play "11P" | | O | | | | | | | | | | | X X X | | X | | X X X | | X X X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 89% success. For the most part, respondents chose the 9pt because it looked like the strongest point that can be made. By the letter of the law (not yet published), though, or rather by the law of the letter, P can only mean Bar/24 11/9 10/9. P's dedication clause (introduced at the fourth roll of this sequence, Blue's 41) disallows left-over portions; it is only the entering portion of the move (Bar/24) that is waived. For moves that make the 10pt or 7pt plus leftover, (assumption or) complex doublet application is needed. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O X | | O X O O O | | O O X | | X O | | O | | | | | | | | | | | | | X to play "54D" | | | | | | | | | | | | | X X X | | X | | O X X X | | X X X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. "What would 13/8 12/8 be?" I'm glad you asked, Ian. Answer: By most points convention, we cover the 8pt, but that could be one of two plays. As discussed earlier, for a blot or spare in a player's own outer board (the lower right quadrant for Blue), the destination furthest from the 6pt gets the capital; hence, D = 13/9 13/8, and d = 13/8 12/8. The wretched (fewer points) play of 13/9 12/7 would be D. 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O | | O X O O O | | O O | | X O | | O | | | | | | | | | | | | | O to play "32C" | | | | | | | | | | | | | X X X | | X X | | O X X X | | X X X X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 89% success. C means Cross the bar with the forward half of the play, and move back checker(s) with the other half. C is illustrated in a couple of places in the tutorial and in the fourth diagram here. The one wrong respondent (who revealed at the outset that he doesn't know any of the BEACON letters) excluded the right move from contention because he seemed to think that you don't touch a back checker unless U is used. That is a far cry from the truth, though it does bring up the point that one can reasonably nactate the move played as U, which works either by assumption or by 6pt convention. The move that respondent defaulted his answer to (and another respondent wondered about the Nactation for) is 8/6 5/2, which is A. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O | | O X O O O | | O O | | X O O | | | | | | | | | | | | | | | X to play "557" | | | | | | | | | | | | | X X X | | X X | | X O X X | | X X X X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 78% success. I chastise myself for being lazy and sloppy. The best move is so much better than any other that I thought it hardly mattered which letter I chose. I knew that the "bulletproof" Nactation of O wouldn't be understood at this point, so I grabbed "I," to indicate that a bunch of checkers were being played in (by the old-fashioned definition) and how could the reader get it wrong? However, players do sometimes make awful moves; and, from the reader's perspective, why would I have chosen "I"? Understandably, two respondents interpreted that all four checkers were played in with 9/4* 7/2(2) 8/3. I realized after the fact that "7" (as captioned above) would have been a strong assumptive choice, a conclusion that one of the two victims (Petter) came to as well. After being pushed in the right direction by 12/7, the reader is on his own for finding the even more obvious best move. Indeed, the proper letter of O (met by blank stare) or no symbol at all would likely have achieved 100% success; for a move like this, about the only way the nactator can go wrong is to mis-lead the reader. As mentioned earlier, there are three letters with near-side-only usage that have changed. The definition of A is streamlined, and the old definitions of I and J (which were of little use) are dead. The modified or new definitions are: A = Attack: Half the move is played into the inner board and half within the inner board. I = Inside: Both (or all) portions of the move are played within the inner board. J = Jump: Both (or all) portions Jump over the bar (from outer board to inner board). There will be plenty of diagrammed best-move examples in the tutorial update, but here, for simplicity's sake, are crude examples from the opening position: 43A = 8/5 6/2, 43I = 6/3 6/2, and 43J = 8/5 8/4. O cubes; X takes. 