Early Doubles
GammonLife Article 1
by
Nack Ballard

 

Introduction

Welcome to the first article of this series, entitled Early Doubles.

“Early” applies to the early stage (opening phase) of a backgammon game.

The meaning of “Doubles” is two-fold, pertaining to:

•  Doubles that are rolled with the dice (i.e., doublets), and
•  Doubles that raise the stakes of a game (i.e., turning of the cube).

In short, Early Doubles refers both to doublets that are rolled and to cubes that are turned in the first few moves of the game.

I have spent several years compiling rollout data for early game moves. This has grown to become a large-scale project with many people contributing their CPU time.

In this series of articles, Black is on roll. Problem positions appear in the center or on the left-hand side of the page and are designated with a pound sign (#1, #2, #3…).

Candidate plays (i.e., Black’s choices) appear on the right-hand side of the page. They are designated by lower-case letters (a, b, c…) and appear in order of strength. For example, for problem #1, the best play is 1a and the second best play is 1b.

You can regard 1a as the right “answer” (proper play) to the question (problem) posed in #1. If a similar answer has been diagrammed before, there may not be an answer diagram, though the answer is still made clear in the text (e.g., “priming,” or “8/7(2) 6/5(2)”). If you like testing yourself, cover the text to the right of (or below) the problem diagram with your hand.

The caption to a problem diagram denotes the sequence of rolls and plays that occurred to reach the position. For example, the caption to problem #1 is “41$-11,” an abbreviation for: “White opened with 41-slot (13/9 6/5) and in response Black has 11 to play.” This information is entirely nonessential to understanding the text, but if you intend to memorize the positions or want to save on typing or are interested in other useful applications of nactation, click here.

In standard fashion, point numbers for Black appear in lines above and below the diagrams, and point numbers for White are reversed — on the opposite side of the board. In the text, point references are abbreviated; for example, what you may have seen in print elsewhere as the “five point,” “5 point,” or “5-point,” I refer to as the “5pt.”

Pipcounts appear (in green) in the center of the point-number lines. Cool, huh?

When listing rolls, I mostly dispense with punctuation. For example, I might say, “The five best opening rolls are 31 42 61 53 65.” There are no hyphens or commas, and I include “and” or “or” only if clarification seems necessary. These shortcuts help to keep the text crisp.

To spice up the analysis, I often refer to Black as male (he, his) and White as female (she, her). I apologize to dark-skinned women and light-skinned men if you feel left out. I love you all.

Problem positions are for money. The broader definition of “money” includes match situations in which both players still need many points to win; i.e., they can gain full value from gammons and an adjustment would be negligible unless the cube is later turned more than once.

Assume that the best play is best regardless of the match score, unless an exception is explicitly stated. If the best play is overturned (“tied” doesn’t count) at DMP (double match point), GS (gammon save) or GG (gammon go), the best play for that score will be listed in a text box. If you are not interested in match play exceptions, skip over the text boxes.

All plays (unless hugely wrong) have been rolled out at least 20,736 trials (full 3-ply precise, live cube) on Snowie and 15,552 trials on GNUbg.

Error Scale

This series of articles employs an “error scale” that Paul Weaver and I created for Backgammon Openings. (For reviews of this book series, click here.)

If you focus on a mere few thousandths of a point of equity, you are likely to miss the forest for the trees. The idea behind the error scale is to convey approximate error sizes. Common words are used to describe whether a play is right or wrong and to what degree.

For many of you, cubeful equity margins may hold little interest or value. In that case, you can skip the next few paragraphs and go straight to the first diagram.

However, those of you who work with bots and have developed an affinity for cubeful equities may want to (a) memorize this verbal list of error scale ranges, or (b) jot it down so that you won’t have to scroll back, or (c) keep your copy of Backgammon Openings, Book A open to page 93 or 126 as you read these articles.

Example: If Play A is better than Play B by a cubeful equity of .024, I say that Play A is “marginally correct.” This term is not as specific as .024, because it refers to a range between .02 and .03, but the average reader finds it easier to relate. Besides, there are few if any players in the world who can meaningfully feel the difference between .024 and (say) .029.

The terms in the left column of the table refer to the best play in relationship to the second best play. For example, if a rollout indicates the best play is .012 (in cubeful equity) better than the second best play, the best play is “barely correct.” If a rollout indicates the best play is .065 better than the second best play, the best play is a “blowout.”

The terms in the right column refer to inferior plays in relationship to the best play. For example, suppose the rollout indicates that play A (the best play) is .012 better than play B, .037 better than play C, and .071 better than play D. In that case, B is barely wrong (or very close), C is wrong (or a mistake) and D is a blunder.

Without further ado, let’s get to the first article!

 

Double 1s: Hit or Prime (Second Roll)

Problems in this article are always Black to play double 1s, indicated by the black dice. How would you play double 1s in Problem #1 (below)?

#1            41$-11

 

1a
                                                                                               
 
Hitting is barely correct. With this move, Black sends a third checker back, gaining 20 pips, and threatens to hit again or make the golden anchor.

                                                                             

In 1a, White 6s are painfully unproductive. Assuming she doesn’t fan, she must enter with the non-6 half of the roll and use the 6 to totter to her 3pt or expose another blot in the outfield.

                                                                                

White’s 4s are duplicated. (She should hit with 41 44 but not the other 4s.) On the surface, Black’s 4s are also duplicated, but by the time he rolls, that duplication may no longer exist.

 

1a    Best
 
1b
                                                                                                         
Priming (7(2) 5(2)) is barely wrong. It gives White the freedom to play her entire roll without restriction.

