Study and Tutorial Supplement
Inspired in part by Stick’s insightful post, several days ago I launched a Nactation Study on match annotation (i.e., annactation). The post I am writing now began as a brief report but has expanded into a full-blown Annactated Game (with a summary of the study findings at the end).
I am steadily chugging away on a tutorial update, but it may be a while before I finish. In the meantime, please consider this post to be a Tutorial Supplement (and partial update) as well — a down payment of sorts. The majority content of this supplement is advanced information. The main guide is still the current Nactation tutorial.
I would like to acknowledge and express my gratitude to the participants of this study: David, Petter, Storm, Stein, Daniel, Havard, Maik, Golden and Ian. Their answers and comments will help me create serviceable examples and explanations for the pending update and have provided a valuable basis of comparison for the future.
This is how the study was created: I googled "backgammon annotated matches" and clicked on the first link, which brought up a 1994 FIBS match between Kit Woolsey and Jeremy Bagai (the current score being 2 to 4, played to 9 points). The first three games were too long for my purpose, so I nactated the fourth game and asked anyone interested to please interpret my Nactations. The column of three-character entries (each being a roll+play) is the move sequence of the game.
In this post, you will see before- and after-diagrams for every play of the game. Under each diagram pair, I discuss and/or summarize the respondents’ guesses, explain my choice of Nactation, offer alternatives, and address the respondents' comments and questions.
If you missed the original thread and this is the first time you are playing through the game, or if you can benefit from the review, I recommend that you look only at my left-hand diagram, covering the right-hand diagram as best you can, and guess what the Nactation means. For example, in the first diagram, White is about to play 21S, meaning that he has rolled 21 and is going to play “S.” What play does S stand for? Does the right-hand (answer) diagram confirm your guess? Then read through the segment (or not), and guess what S (with a roll of 41) means for Blue in the next left-hand diagram. And so on.
A nacbrac appears at (or near) the end of most annactated segments. If you like, you can further test yourself by guessing what plays the letters in the nacbrac designate, and then compare to the Game 4 page, where you will find the traditional notations and TD-Gammon evaluations that the condensed nacbrac format represents.
Without further ado...
Annactated Game
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“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. (The "…or only" is a convenience clause, allowing people to use S, the first letter of Split, rather than Z, most of the time.)
In the early game, and sometimes until the end of the game, the 12pt is occupied by the opponent; it is therefore not legal to come down to the 12pt with the ace. If the 12pt happened to be vacant, then 21S would be 24/22 13/12, and 24/23 13/11 would (still) be Z.
“Nacbracs” (Nactation brackets) is an abbreviated way of writing candidate plays and their error sizes according to rollout(s). Although it is tangential to the study, readers may find it interesting to see TD Gammon’s opinion (published here) for each of the moves in the game, starting with…
[S $18 U26] _e
This means that S (Split, 24/23 13/11) is best, $ (Slot, 13/11 6/5) is –.018 (i.e., its equity is .018 worse than S), and U (Up, 24/21) is –.026. The "_e" (after the brackets) means that it is a TD-Gammon evaluation.
Modern rollouts yield [$ S9 U57]a (where "a" means an aggregate of bot rollout results). Over the last 15–20 years, popularity has shifted from opening 21S to 21$.
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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.)
Bot info: [S K3 U16] _e, but today we have [K U45 S47 T53 X62] ~5 (i.e., a Snowie 5000+ trial rollout). That’s quite a swing.
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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). I believe these five respondents had not progressed far enough in the tutorial (Section 5) to know what M means (though in Maik’s case perhaps it was just that his coffee had not yet kicked in); however, knowing that H wasn’t chosen eliminated the hit, and in four of the cases knowing that N wasn’t chosen likely eliminated 13/11(2) 6/4(2), so they picked the multiple quadrant play they liked best.
As far I can tell, all but one (maybe two) of the respondents, if shown the two plays (23/21 13/11 6/4(2) and 24/22 13/11 6/4(2)) side by side would have been able to confidently distinguish M from m, despite the fact that no mention is made in the current tutorial of lower case letters and how to handle them. Evidently, they have picked up that knowledge (use and application of the 6pt convention) from reading Nactation posts.
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).
From the four correct answers, I’m sure that Golden and David reasoned out "m" precisely, and Storm and Petter probably did as well. I paraphrase Golden: "M = Mayfair Split. Make a home board point, move a checker down and move a back checker. Here, there is a choice of back checker… apply hit/most/6. No hit or point to be made with the back checker, so closest to 6pt gets the capital. Therefore, M is 23/21 and m is 24/22."
