I'm not surprised you found it a challenge to nactate the candidate moves in the (left-hand) position diagrammed below. Of the ten listed candidate plays (according to XGR++), eight are complex doublets, due to the 11/8 lift portion being a natural part of most moves. Complex doublets (those which aren't simply played in two pairs) are by far the most difficult moves to nactate. They are in a class by themselves.
(Fortunately, complex doublets come up a low percentage of the time. They just tend to be the ones that get bgonline exposure because they are the ones people stumble over and thus appear to arise a lot more often than they actually do.)
Moreover, many of the complex doublet plays in this position happen to be close in equity/value, making the use of assumption more elusive than usual.
First, I'll explain how to nactate these moves using assumption (as described in Section 6 of the current tutorial); then I'll illustrate Nactations that are bulletproof (i.e., by "proper" or "strict" usage).
|
| ||||||||||||||||
The most logical assumption is that three 3s are played 11/5 8/5 (making the 5pt and remaking the 8pt) as shown in the right-hand diagram. This simplifies your task to nactating (or interpreting) only the fourth ace.
For the fourth ace, 13/10 can thus be nactated D (Down), and 6/3 can be I (Inside). The only two moves strictly in the D family are 13/10(3) 11/8 and 13/10(4), and the only move strictly in the I family is 6/3(4); those are all such bad plays ("he can't mean that!") that assumption can be safely employed, as long as you are communicating with someone other than a complete novice (or a bot).
There is no way to interpret U or V by strict usage (it is not possible to play all four 3s in the 24pt–18pt area); hence the reader is already signaled that assumption is employed. The fourth ace 23/20 can thus be nactated U (Up), and 24/21 can be V (Variant up; i.e., the second member of the U/V family).
The BEACON letters (see Section 3 of the tutorial) are handy; by their nature either two portions (by assumption) or four portions (by strict usage) are addressed. By strict usage, C = 24/18 8/5(2) and c = 24/21 23/20 8/5(2), but those chin-leading plays are clearly too loose for a decent player to ever make. "Therefore," C = 23/20 8/5, and c = 24/21 8/5, with 6/3(2) being the simple pair of 3s to finish off the play.
Generally speaking, the weaker the play, the trickier the assumption. Unless the nactator and interpreter have developed a rapport or implement corollaries (such as a numeral refers to a blot that is not covered), it's a bit like threading a needle. Cooperative deduction can help ("if he meant play 1, he would have used this, therefore he must mean play 2), but details are beyond the scope of what I want to post here. Let's just say for the 9th and 10th best plays down the list (23/20 13/10 6/3(2), and 11/5 6/3(2)), either that you'll rely on the player being strong enough not to make those inferior plays or that you'll learn proper usage rules (explained momentarily) in order to have any play (no matter how big a blunder) covered with 100% non-ambiguity.
| |
|---|---|
| Blue to play 33 | |
- A = Attack (8/5(2) 6/3(2))
N = Near (13/10(2) 6/3(2))
O = Outer (13/10 11/5 8/5)
For explanations of A, N and O for doublets, you can review the tutorial (diagrams #12, 14 and 15), but I'll also define them here.
A (Attack) means to play half the move from outer to inner board, and the other half of the move within the inner board. There is only one such play, which is 8/5(2) 6/3(2). Easy peasy.
N (Near) means to play half the move to or within the outer board, and the other half of the move within the inner board. There are two such plays. 13/10(2) 6/3(2) earns the capital N by virtue of making the most points. (Lower-case "n" = 13/10 11/8 6/3(2), an unlisted play.)
O (Outer) means to play half the move to or within the outer board, and the other half out of the outer board. There are two such plays. O = 13/10 11/5 8/5, and the unlisted play of "o" = 13/10(2) 8/5(2). Both plays make/retain the same number of points, but by the (closer-to) 6pt convention, ownership of the 8pt trumps ownership of the 10pt.
A and N are known as "simple" doublets (i.e., both halves of the moves are played in pairs). In this case, capital O is technically a complex doublet but it is simple enough in nature that I wouldn't recommend using assumption. That is, O follows a precise, reasonably easy definition, whereas if D (mentioned earlier) is used for this play, the interpreter must figure out to assume the other three 3s are played well.
