This article is aimed at improving the skill level of backgammon players of all strengths. Starting with the opening move, Part 1 of this article aims mostly at teaching beginning and intermediate players, though it is also written in such a way that we believe advanced players will have an opportunity to sharpen their awareness of the opening phase of the game. Parts 2 and 3 build on earlier knowledge and gradually present a greater challenge.

Some of the diagrams in this article have been intentionally repeated, to minimize your need to scroll up or down in order to follow the text.

Please note the following conventions we have adopted in the text:

1. When referring to dice rolls, we use no hyphens, and usually no commas or conjunctions to separate them. So, for example, 31 42 61 53 64 are the opening rolls that allow a player to make a point.

2. We abbreviate point to pt, placing it immediately after the point number. So, for example, 31 makes the 5pt, or 42 makes the 4pt, and so on.

3. The player at the bottom of the diagram (e.g., in Part 1 it is Red) is referred to as he, or occasionally you. The player at the top of the diagram (e.g., in Part 1 it is White) is referred to as she.

The answer is simple: It is the starting position, shown below. Because this position arises more than any other position in backgammon, it is important to make sure that you know the best play for each possible roll here, more so than in any other position.

The best play for a particular roll may vary, depending upon the score of the match, the relative strength or style of the opponent, or even circumstances of the moment. But, once these factors are taken into account, there is a play that optimizes a player's equity, and that is what we mean by best play.

The Starting Position

There are 17 legal ways of playing an opening 32, and about half of them have probably been tried, by somebody, somewhere, sometime.

For an opening roll, stacking is to be avoided, if possible. This eliminates 13/8, or in particular, any play that moves a two from the 8pt to the already-tall 6pt.

Moves that use the deuce to slot the 4pt, or the three to slot the 5pt, had a brief stint of popularity in the late 70's and early 80's, but were convincingly shot down.

We are left with four serious contenders for the best opening 32. One can move:

1. 32-down: Both midpoint checkers (13/11, 13/10).
2. 32-split: A back checker 3, and a midpoint checker 2 (24/21, 13/11).
3. 32-reverse-split: A back checker 2, a midpoint checker 3 (24/22, 13/10).
4. 32-up: Both back checkers (24/22, 24/21).

1A: 32-down	1B: 32-split
1C: 32-reverse-split	1D: 32-up

Let us now isolate and compare these two different threes:

1E: Lone 3 played down

1F: Lone 3 played up

What are the liabilities of each of these threes?

In diagram 1E (left), where 3-down is played, Red allows White to hit outside with 4 numbers out of 36. These numbers are 63 54 (we are not counting 33 because it is just as good for White not to hit with that number).

In diagram 1F (right), where 3-up is played, Red allows White to point on his blot with 5 numbers (42 44 22 11).

Getting hit outside (in 1E) costs Red 11 more pips, but getting pointed on inside (in 1F) risks 3 more painful fanning numbers (64 44). Let's call these liabilities a wash.

What are the assets of each of these threes?

In 1E, Red's 10pt builder gives him 10 new numbers to make the 7pt, 5pt or 4pt (63 53 51 64 62), and makes it more dangerous for White to split to any of those three points. Additionally, Red's 43 32 21 can make his 10pt next turn.

In 1F, Red's 21pt checker threatens to run to safety with 62, or to make a good anchor (18pt, 20pt or 21pt) with 63 41 53 43 32 21. Furthermore, it hinders White from slotting, or bringing down a builder to the 10pt or 9pt.

On balance, these assets seem to favor coming up (1F). However, there are two final minor points not yet mentioned:

1. Coming up gives White more hitting options to gain a tempo. Hitting puts a lot of pips at risk for White, but rates to take the pressure off her elsewhere and impede Red's development.

2. Doublets tend to play better if the two back checkers are on the same point. This is always a hidden drawback of splitting. In this case, it is mostly Red's 66 that will be affected, and to a lesser degree his 44.

1G: Lone 2 played down

1H: Lone 2 played up

What are the liabilities of each of these deuces?

In 1G, with 2-down, Red allows White to hit outside with 64.

In 1H, with 2-up, Red allows White's 33 and 53 to point on him, and her 55 to double-point on him. White's attacking 55 was featured as the main reason for not splitting with a deuce in old backgammon literature, but in reality it is only a small part of the equation.

It appears that the liabilities of the two deuces are close to a wash.

What are the assets of each of these deuces?

In diagram 1G (left), 2-down gives Red new numbers on the next roll to make his 7pt or his 5pt, namely 64 41 63 (and 61 now makes the better of the two points). It becomes more dangerous for White to split to either of these key points. Moreover, Red's 62 52 32 21 can make his 11pt next turn.

In diagram 1H (right), Red's 2-up will be able to run to safety with 63 or 54, anchor on the 18pt with 64, or on the 22pt with 52 32. Also, White is inhibited from bringing down a builder with a 2, 3 or 4 (particularly a 4), or from slotting.

From this analysis, preventing White from splitting or building appears to be equally valuable. However, running or anchoring on the 22pt in 1H does not sound as valuable as the offensive point-making numbers in 1G. Why is the asset side of the ledger so light for 1H?

Much of the reason 1H falls short has to do with the fact that Red's 24pt checker and 22pt checker are two pips apart, just like his 8pt and 6pt. By splitting to the 22pt, Red duplicates some of his point-making rolls on both sides of the board.

Splitting with a deuce gives Red 6 numbers that make an advanced anchor on his next shake: 31 42 64. But of these, Red's 64 is the only roll that plays much better on his next roll as a result of his splitting. The point is that 31 and 42 are already strong rolls for Red, making his 5pt or 4pt.

