Backgammon Articles

In the Beginning
by Nack Ballard & Paul Weaver
Thank you to Nack Ballard and Paul Weaver for their kind permission
to reproduce this article, which originally appeared in GammonVillage in 2003.

This is Part 2 of a three-part series.  Part 1 begins here.

Do you have Snowie 4 or Gnu BG?  Backgammon Openings, Book A is on the verge of going to press, and the Backgammon Openings project (which will cover many more books) is going strong.

We still need help with rollouts. If you would like to be involved in this exciting project, please contact Nack Ballard at or Paul Weaver at There is no commitment, no obligation. You can stop any time.

We thank those who help us with the rollouts in acknowledgment sections of our books and give complimentary copies to the five volunteers who do the most rollouts for us. This is a standing offer for every book that we write in this series. Regular rollout participants are also sent instructive analyses (on positions rolled out) from time to time.

We are rolling out some fascinating and controversial third-roll positions, and rollout participants are learning a lot! We all look forward to you joining us.

In the Beginning, Part 2
As we left it at the end of Part 1, Red had chosen to play his opening 32 by coming up with the 3 and coming down with the 2. This move is notated "24/21, 13/11", or simply "32-split". The position after Red has made his 32-split is shown in the main diagram below.

Now it is White's turn, and she rolls 51. What is her best play?

To be better equipped to answer this question, let us first learn what we can about how to play a 51 on the very first roll.

How to Play an Opening 51
Opening Position

2A: White to play 51

The two popular plays, 51-split and 51-slot, are diagrammed below.

After splitting (24/23, 13/8) with opening 51, White's position (2B) may look stiff and awkward, but two-thirds of her numbers make a new point somewhere on her next roll. Most of her remaining numbers run into the outfield.

White will frequently develop a strong offensive position by patiently waiting for good rolls. She incurs much less risk by employing the seemingly unsophisticated strategy of splitting instead of slotting with opening 51.

2B: After opening 51-split

2C: After opening 51-slot

In backgammon archives as far back as 1745 (A Short Treatise on the Game of Backgammon, by Edmund Hoyle), and up to the literature of the present, 51-split and 51-slot have been correctly touted as the best opening plays for 51. (Thank you, Mark Driver, for all your helpful input and research.)

So, contrary to what many people believe, slotting with opening 51, 41 or 21 is not just an invention of the 1970's. For over 250 years, various backgammon players have experimented with slotting the 5pt on the opening roll.

But the 70's was the decade in which slotting peaked. This movement is largely accredited to Barclay Cooke, a very successful player who routinely slotted in the late 60's. By the latter half of the 70's, and into the 80's, virtually every strong player slotted with 51 (and 41 21).

In Backgammon the Cruelest Game (1974), coauthor Cooke asserted:

"... [White] has no better option than to attempt to secure her 5 point ... Under no circumstances should she split her back men ... the [opponent's] 1 point is her main security ... The risks are serious, the rewards slight."

Soon after, anyone who did not slot was automatically considered to be a weak player. It was assumed paramount to slot in order to vie for key offensive points as early as possible and put checkers efficiently into play. Losing ground in the race (by getting hit) was hardly thought to matter, as long as the position was pure, and a backgame was still a live possibility.

However, in the last decade or two, computer rollouts have proven that the race is important even at the beginning of the game. As a result, the modern thinking is that slotting with 51 is (slightly) worse. Consider this:

  • Red hits with 14 numbers, and the cost to White is substantial.

  • Even when Red misses, he might get another crack. White has 10 numbers that fail to cover (or hide) the blot on her 5pt.

  • White has a better chance than was previously believed, of developing a strong offensive position without slotting.
Current Snowie-4 rollouts favor 51-split (2B) over 51-slot (2C), by .014 cubeless. [At the gammon go match score (you need two points, opponent needs one point, Crawford), 51-slot is tied with 51-split.]

A difference of .014 between two plays is not large. Therefore, many players will slot anyway, if they think that they will make fewer errors than their (weaker) opponents will make in the ensuing complications.

Perhaps it is because most players believe they are stronger than at least 90% of their opponents that 51-slot still enjoys a bit of a following. Or, perhaps they do not quite believe the computer. Or, perhaps they simply prefer to play more interesting games.

Other ways of playing opening 51 have been attempted as well. For example, in Modern Backgammon, written by Grosvenor Nichols in 1928, it is mentioned that "some players like 13/7" (see position 2D, left).

Any player who might have tried slotting the 7pt was probably unaware that the 5pt is a more desirable point to make. After all, the opponent has more numbers that hit the 7pt blot. And if the blot is missed, just as many numbers cover the 5pt as the 7pt.

