Early Doubles
GammonLife Article 2
by
Nack Ballard

 

Introduction

Welcome to the second article of the Early Doubles series. “Early” refers to the first few moves of the game. “Doubles” is a pun that refers to both (1) checker plays with doublets and (2) cube decisions.

This series of articles is formatted in a style similar to that of Backgammon Openings. To find out more about this path-breaking book series, click here.

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 (Black’s choices) appear on the right-hand side: they are designated by lower-case letters (a, b, c…) and appear in order of strength.

For example, for problem #1, the best play (or “answer”) is 1a and the second best play is 1b. If you like testing yourself, cover the text near the problem diagram with your hand.

The caption to a problem diagram (e.g., “42P-11” for problem #2) denotes the sequence of rolls and plays that occurred to reach the position. This information is entirely nonessential to understanding the text, but if you are interested in applications of nactation, click here.

Point numbers are abbreviated; e.g., I call the 4 point the “4pt.” When listing rolls, I dispense with hyphens, commas and conjunctions; e.g., “The best opening rolls are 31 42 61.” Finally, I often refer to Black as male (he, his) and White as female (she, her). These conventions help to keep the text crisp.

All competitive plays have been rolled out full, 3-ply precise, live cube, and at least 15,552 trials on both Snowie-4 and GNUbg. If you are interested in the Rollout Project, click here.

These articles employ “error scale” terms that describe the relative value of the best play (tied, barely correct, marginally correct, correct, blowout, wipeout) and of inferior plays (tied, very close, close, mistake, blunder, whopper). These terms are easy to grasp intuitively. However, if you would like to know the corresponding equity ranges or learn more about the Error Scale, click here.

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.

If the best money play is overturned (and better than tied) at DMP (double match point), GS (gammon save) or GG (gammon go), the exception is listed in a text box. If you are not interested in match score exceptions, skip the text boxes. To better understand money, DMP, GS and GG, read the Match Score Explanations article.

Okay, on to the article!

 

 

Double 1s: Prime or Split vs a Point

Once upon a time, the rules of backgammon allowed for the player with the higher initial die to reroll both dice. Throwing doublets was therefore possible on the very first roll of the game.

#1    Black to play two aces

  
#1
                                                                                                       
To better understand the theory of double 1s in the early game, let us travel back in time and imagine that we have thrown double 1s as an opening roll.

In the early game, it is almost always right, when possible, to make the 5pt while unstacking the 6pt with part of a double 1s roll, as shown.

In position #1, Black has two more aces to play.
 

1a
                                                                                                 
Priming (at right) is correct. Black builds three points in a row and threatens to make a fourth (and usually consecutive) offensive point with a majority of his numbers.

Black’s liability in 1a is his 8pt blot. He will “regret” his play if he is hit (by 61 52 43), but even then he retains the asset of his bar point.

In a proposition (conceived decades ago), White is given the cube and is on roll in 1a. Cube ownership is valuable, but it is insufficient to compensate White for Black’s powerful position.

 

1a    Best

1b           
                                                                                                       
Splitting (as shown) is second best. This play increases Black’s outfield control, inhibiting White from bringing down builders; even so it is

a mistake.

Black should save the easy task for next turn. In 1a, he poised to split with an abundance of numbers; by contrast, in 1b, he poised to make his bar point with only 5 numbers (66 61 33 11).

In failing to seize the opportunity to block White’s 6s, Black’s play in 1b is too easygoing.

  

 1b    Mistake
 

In this article and in the next two, we will examine positions on the second roll that favor splitting with double 1s or in which splitting is a closer play than it would be on the opening roll.

Problems are always Black to play double 1s, indicated by the black dice. How would you play double 1s in Problem #2 (below)?

#2            42P-11



2a
                                                                                                
Priming (at right) is marginally correct. The reasons that support priming in 1a apply to 2a as well.

After moving, Black trails by 2 pips plus the roll — another aspect favoring the 2a play. In a battle of primes, Black has a small advantage in timing.

Black’s 5s and 3s, which are blocked on the other side of the board, attend to his 8pt blot (assuming it is not hit): he will cover it with a 5 or sometimes lift it with a (non-covering) 3.

  

2a    Best
 
2b
                                                                                                         
Splitting (at right) is close: it is a smaller error here than in the opening position.

After White makes a high inside point, Black should give greater credence to splitting (relative to moves that focus solely on offense) because

• White is starting to build a prime; Black has
  more reason to activate his back checkers.
                                                                                                            

• White’s 8pt is stripped. If she uses one checker
  from her 8pt to make a point (or hit), she will
  expose a blot there.
                                                                                                    

• If Black’s 8pt blot is hit in 2a, he will fan with 3
  more numbers and hit back with 2 fewer
  numbers than he will if he is hit in 1a.