                                                                                                        

If White does not roll a 5 or a 6, she will usually take over the advantage by covering the 5pt and (a) splitting, (b) promoting her anchor, or (c) making a fourth offensive point.

                                                                                                        

In both 1a and 1b, most of White’s worst rolls contain 6s, but at least she can use those rolls to make an offensive point in 1b.

 

1b    Very close


Let us now examine the same situation with White’s outfield builder on her 11pt instead of her 9pt. How would you play double 1s if you were Black in the position below?

#2           21$-11

 

2a
                                                                                                
Priming is marginally correct. If White now covers her 5pt, Black can add a point to his blockade or advance his anchor with two-thirds of his numbers.

                                                                                      
Why should Black hit in one position (#1) yet prime in another position (#2) that is so similar? Read on.

 

2a    Best

2b           
                                                                                                       
Hitting is marginally wrong. Here, White’s numbers are well diversified: indeed, all 35 entering numbers hit or make a point! She hits with 6s, 3s, 1s and 55, anchors with 54 44 and covers her 11pt with 52 42 22.

                                                                                                        

In any hitting decision, it is important to contemplate how the opponent's 6s play. This aspect does not automatically dictate the best move, but it is the major factor that guides Black to hit in #1 and not in #2.
                                                                                                        
A similar comparison (between 65R-41$-31 and 65R-21$-31) can be found in Backgammon Openings, Book A (A133 and A137).

 

 2b    Close

2c 
                                                                                                        Splitting (24/22 6/5(2)) is a mistake. It works better than 2a if White rolls 64 43 41 (covering but leaving a direct shot); otherwise, though, Black’s deuce-split gains less than making the bar point.
                                                                                                         Black will especially regret his splitting play if White uses one of her three worst rolls in 2a — 55 54 52 — to point on Black in 2c.

                                                                                                        

In problem #1, Black’s splitting play (not diagrammed there) would be a blunder.

 

     2c    Mistake


Summary Contrast

As Neil Kazaross says in his rave about Backgammon Openings, Book A, after which these articles are fashioned, “The discussions and comparisons of follow-up plays, which often show why a seemingly small thing can really matter, are extremely valuable.”

Here, Black’s selection of play hinges on whether White’s builder is on her 9pt or 11pt. The two contrasting positions are repeated below, one under the other. The problem diagrams are on the left and the solution diagrams are on the right.


#1    41$-11
 

1a    Best

#2    21$-11
 

2a    Best


Some people misplay #1. Others misplay #2. At the time of this writing, few people get both plays right.



Bonus

As a bonus, I offer some related positions. There are answers but no answer diagrams.

#3    31$-11
 
#3
                                                                                                       
Stan Tomchin, one of the best players in the world thirty years ago, occasionally slotted with opening 31 (as shown), a subtle though unwarranted gambit.
                                                                        
In #3, it is correct (almost a blowout) for Black to hit with double 1s. After Black hits, White is saddled with terrible 6s just as she is in 1a. In addition, Black’s 4s (24/20) and 5s (20/15*) will sometimes be diversified on the next roll.

                                                                        

You are unlikely to encounter positions #3 and #4 (below) in a game. However, it is instructive to compare them to the other problem positions in this article.

#4    61N-11
 
#4
             

In the late 1970s and early ‘80s, a few experts, most notably Paul Magriel, experimented with slotting both the 7pt and 5pt (as shown) with opening 61 against significantly weaker opposition.

                                                                                             
If White makes this swashbuckling play, it is correct for Black to prime (i.e., 8/7(2) 6/5(2)) with double 1s. If Black mistakenly hits and White rolls a 6, she will be able to enter with the non-6 and cover her bar point with the 6.

#5    51$-11
 
#5
               
Priming (8/7(2) 6/5(2)) is a blowout.
                                                                             
If Black hits, it is true that White will have no useful 6. However, White’s inflexibility, which substantially reduces Black’s incentive to hit, is an overriding factor. White’s new builder is on her 8pt instead of a more flexible location.
                                                                              
After Black primes in #5, White has fewer numbers that cover her 5pt than in the other four positions. (For example, in 1b, where White has a builder on her 9pt, she can cover her 5pt with 64 54 42.) Black’s motivation to hit on this roll is therefore considerably diminished.


If White rolls opening 62 and plays 13/5 (not diagrammed), she has the same position as in #5 except one of her 8pt checkers is moved to the stack on her 6pt. In that case, White’s distribution is less balanced; she is that much worse off in a priming battle. In that position, Black’s decision is even more one-sided: priming (8/7(2) 6/5(2)) is a wipeout.

If White slots the 5pt with any opening roll and Black rolls 31 (instead of 11), he should hit. It is a whopper for Black to make the 5pt (passing up the hit) if he cannot also make the 7pt.

It is instructive to contrast the primability of the two 4-pip rolls. If White slots her lowly 4pt (as opposed to her 5pt) with the opening roll, it is hugely right for Black to hit there with 31 but hugely wrong for Black to hit with 11.

To learn more about hitting on the opponent’s 5pt or 4pt with a roll of 31, see Backgammon Openings, Book A, pages 16–18 (second roll) and 53–56 (third roll). To learn more about hitting (and other decisions) with a roll of 11, stay tuned to this series of articles (Early Doubles) on GammonLife.

 

Conclusion

After White slots her 5pt (with a standard play) or her 4pt on the opening roll:

• If Black rolls 31, he should hit.

• If Black rolls 11, he should prime (i.e., 7(2) 5(2)). Exception: If White slots with opening 41 (i.e., 13/9 6/5), Black should hit (for money or at GS).


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