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O | | O X O O O | | O O | | X O O | | | | | | | | | | | | | | | O to play "11F" | | O | | | | | | | | | | | X X X X | | X | | X X X X X | | X X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 78% success. Two respondents chose the spare-stacking play of Bar/24 6/4 5/4. However, the tutorial states: "F refers to moving a lone spare (usually a small number of pips) from one point to another, thereby "Floating" it on top of those points. In the position at hand, the entering portion is forced, and for the best three aces that include a float, 8/7(2) 5/4 looks natural to me. For the spare-sTacking plays, I'd be inclined to use "t" for Bar/24 6/4 5/4, and T for Bar/24 8/7(2) 6/5. Without assumption (and therefore with zero ambiguity), these three plays can be nactated with complex doublet letters, which will be explained in the updated tutorial. Alternative words for Float are Fudge, Fiddle and Finesse (good guess, Daniel). 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O | | O X O O O | | O O | | X O O | | | | | | | | | | | | | | | X to play "64H" | | | | | | | | | | | | | X X X X | | X | | O X X X X X | | X X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 89% success. H means hit, which (naturally) must include 7/1*. Unfortunately, the lone wrong respondent reasoned that two hitting plays keep an equal number of points (five), and so by 6pt convention the 4 should be moved from the 5pt instead of from the 8pt. There are three problems with that analysis. The first is that H means to Hit loose (admittedly, it was once the vaguer "usually loose"). If you use H to hit, thou shalt not cover that point (P's job). That covenant alone makes 8/4 6/1* the only H play that retains five near-side points. The second problem is a misunderstanding of convention. The 6pt convention has two stages: 1. The point owned closest to the 6pt gets priority. 2. The blot/spare destination closest to the 6pt has next priority. Thus, even if we ignore the "don't cover where you hit" commandment, the first stage of the 6pt convention tells us that the 5pt (retained by 8/4) is closer to the 6pt than is the 8pt (retained by 5/1). The third problem is a misconception implicit in the respondent's notes. The 6pt convention is not based on points of origination. When applying the convention to a blot or spare, the destination is the determinant. This distinction makes no difference when comparing a 3 played 24/21 vs 23/20, for example, but it makes all the difference when comparing a 3 played 8/5 vs 6/3. The destination of the 8/5 movement is closer to the 6pt. Nactation rules have been created (more sparingly than it may seem) after countless hours of research and experimentation. When the best play matches up to the capital letter most of the time, an additional benefit is reaped: that of bridging or diminishing the gap between technical interpretation and assumption. In this position, H means 7/1* 8/4 whichever mode of translation is employed. You can also nactate 8/4 7/1* with J (Jump over the bar). Jumping without hitting (8/4 8/2) is j (or "2" with assumption). O fans. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O | | O X O O O | | O O | | X O O | | | | | | | | | | | | | | | X to play "422" | | O | | | | | | | | | | | X X X X X | | | | X X X X X X | | X | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. "2" is very clear, by assumption. By now, you can hopefully see that A is the 100% unambiguous choice for this play. (If not, review the definition of A under Blue's 557 play and the conventions explained in this post.) 1 2 3 4 5 6 7 8 9 10 11 12 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O | | O X O O O | | O O | | X O O | | | | | | | | | | | | | | | O to play "41C" | | O | | | | | | | X | | | | X X X X X | | | | X X X X X X | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 24 23 22 21 20 19 18 17 16 15 14 13 100% success. This play resembles White's earlier 32C. Here, 41C has White moving the back checker (coming in) with the 1 and Crossing the bar with the 4. As the ace is forced, you have the foolproof option of nactating just the 4 portion of the move: either J (Jump) or "5" (5pt) is fine. 24 23 22 21 20 19 18 17 16 15 14 13 +---+---+---+---+---+---+---+---+---+---+---+---+---+ | O X O O O | | O O | | O X O O O | | O | | X O O O | | | | | | | | | X | | | | | | X to play "63H" | | | | | | | | | X | | | | X X X X X | | | | O X X X X X | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 2 3 4 5 6 7 8 9 10 11 12 100% success. Hard to go wrong here; there is only one legal play with 63! O fans. X redoubles; O passes. ************************ In the move sequence below (with the Nactations used in the study), the numbers of erroneous responses (out of a total of 9 each play) are listed above the corresponding plays. 