According to TD-Gammon, m (the play actually made) is fourth best, but four plays are all very close: [N M9 H11 m16] _e
Daniel asks, "…is M ever but rarely used except with 2-2 or 3-3? Answer: In the early game, M occurs rarely for 66 but does occur for the other doublets (especially 22) with some frequency. Evidently, you’ve seen M for 22 and 33, so I’ll provide examples of the others:
- 32S-52H-11, M = Bar/24 11/10 6/5(2); or 54S-21H-11, M = Bar/24 8/7 6/5(2)
43Z-65R-44, M = 24/20 13/9 9/5(2); or 64S-61P-44, M = Bar/21 13/9 9/5(2)
54S-62H-55, M = Bar/20* 13/8 8/3(2); or 64R-21X-55, M = Bar/20 13/8 6/1*(2)
54S-66B-66, M = 20/8 8/2(2); or 62S-62X-F-66, M = 22/16 13/7 7/1*(2)
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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."
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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), as listed in the caption above (right). 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.]
Bot info: [p A56 O67] _e
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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).
Bot info: [T N7 n15] _e
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@ 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...).
Bot info: [V @1 E25] _e
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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).
Bot info: [B b15 V38] _e
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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).
Golden noted that, "Any other move with 13/8 or 8/6 would have a different symbol e.g. N, D…" True, but T is already precise; there is no need for process-of-elimination logic.
Alternatively for this 13/6 play you can use O: playing into and out of the Outer board.
Several moves later, Daniel inquired, “Up above, 616 instead of 61T would still have been Nactaperfect, no?” There was no roll of 61 in this game, so I wonder if he referred to this 52T play. In any case, the answer is: 526 is a fine though not “perfect” choice. The rules for using numerals are considerably looser; it’s almost as if to say, "Okay, I’m playing a checker to the 6pt (and stopping there, which nixes 8/6/1*); you figure out the rest." As 8/6 is the only clearly indicated portion of the play, you are relying almost entirely on assumption to imply 13/8 rather than 8/3 for the other part of the move. Granted, it is an overwhelmingly justified assumption (because 8/6 8/3 is a horrid play), which makes “6” a fine choice.
Bot info: [T H17 n32] _e
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While neither U nor P is as common these days, you can certainly use either here instead of @.
Bot info: [@ A109 D137] _e
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The updated tutorial promises three modified letter definitions on the near side. Previously, A had too heavy a load, while I and J had too light a load (more on I and J later). The definition of A has been narrowed to specify that half the play is played from outer to inner board, and the other half is played within the inner board.
For the position and roll at hand, the narrowing of the A definition did not affect anyone’s perception or comments except those of Golden, who will be relieved to hear that the quintuple whopper 6/1 5/2* is no longer in the A family, and even if it were then 8/5 6/1 and 6/1 4/1 would both rank higher. (The hit/most/6 rule has a home quadrant clause: Most points in the home quadrant overrides any hit. This prevents crazy board-breaking hits from getting the capital letter.)
Bot info: [A D26 O46] _e
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Bot info: [R C6 S41] _e
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Bot info: [R X69 O101] _e
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Bot info: [P p44 O77] _e
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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.
Bot info: [N O201 D275] _e
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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 (above, right) B or 7.
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Answer: No. It is true that for early game plays, D usually translates to two checkers down from the midpoint, but the definition is broader. D means that both (or all) portions of the move are played to or within the player’s own outer board.
In the position at hand (above, left), with White’s roll of 52, d = 13/8 10/8. If White’s roll is changed to 41, D = 13/9(2), and d = 13/8 (most points decides the capital). If the roll is changed to 63, D = 13/7 10/7 and d = 13/10 13/7 (closest owned point to the 6pt decides the capital.)
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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.
One respondent seemingly didn't understand that "down" move portions can be played within the outer board and chose 13/12(2) for the outer board half of the play. However, even the current tutorial example shows the outer board half of theoretical opening 11N to be 8/7(2).
The remaining four respondents cannot be faulted in the least for their choice of 8/7(2) 4/3*(2), even though the play made, 13/12 8/7 4/3*(2), is in fact N. The reason (that they couldn't have known) is that the 6pt convention has a final tie-breaker that states:
furthest from 6pt gets preference.
On the surface, this clause may sound arbitrary and unnecessary, but it greatly helps with matching up the best plays with capital letters. Blots are urged to move safely from the opponent’s outer board (e.g., 63R-61P-43D is 15/11 13/10 instead of the 13/10 13/9 whopper), and it often avoids slotting the 7pt (e.g., 65R-51S-21D is 13/10 instead of the 13/11 8/7 whopper).
In the position at hand, 4/3*(2) is half of 11N (by hit and most points conventions). For the outer board half: The first part of the 6pt convention favors owning a point closest to the 6pt, hence 8/7 for the third ace, covering the 7pt. For the destination of the fourth ace, you either end up with a blot on the 12pt or a spare on the 7pt. The 12pt is further from the 6pt, and therefore 13/12 is your fourth ace. In short, N = 13/12 8/7 4/3*(2), n = 8/7(2) 4/3*(2), N = 13/12(2) 4/3*(2), and n = 13/11 4/3*(2).