  

2b    Close
 
2c
                                                                                                         
Splitting and fudging (the 6pt spare) is a big mistake. This play is an inferior version of 2b on both sides of the board: Black weakens his offensive structure with 6/5 instead of upgrading his defensive stance with 23/22.

In playing 2c, Black avoids the duplication of his own 42 (see 2b), but he duplicates 65 instead.

In #2, anchoring on the 23pt (24/23(2) 6/5(2), not diagrammed) is no better than 2c.



  

2c    Mistake
 

Let us now examine the same situation with White owning her 5pt instead of her 4pt. How would you play double 1s if you were Black in the position below?

#3           31P-11

 

3a
                                                                                                 
Splitting (at right) is tied. This information is not yet widely known.

The three bullets in 2b (which address White’s developing prime, frozen 8pt, and second inside point) also apply to 3a. The first bullet applies even more to 3a, because White’s 5pt has greater priming potential than her 4pt: Black has that much more incentive to escape.

An interesting supplemental factor is that Black has duplicated his own 42 in 2b, whereas he has not duplicated his own 31 in 3a.

  

3a    Best (Tied)

3b           

Priming is also tied. Factors in favor of this play are discussed in 1a.

When two plays are tied, the play diagrammed first (in this case 3a, splitting, shown above) is a hair better (than 3b, shown at right) based on an average of Snowie-4 and GNUbg rollout data.

Priming is sensible if Black trails in a match.


  

 3b    Best (Tied)



Summary Contrast

Positions #2 and #3 do not illustrate a full contrast, because splitting does not clearly dominate priming in #3. Notwithstanding, it is useful to compare the two positions, one under the other. The problem diagrams are on the left and the solution diagrams are on the right.


#2    42P-11

  

2a    Best
     

#3    31P-11

  

3a    Best (Tied)
   

3b    Best (Tied)
     

In short, Black is more eager to prime and less anxious to split when White owns her 4pt (in #2) than when White owns her 5pt (in #3).



Bonus

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

#4    61P-11
  
#4
                                                                                                       
Priming (8/7(2) 6/5(2)) is barely correct. In #4, White has three points in a row. Compare with #2, where she owns her 4pt instead of her 7pt and has two gaps in her blockade. Black has greater motive to split in #4 than in #2.

On the other hand, compare #4 to #3. White’s prime is slightly superior here but her board is clearly inferior. If Black primes and his 8pt blot is hit, he faces a stronger board in #3 (also in #2, but less so) than he does in #4.

Recap: Comparing #4 to #2, we see that Black’s decision is affected more by the strength of White’s prime than by the strength of her board. Comparing #4 to #3, we see the opposite is true, because White’s 5pt is stronger than her 4pt in both respects.

On balance, conditions uphold Black’s priming play after White’s 42 more than after White’s 61. Black has the most incentive to split after White’s 31, when Black’s priming play is only tied.



#5    11N-11
  
#5
             
As mentioned above the #1 diagram, double 1s was once a legal opening roll. Here (on the left), White has played it.

In response, suppose Black also rolls double 1s. Splitting (24/22 6/5(2)) is correct. Facing a stronger prime here than in the other four positions, Black is compelled to escape or secure a better anchor as soon as possible.

Splitting, moreover, threatens White’s 8pt blot. The second best play, 24/23(2) 6/5(2), does so, too, but in a less positive fashion: it is a mistake.

Priming (8/7(2) 6/5(2)) is a blunder that puts Black down a tempo in development. In order to minimize his disadvantage, he should strive for dynamic imbalance by splitting (24/22 6/5(2)).

The value in understanding position #5 is not just theoretical. There are many positions that arise on the third and subsequent rolls in which splitting with double 1s (or any roll) is urgent because the opponent is rapidly building a prime.

Homework (if you like): Before you read my next two Early Doubles articles (here on GammonLife), list other situations on the second roll (i.e., in response to an opening play) where you think splitting with double aces may as good as or better than priming.

 

Conclusion

If White has made a point on the opening roll (with standard backgammon rules in effect), Black should make the priming play (8/7(2) 6/5(2)) with double 1s.

Exception: If White opens with 31, Black’s splitting play (24/22 6/5(2)) is tied with — actually, a touch better than — his priming play. (Also, if White opens with 61, Black should split at GS.)




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