Tried in the 1920's

2D: After 51-down
For Backgame Lovers

2E: After 51-double-slot

Starting in the 1960's or 70's, backgame fanatics tried some ultra-aggressive openers, such as the 51-double-slot in Position 2E (right). However, as human players got stronger at out-timing backgames, these wild plays died out.

In the 1990's, it was possible to trick some computer programs with such plays. Bots routinely doubled and redoubled well-timed backgames, so a human could escalate the cube to practically any level desired. (Winning even a slight majority of the huge games more than made up for losing most of the small games.)

Nowadays, the 51-double-slot is a poor gambit even against computers. Bots that still underestimate backgames have a cube cap that evades the trap.

Another alternative with opening 51, more sensible than 2D or 2E, is to run a back checker out to the opponent's bar point (24/18). The position after making this 51-run play is shown below (2F).

We will pay special attention to this 51-run move, because it was the move chosen (albeit on the second roll) in the actual game.

2F: After opening 51-run

While less commonly played than 51-split or 51-slot, over the years 51-run has enjoyed a few stints of popularity. Surprisingly little, though, has been written on it.

After extensive research, we were able to uncover a handful of books that mentioned 51-run. Of these, only two actually recommended it:

In Vanity Fair's Backgammon to Win, written in 1930, author George Mabardi asserts that 51-run is clearly the right play, listing 51-slot and 51-split as the "wrong plays". He goes on to describe splitting with the ace as "futile exposure".

Almost as if in answer to the use of the word "exposure", Oswald Jacoby and John Crawford, in The Backgammon Book (1970), defend the virtues of the ace-split by demonstrating that it is not as dangerous as Mabardi (or later Cooke) apparently believed.

However, note that Mabardi's full phrase was "futile exposure". His implication seems to be that if White is going to turn her back anchor into blots, she may as well try to get something useful for it (in this case, the opponent's bar point). This perspective seems worthy of some consideration.

Indeed, Jacoby and Crawford were anything but closed-minded. They lent part of their support to 51-slot, and also to 51-run:

"... a good deal to recommend [it] ... to move a back man right to the [Red] bar point. It's an interesting gambit—you have lost little if your opponent takes the bait and hits that blot, and moreover you have a very good chance of hitting him back when coming off the bar."

All during the 20th century, the 51-run play enjoyed a following, albeit a minority following. It was not until the 1990's, when computers got their teeth into it by rolling it out, that 51-run went out of fashion.

In the pre-bot days, it was believed that 52 and 51 were "clearly the worst opening rolls". Modern rollouts suggest this is not quite true, but even if so, it is only a matter, at most, of a few thousandths of a point in equity.

This doctrine, that 51 was such a poor roll, caused many players to view running out to the opponent's bar point (24/18) as the best play of a bad lot. With 51, one cannot also bring down a builder as with 62, 63 or 64, but since 51 was believed to be such a terrible roll, it seemed quite reasonable to settle for less.

However, it is not necessary to settle for that much less. An opening roll of 51, if played correctly, is only a hair worse (if worse at all) than the 62 63 64 rolls.

What has been ignored, completely in the older literature, and to a large degree even in modern literature, is how valuable it is to bring down a five from the 13pt to the 8pt.

2G: Before bringing down a 5

2H: After bringing down a 5

Until recently, Positions 2G and 2H were adjudged to be essentially equivalent in value. 13/8 was imagined to be a neutral way to play a five.

Because it does not threaten to make any new points, the addition of another spare on the 8pt has been viewed as a redundancy, having little or no bearing on the strength of White's position.

In fact, 13/8 is a significant positional gain for White, for these reasons:

  • By reinforcing the underrated 8pt, it is possible to use one of its spares to make a new point without stripping the 8pt. Also, it is possible to avoid breaking the 8pt when rolling doublets (or when hitting from it a second time). For example, White can now make a four-point prime with double 1's.

  • By adding another checker to her side of the board, White can attack more effectively, with a greater chance of closing Red out. Hence Red will incur a greater risk if he splits his back checkers.

The Game Position
Returning to the game position, White has a 51 to play on the second roll. How has the situation changed from the opening roll?

White to play 51

One change is that Red's back checkers are split. As a result, if White slots (either the 7pt or the 5pt), she will be giving Red a double-shot. If it is arguably a misuse of an ace to play 51-slot on the opening roll (leaving a single shot), then slotting is certainly wrong after Red splits.

By process of elimination, the best way for White to play her ace is 24/23.

Having played the ace, the position is:

2I: White to play a lone 5

Now the question is: Which five should be played?

There are four legal fives: 8/3, 6/1*, 13/8, and 23/18.