Alternatively, you might assume that the obvious 4/3*(2) is played for two aces, and nactate the leftover 13/12 8/7 as D (Petter’s suggestion). And you can nactate Stein’s play of 13/12 7/6 4/3*(2) with O; this is a stronger assumption because there is no play that jumps two aces over the bar anyway. (There is also a bulletproof Nactation for Stein’s play; explanations will be forthcoming in the tutorial update.)
Bot info: [O N9 n50] _e
Blue’s next play (with 54) will reveal yet another example (though a milder one) for which the 6pt wrinkle deprives an inferior move of the capital letter.
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For moves that make the 10pt or 7pt plus leftover, (assumption or) complex doublet application is needed.
Bot info: [P Y37 G64] _e
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Bot info: [D d2 S22] _e
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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.
Bot info: [C A239 e376] _e
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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.
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I used "Cub" and "Tak" so that all moves and cube actions in the column had three characters, and therefore all respondent answers would be equally indented (for legibility). More commonly seen are "C" and "T," as listed in the above diagram captions.
The reason I prefer "C" for the verb Cube (instead of "D" for Double) is that D denotes Double Match Point at the end of a move sequence. If I write 21$-11N-55-D, do I mean that it is 55 to play at the DMP score, or did I (either accidentally or on purpose) omit the Nactation of the 55 play and now a Double is being offered? Hence, "C" = Cube. (To further avoid potential confusion, I also now refer to dmp in the lower case and type 21$-11N-55-d.)
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By its nature, F (more than any other letter) tends to assume the best play that incorporates the key word (Float) concept of its definition. Of course, the wisdom of any assumption is a judgment call.
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.
Bot info: [F T23 t28] _e
Alternative words for Float are Fudge, Fiddle and Finesse (good guess, Daniel).
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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).
Bot info: [H j40 J373] _e
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As Golden noted, if you want to record the fanning roll as well, the fanning symbol of ^ is appropriate. (For entering, you can use > and for partial entering <.) In this case, the fanning roll was 64; the three-character string is therefore 64^.
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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.)
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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.
Bot info: [E C24 e468] _e
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Below is the move sequence of this game, with three characters for each roll+play (or cube action). Typically, I type six or eight plays per line (I chose eight in this case), which is still few enough so that at a glance one can determine which player made a specific play. Here, White made the first play in each line and Blue the last.
For example, who played 42P on the second line? Well, Blue played 31$; therefore (alternating back), Blue must also have played 42P.
21S-41S-22m-41P-33p-43H-31@-21L-
52T-21@-53A-53R-63R-42P-53N-31$-
52D-11N-11P-54D-32C-557-Cub-Tak-
11F-64H-64^-422-41C-63H-43^-Rcb-Pas
If you don’t care about alignment, you may as well shorten, Fan, Cub, Tak, Rcb and Pas, to F, C, T, R and P, and fit the game onto a line or two, like this:
- 21S-41S-22m-41P-33p-43H-31@-21L-52T-21@-53A-53R-63R-42P-53N-31$-
52D-11N-11P-54D-32C-557-C-T-11F-64H-F-422-41C-63H-F-R-P
As a group, the nine participants of this study were able to figure out the moves of the nactated game score with this rate of success:
- 221/243 = 90.9% (unforced checker plays only)
239/261 = 91.6% (includes fans)
275/297 = 92.6% (includes fans and cube decisions)
Out of 27 non-fanning rolls, 22.2% were doublets, which is higher than the expected 16.7%. Based on the so-many-doublets factor, this game had a somewhat lower-than-average accommodation factor for Nactation. (The non-doublet plays yielded a success rate of 97%, whereas the doublet plays yielded only 70%.) If you feel it is fair to adjust for the so-many-doublets factor, tack on 1.4% to the percentages listed above this paragraph.
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 in red above the corresponding plays. (The absence of a number means zero.)
----------------------------------------------------------------
..........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 (i.e., less than 3%): 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. I’m unconcerned; with a little more study, non-doublet errors will disappear.
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)]. For those seven wrong answers, I cannot fault the respondents one iota.
That leaves just nine "chargeable" doublet errors. 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).
I am confident that all nine respondents (except David, who was error-free!) are capable of understanding their errors that surfaced in this study and transcending them, if they so choose.
In a non-trivial number of cases the respondents did not know or fully understand the Nactation and guessed the intended play anyway, but the word "clueless" hardly applies when one can narrow the field of candidates or make deductions based on letters not used. Without much effort, any feeling of cluelessness that may exist will fade.
Lest we get carried away, I’ll repeat my assertion that Nactation is primarily intended for early game study (and all the applications that entails). Notwithstanding, this study has shown me that it is not necessary to eat, sleep and breathe Nactation in order to interpret entire games or matches, or for that matter to nactate comprehensibly for oneself (certainly) and even for others as well; those feats are already within the grasp of several people. The motivation and desire to do so is another question; time will tell.
Nack