The "hit/most/6" rule, which has been explained in many bgonline posts, is not mentioned in the current tutorial. It means that the play that HITS is awarded the capital letter; if two plays hit the same number of checkers, you prioritize the play that makes or retains the MOST number of points; if all is still equal, the (closest to) 6pt convention applies, first owned points, then blot/spare destination. (If you were confused about the hierarchal pairs of plays I earlier identified as U V, C c, N n, and O o, following the "hit/most/6" rule should clear it up.)
That said, I'll now explain, on bgonline for the first time, the proper (strict-usage) way to nactate complex doublets. [Updating the tutorial is taking longer than I planned, so my self-inflicted punishment is to write up additional explanations. :) ]
Proper Usage
A doublets move has four "portions," each of which is considered separately. There are four possible areas in which a portion can be played:
Far: A portion played on the far side of the board.
Point of origin can be as high as the 25pt (roof). Destination can be as low as the 13pt (midpoint).
Down: A portion played to or within the outer board.
Origin can be as high as the 18pt (i.e., a 6 played 18/12). Destination can be as low as the 7pt.
Jump: A portion played from the outer board to the inner board.
Origin can be as high as the 12pt (i.e., 12/6). Destination can be as low as the 1pt (i.e., 7/1).
Inside: A portion played within the inner board.
Origin can be as high as the 6pt. Destination can be as low as the 0pt (bear-off tray).
We will use the above four terms as nouns. For example (for doublets), an E play is composed of two fars and two insides. An O play is composed of two downs and two jumps. (For practice, visualize.)
Any doublets move can be designated by a four-digit code, the first digit denoting the number of fars, the second digit refers to the number of downs, the third to the number of jumps, and the fourth to the number of insides. For example, "2200" is two fars and two downs (and zero jumps and zero insides). "1111" is one of everything.
The top ten plays for the 41S-21S-65@-33 position, according to XGR++ (and listed in its order of strength) are encoded below. You can refer to the diagram below as a visual guide.
- 0022 ... 8/5(2) 6/3(2)
1120 ... 23/20 11/5 8/5
0202 ... 13/10(2) 6/3(2)
1012 ... 23/20 8/5 6/3(2)
1120 ... 24/21 11/5 8/5
1012 ... 24/21 8/5 6/3(2)
0121 ... 11/5 8/5 6/3
0220 ... 13/10 11/5 8/5
1102 ... 23/20 13/10 6/3(2)
0112 ... 11/5 6/3(2)
| |
|---|---|
| Blue to play 33 | |
Any code with two 2s and two 0s is nactated with a BEACON letter. Any code with one 1, one 3 and two 0s is an underlined BEACON letter (with the exception that S and Z replace B, for greater flexibility).
"4000" means that all four portions are fars, and the play will be nactated with either R or U/V, in the same way that non-doublets with two fars are R or U/V.
The code with 4 downs is D, four jumps is J, or four insides is I; these are 0400, 0040, and 0004, respectively. Codes with two downs or two jumps or two insides, with one each of the others (and zero fars) are the underlined versions of the same letters: D, J and I; that is, 0211, 0121, and 0112, respectively.
The remaining 10 codes (out of 35 permutations altogether) are divided up among non-underlined and underlined M, Y, G, and Q. These will be detailed in the updated tutorial (or on bgonline sooner, if they arise) and there will be a chart for easy reference. For the position at hand we need: M, for Mayfair split, is equally 1102 or 1120; and Q, for Quirky split, is 1012.
The ten plays are repeated below, this time by Nactation in alphabetic order. Codes are still included in the far left column. Again, there is a diagram below, for visual reference.
- 0011 ... A = Attack (8/5(2) 6/3(2))
0112 ... I = 11/5 6/3(2)
0121 ... J = Jump (11/5 8/5 6/3)
1120 ... M = Mayfair split (23/20 11/5 8/5)
1120 ... m = Mayfair split (24/21 11/5 8/5)
1102 ... M = Mayfair split (23/20 13/10 6/3(2))
0202 ... N = Near (13/10(2) 6/3(2))
0220 ... O = Outer (13/10 11/5 8/5)
1012 ... Q = Quirky split (23/20 8/5 6/3(2))
1012 ... q = quirky split (24/21 8/5 6/3(2))
| |
|---|---|
| Blue to play 33 | |
- A M N Q m q J O M I
Nack