First of all, we can eliminate 8/3 as a candidate. This would be completely counter-productive, stripping the 8pt and leaving a deep blot.

Hitting with 6/1* deserves a bit more contemplation. When you have a legal play that hits, it should at least be considered, because it deprives your opponent of most of his offensive point-making numbers (all but doublets).

To help us decide, let us explore the following question:

On the second roll, when is it correct to split the back checkers and hit on the ace point?

When to Split and Hit on the Ace Point
When splitting, there are two reasons to hit on the ace point:
  1. To protect a split back checker that is exposed to three builders.
  2. To break communication between enemy blots on the 7pt and 1pt.
For example:

2J: White to play 52

2K: White correctly
hits and splits with 52

Let us examine these two reasons for hitting on the ace point, as they apply to Position 2J / 2K (above):

  1. To protect a split back checker that is exposed to three builders. By splitting, White has exposed herself to attack by Red's 9pt, 8pt, and 6pt builders. She hits on her ace point to force Red to use half his roll to enter, deflecting him from making an offensive point (on White's head or otherwise). White thus transforms her 22pt checker from a target into a weapon.

  2. To break communication between enemy blots on the 7pt and 1pt. After Red splits with a six, White hits on the ace point to decrease Red's chance of anchoring on White's 7pt.
It turns out that both of the above reasons must be in effect for it to be clearly correct to hit on the ace point. If only one reason is in effect, it is usually a borderline decision. If neither reason, it is definitely wrong to hit on the ace point.

Let us now return to the (post-ace) game position and apply what we know.

White to play a lone 5

Let's see ... On the far side, White's split checker on Red's 2pt is relatively safe. Red has only two builders (on his 8pt and 6pt) bearing on his 2pt.

On White's side of the board, Red has not split to White's 7pt, only to her 4pt. White's purpose of hitting on the ace point is defeated because Red has direct 4's (from the roof) to make an advanced anchor.

Neither of the two pivotal reasons for hitting exists, so it would clearly be a mistake for White to exile a checker to her ace point.

Thus, we are left with two reasonable plays, shown in 2L and 2M (below):

51-Run on the Second Roll

2L: After White runs
with the 5 (23/18)

2M: After White comes
down with the 5 (13/8)

In Position 2L, White has gone out to the 18pt with the five. Her goal is the same as when making this play on the opening roll. That is, she hopes to accomplish one of three objectives:

  1. Make the opponent's bar point,
  2. Escape a checker to the midpoint (13pt), or
  3. Hit a return shot from the roof if Red hits either of White's blots.
There is no guarantee that White will be able to accomplish any of these three objectives. There is a risk involved in running to the 18pt. Red has 10 great attacking rolls (41 61 64 11 33 55 66) after White runs in 2L.

In spite of this, on balance there is more reason to run after the opponent has brought a builder down! A fourth objective comes into play: To confront Red's outfield blot and present him with a dilemma between hitting and making a key point.

For example, with 63 or 31, Red would love to make the 5pt. With 42, he would love to make the 4pt (indeed, he probably should anyway). However, by doing so, he not only fails to hit a blot that is threatening to anchor, but he also exposes his 11pt blot to a direct shot. This theme is important in the next several positions of this article, as well.

Running with 51 in 2L is still a mistake—just not as big a mistake as running with 51 on the opening roll.

Whether on the first or second roll, it is clearly a gain to advance the blot from the 23pt to the 18pt. However, it is a larger gain to come down from the 13pt with the five (as in Position 2M). Adding a ninth checker to the zone increases the pressure on Red's back blots, and balances White's distribution. (To review the virtues of this five, see the text following Position 2G.)

So ... is there any opening play after which White should run with 51 (24/18) on the second roll?

The answer is no. However, there is one opening play against which 51-run is almost correct:

Assume for the moment that Red's opening 32 had been played as in Position 2N, left. (This alternate split was discussed in Part 1. Though it is seldom seen, a lengthy Snowie-4 rollout indicates its value is very close to the more common move shown on the right.)

Red played 24/22, 13/10

2N: White to play 51
Red played 24/21, 13/11

2O: White to play 51

There is a much stronger case for playing 51-run (24/18) in Position 2N than Position 2O. Although very few backgammon players seem to realize this, coming out to the 18pt is a more reasonable play when Red's outfield blot is on his 10pt (Position 2N) than when it is on his 9pt or 11pt (as in Position 2O).

Playing 24/18 in Position 2N, to reach Position 2P (below) will duplicate Red's 3's. Red can make his 5pt or 10pt with virtually all his 3's (including 21), the same 3's that are needed to hit with his outfield builder.