Also, there are the same two minor factors against splitting as mentioned earlier (gives up tempi to White's hits, and Red's doublets play worse).

We cannot eliminate them automatically without considering the dynamic interplay between the choice of the 3 and playing 2-up. However, we have done that as well (the details of which are beyond the scope of this article).

Our conclusion is that interplay narrows the gap, the inferiority of playing the 2-up remains the deciding factor. In the case of combining 3-up with 2-up, it is clearly insufficient to overcome 2-up's inferiority. However, in the case of 3-down with 2-up, we discovered enough positive interplay to cause 32-reverse-split to be a very close third choice. Still, as spectators love a showdown between two entities, and two candidates are more easily compared than three, we have simplified the contest to the two finalists that play the proper deuce (2-down) from the cross-table of diagrams presented earlier (i.e., 1A and 1B, but not 1C and 1D):

1I: 3-down with 2-down

1J: 3-up with 2-down

And now let us analyze the interplay between our two finalists:

The negative aspect of combining 3-down with 2-down (as shown in 1I) is that it reduces the flexible midpoint to three checkers. If a third midpoint checker is subsequently used to make a point or hit, then the midpoint would be stripped to two checkers; to use it yet again would either leave a blot, relinquish outfield control, or both.

The positive aspect of combining 3-down with 2-down is the synergy between the 11pt and 10pt checkers. If White hits with a 9, Red has added 51 41 21 11 to his arsenal of numbers that hit back. If Red is not hit, 30 numbers will make a key point (7pt, 5pt or 4pt) on his next roll.

The negative aspect outweighs the positive aspect by a tiny margin. However, for practical purposes, 32-down (1I) can be considered tied with 32-split (1J). They are close enough that stylistic preference will often be the deciding factor.

In the majority of these books, the 32-split in the right diagram (1J) is not even mentioned, and when it is mentioned, it is dismissed as "inferior".

There are three notable exceptions: The New York Times Book of Backgammon (James and Mary Zita Jacoby, 1973), The Clermont Book of Backgammon (David Dor-el, 1975), and Backgammon (Paul Magriel, 1976). These books give diagram 1I and 1J as the two good ways to play an opening 32. This is a more appropriate representation, although no books give any serious mention to 32-reverse-split (24/20, 13/10, diagrammed in 1C), a third play that is so close in value to the other two that we can recommend it as a fine alternative.

Perhaps the historical bias against 32-reverse-split is tied in with the historical bias against opening 52-split (13/8, 13/10), based on the fear of being blitzed by the single number of double 5s.

The regular 32-split (1J) was rarely seen on an actual backgammon board in the 70's. One of the co-authors of this article adopted it in 1980, though he usually used it as a weapon only when leading in a match. Gradually, year by year, the 32-split gained in popularity. By 1990, it was given equal time with 32-down, and by 1995, helped along by players' access to and belief in backgammon software, 32-split had become the play of choice.

In the mid to late 1990's, state-of-the-art rollouts even supported the reverse 32-split (diagram 1C, also repeated in 1K below) as the second best play. One of the co-authors of this article happened to witness a semi-finals match played by Kent Goulding a decade or so ago. He opened a game with 32-down, and his opponent chirped, "third best!" Kent won this game and subsequently the match, advancing to the finals and relegating his opponent to third-place prize money. As he rose from the table, he pointed at his opponent and chirped back "third best!"

As backgammon programs became stronger, they gradually pushed out the reverse split (see 1K below) and claimed, through rollouts, it to be an insufficiently strong contender.

In a recent and little-known reversal, Snowie-4 rollouts have put 32-reverse-split back into very close contention. Nevertheless, the earlier claims of this play being wrong by as much as a percent or two seem to be enough to spook virtually everyone from playing it.

The Uncommon Opening 32 Plays
1K: 32-reverse-split	1L: 32-up

By bringing two checkers down, you are concentrating on offense, giving yourself a greater chance to prime or attack your opponent. This play will win more gammons. Conversely, you are damaged to a lesser extent when your opponent's 9's hit you and send a third checker back, because getting gammoned costs you no more than losing a single game.

In fact, anytime you are substantially behind in the match (or also if you are a significantly stronger player than your opponent), 32-down is generally the recommended approach, to mix things up (increase volatility).

If the situation is reversed, and you are leading in the match, or gammons help only your opponent, then the 32-split (repeated in 1N below) is preferred.

By splitting with the 3, you are less likely to have a third checker sent back, and more likely to obtain an advanced anchor, which is a great defense against getting gammoned.

At a pure gammon save score (gammons help only the opponent), 32-up (1L) and 32-reverse-split (1K) do nearly as well as 1N, and have the potential advantage of giving the opponent unfamiliar decisions.

For example, in diagram 1L (above), ask yourself how you would play the following numbers for White: 65 64 62 54 52 43 32. We believe that most players would get at least half of them wrong. (If you join us as a Snowie-4 rollout participant, we will tell you the rolled-out answers).

[A similar case might be made for the 32-reverse-split (diagram 1K), though 64 43 51 41 would seem to be the only error-prone responses].

This should be welcome news for those of you who like to experiment. If you are the one playing one of these offbeat 32 openers, it is only your opponent who has to be concerned with playing the correct responses.

In money play, in level match play, or at double-match point, rollouts currently support the 32-split (repeated in diagram 1N, on the right here), but only by a smidgen over 32-down (diagram 1M, left).

The Popular Opening 32 Plays
1M: 32-down	1N: 32-split

In fact, 32-split (right diagram) was the move chosen in the actual game we will be analyzing. In the next installment or two of this article, we will explore White's response, and Red's next roll in reply.

Continue to Part 2