5 2 1 1 21S-41S-22m-41P-33P-43H-31@-21L-52T-21@-53A-53R-63R-42P-53N-31\$- 6 1 1 2 2 1 52D-11N-11P-54D-32C-55I-C-T-11F-64H-64^-422-41C-63H-43^-R-P First, let's examine the non-doublets. Only six were missed: one oversight (not seeing the hit on the 10pt), one not knowing the A-word, one thinking only U could move a back checker, two failing to Hit on highest point, and one being too creative with the 6pt convention. As expected, the doublets were noticeably more difficult. Out of 54 respondent answers, 16 were wrong. However, of these, two were a consequence of my thoughtless 55I Nactation and five hinged on a couple of rules that were previously undisclosed [the 6pt convention wrinkle (see 11N), and P's dedication clause (see 11N and 11P)]. Five were from not knowing M and/or not knowing what to do with lower case (see 22m), two were from misunderstanding or misremembering N (see 11N), and two were from an extreme treatment of spares (see 11F). ```

### Opening Rolls

At different match scores  (Louis Nardy Pillards, July 2002)
Average advantage of winning opening roll  (Chuck Bower, Oct 1998)
Choosing a strategy  (Daniel Murphy, June 2001)
Early game rule of thumb  (Rich Munitz, Feb 2009)
Factors to consider  (Kit Woolsey, July 1994)
How computers play  (Kit Woolsey, Mar 1995)
Magriel's Chapter 5  (Hayden Alfano+, May 2006)
Mloner vs Jellyfish  (Kit Woolsey, Dec 1995)
Nactating a whole game  (Nack Ballard+, Jan 2011)
Nactation  (Jim Stutz+, June 2010)
Nactation overview  (Nack Ballard, Oct 2009)
Nactation--Why use it?  (leobueno+, Jan 2011)
Opening 1's: Split or slot?  (Douglas Zare, Dec 2003)
Opening 21: Rollout  (Stick, Mar 2006)
Opening 21: Split or slot?  (Dick Adams+, Dec 2003)
Opening 32: Rollout  (Stick, Feb 2006)
Opening 43: In GOL online match  (Raccoon+, Feb 2004)
Opening 43: Pros and cons  (Stick+, Jan 2006)
Opening 43: Which split is better?  (Peter Backgren+, Aug 2000)
Opening 43: Which split is better?  (Michael J. Zehr+, Mar 1996)
Opening 51: Rollout  (Stick, Feb 2006)
Opening 52: Merits of splitting  (Peter Bell, Apr 1995)
Opening 53: Magriel's recommendation  (George Parker+, July 1997)
Opening 53: Split to 21?  (Alex Zamanian, Aug 2000)
Opening 53: Why make the three point?  (Kit Woolsey+, Feb 1996)
Opening 6's: Slot the bar point?  (Chuck Bower+, Feb 2000)
Opening 6's: Slot the bar point?  (David Montgomery, June 1995)
Opening 62: Could running be best?  (Gary Wong, Sept 1997)
Opening 62: Split, run, or slot?  (Chuck Bower, May 1997)
Opening 63: Middle Eastern split?  (Mark+, Apr 2002)
Opening 63: Slot the four point?  (Dennis Cartwright+, Mar 2002)
Opening 64: Make the two point?  (William Hill+, Jan 1998)
Opening 64: Make the two point?  (Darse Billings, Feb 1995)
Opening 64: Rollout  (Peter Grotrian, Jan 2006)
Opening 64: Split to 20?  (Peter Bell, June 1995)
Opening 64: Three choices  (Brian Sheppard, July 1997)
Opening 65: Becker on lover's leap  (Jeffrey Spiegler+, Aug 1991)
Opening 65: Computer rankings  (Chuck Bower, Jan 1997)
Opening rolls ranked  (Arthur+, Apr 2005)
Rollouts of opening 21 and replies  (Alexander Nitschke, Oct 1997)
Rollouts of openings  (Tom Keith+, Jan 2006)
Rollouts: Expert Backgammon  (Tom Fahland, Aug 1994)
Rollouts: Jellyfish 3.0  (Midas+, Sept 1997)
Rollouts: Jellyfish 3.0 level 6  (Chuck Bower, Feb 1999)
Rollouts: Snowie 4.1  (Rene Cerutti, Apr 2004)
Slotting the four point  (Joe Loria+, Oct 1999)
Snowie's openers and replies  (rcerutti, Feb 1999)
Splitting versus building  (Dave Slayton+, Aug 2000)
Splitting versus slotting  (Daniel Murphy, Apr 2001)
Splitting versus slotting  (Daniel Murphy, Sept 1997)
Trice's rankings  (Marty Storer, Feb 1992)