By contrast, if White plays 24/18 in Position 2O, to reach Position 2Q (below), Red's medium-sized numbers will be diversified: 3's still make the 5pt (or 21pt), but 4's hit, and 2's make the 11pt.

Moreover: The 10pt builder aims not only at the 5pt, but also at the 4pt (unlike the 11pt builder in 2Q). Accordingly, running to the 18pt (as shown in 2P) increases the numbers that give Red a tough choice between hitting and making a point. Red should not hit with 42 in either position, but in 2P, he should also not hit with 51 53 62 64.

Consequently, although 51-run is clearly wrong in 2O, the rollout suggests that in 2N, 51-run is very nearly as good as 51-split.

2P: Red's 3's are duplicated

2Q: 2's, 3's, 4's diversified

The Effect of DMP on 51-Run
Finally, we will consider the effect of double match point (DMP). There is more support at this score, than at any other, to play 51-run (24/18). [Double match point (DMP) is the final game; if either player wins, he or she wins the match. At this score, neither player has any added incentive to win a gammon.]

Why is DMP an especially efficient score at which to try 51-run?

Running with 51 will win fewer gammons than splitting with 51 because it fails to add a ninth checker to the zone. Also, 51-run will lose more gammons than 51-split, because 51-run is more vulnerable to attack.

However, these gammon considerations are irrelevant at DMP.

The 18pt is a great anchor from which to win single games. It is a (relatively) easy anchor from which to run, and it is a resilient anchor from which to defend a game after the opponent has escaped, because it is six pips away from the opponent's midpoint.

In Position 2N, 51-run is marginally correct at DMP (the after-position is shown in 2P).

51-Run as a Third Roll Play
There are numerous third-roll positions for which 51-run is the best play. Here are four examples:

2R: 54-down, 65-run, 51

2S: 52-down, 65-run, 51

2T: 54-down, 52-down, 51

2U: 54-down, 43-down, 51

In each of the above positions, White has brought down two builders, reducing her midpoint to only three checkers. To bring down yet another five would strip the midpoint and overload the 8pt. Or, to hit on the ace point (after Red runs) fails to accomplish any of the key objectives discussed earlier.

Other possibilities include stacking a sixth checker on the 6pt, or slotting the 5pt or 4pt, but these, too, leave much to be desired. A builder in White's outfield is generally better than a checker that is stacked or slotted.

White is therefore happy to resort to 51-run (24/18) in each of the four positions.

In the last of the four positions (2U), 51-run may look suicidal, but actually it is correct by the largest margin of the four positions! Running to the opponent's bar point functions as a brilliant deflection:

Red is not so thrilled to hit loose on the 7pt, or even to make the 7pt. The 5pt or 4pt is not only more valuable, but many of the numbers that make an inner point also unstack the 6pt.

We have found several other third-roll and fourth-roll positions for which 51-run is best.

Part 2 in a Nutshell
  • With an opening 51, the main plays are splitting (24/23, 13/8) and slotting (13/8, 6/5). Running with 51 (24/18) is a mistake.

  • On the second roll, 51-run is never correct, except at DMP, when it is very close after certain opening rolls.

  • On the third roll, 51-run is sometimes right when the same player has preceded it with a 54-down or 52-down opener.

  • Early in the game, DMP is generally the score at which 51-run is the most favorable, or the least unfavorable.

  • Splitting and hitting on the ace point can be effective under certain conditions on the second roll, but not with a roll of 51.

  • Bringing down a five (13/8) is a much bigger improvement to the starting position than most players realize.

Game Continuation
Roll #1:  Red began with 32-split (24/21, 13/11). This is the most popular play today, and is tied with (or perhaps a hair better than) 32-down (13/11, 13/10). A very close alternative is 32-reverse-split (24/22, 13/10).

Roll #2:  White responded with 51-run (24/18). This demonstrated some insight, though 51-split would have been better (even at DMP).

We have flipped the board back around—showing it from Red's point of view—so that you can contemplate his next roll (see the updated game diagram below).

The subject of Part 3 of this article will be:

How should Red play double 4's?

You may wish to ponder this 44 roll and try to figure out the best play. For extra credit, attempt to determine what the correct play might be at various match scores, because we will be covering those as well.

Continue to Part 3

Nack Ballard is a top international backgammon player. His achievements include winning the Open Section of the World Amateur Championships in Las Vegas in 1982 and reaching the semifinals in the prestigious PartyGammon Million tournament in the Bahamas in 2007. He is currently ranked #1 by his peers on the 2005 Giants of Backgammon list.

Paul Weaver is also a top international player. He was rated #3 on the 2002 edition of Kent Goulding's Rating List (updated by Laila Leonhardt) and is ranked #16 player in the world on the 2005 Giants of Backgammon list.


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