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Backgammon Problems: Early Game

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Structure and Risk-Taking – Part 2 – The Solution

From the November 2024 blog post, here’s a pair of very similar positions that shows how an (apparently) small change in an early-game position can dramatically change your approach.

Cash game. White to play 5-1

 

Cash game. White to Play 5-1

 

These two positions show a routine situation in the early middle game. Both sides have an anchor, and the race is very close. White’s position is slightly preferable since  he has better chances of establishing a block against Black’s anchor.

White’s roll of 5-1 is a pretty routine shot and he has two obvious choices: 9/3, starting the 3-point, and 13/8 9/8, playing safe while keeping all checkers is front of Black. Of these two plays, 9/3 is slightly better; 13/8 9/8 creates a big stack which will prove awkward in some of the upcoming variations. In the middle game, we try to avoid creating big stacks unless alternatives are really weak. There’s nothing structurally wrong with 9/3, so it’s a better play here.

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Early Doubles

Cash game, center cube.

Should White double? If he doubles, should Black take or drop?

In the last post we talked about the importance of cube benchmark positions — positions where one of the cube decisions (either doubling or taking) was perfectly marginal, while the other was completely clear. Learning typical benchmark positions gives us the ability to analyze a wide variety of related positions over the board with unusual accuracy.

This position shows us another type of useful benchmark. We’re currently just four moves into the game. The opening sequence was

White: 5-3, making the 3-point.
Black: 4-3, bringing down two builders.
White: 6-2, hitting.
Black: 6-3, dancing.

With Black on the bar and White clearly having the upper hand, White now contemplates a double. Considering Sylvester’s three criteria for offering an initial double, here’s how White stands:

Race: solid edge for White. His hit and Black’s fan leaves White up 25 pips, 151 to 176.

Threats: small edge for White. He’s threatening to hit Black’s other blot, but White’s weak board means this is really just a threat to gain a little more ground in the race.

Position: Small but solid edge for White. He has a 2-point board, while Black’s board is undeveloped. White’s extra point, however, is just the 3-point, and there’s no prime in the immediate future. White has almost escaped one of his back checkers, another plus.

To summarize, White has a sizeable edge only in the race, while his other edges are small. Rollouts show that this is a small but correct double, which of course means that the take is very clear. White’s problem is simply that a big lead in the race isn’t as significant as one might think if the inner board is weak. The most likely sequences in that case are ones in which Black easily makes a good anchor or exchanges of hits occur; either of these scenarios minimizes White’s racing lead.

If you were at all tempted to drop this position as Black, just remember that the combination of a weak board, few builders, and an anchor for Black almost always guarantees an easy take. That’s the case here.

Once you know the value of this position in a cash game, you can easily make some practical adjustments for tournament play. If White were trailing in a match, this would be an easy double. If White were the better player, it would also be an easy double, since this will be a long game and White should expect to outplay Black in the later maneuvering.

Split to the 18-Point or Something Else?

Cash game, center cube.

White to play 6-3.

This position shows one of the most commonly misplayed early game situations. White opened with a 43 and made the building play, 13/9 13/10. It’s the most aggressive choice for an opening 43, designed to make a prime quickly and create a complicated position. Black responded with a 44, making his 9-point and electing to make an advanced anchor rather than hit. (Hitting is also very reasonable.) Now White has a 6-3 to play.

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Hit or Make a Point?

Cash game, center cube.

(a) White to play 3-1.

(b) Same position, White to play 3-2.

Here we see a typical sort of early game position where neither side has made much progress yet. Black has played a 5-3 and a 6-3, making the 3-point and running a checker into the outfield. White has rolled a 5-1, balancing his builders and splitting his back men.

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Split or Run?

Cash game. Center cube. White on move.

White to play 5-2

The early part of a backgammon game is dominated by two key goals: hit blots and make points. The easy moves are the ones where you can only do one good thing. The hard moves are those where you can do two good things, and you have to make a tough choice, or no really good things, and you have to decide how best to arrange your checkers for future action.

This position is an example of the latter situation. White can’t make any points with a 5-2 roll, and his only hit, 6/1*, doesn’t accomplish anything good. So he has to shuffle his checkers around somehow and get ready for action next turn.

My cardinal rule in these positions comes from the medical profession: “First, do no harm.” In backgammon terms, that means don’t try plays that make your distribution worse rather than better. Here, I’ll reject 13/8 for just that reason. After 13/8, White has gone from a nice position with a spare on both the 13-point and 8-point to a position with a small stack on the 8-point and no spares on the midpoint. That’s not an improvement, so let’s reject all the plays involving 13/8.

Since we’ve already rejected the awful 6/1*, we’re now left with just two candidates: 23/18 13/11 and 23/16. Running all the way out and trying to escape with 23/16 is the safer play: fewer ways to get hit and fewer blots. Since Black has a better board right now, extra safety is not a bad idea.

The alternative, 23/18 13/11, tries for a bit more. White creates a new blot and exposes himself to more hits in return for a chance to make a great anchor on Black’s bar-point. The problem with the move is a bit subtle. The purpose of the new blot on the 11-point is to give White some extra chances to make his 5-point with rolls like 6-3 and 6-1. However, White won’t have a chance to execute those threats because he’ll most likely be on the bar next turn. Black is going to hit on his bar-point with all his ones and sixes, and he will probably hit on his ace-point with fives as well. In fact, Black’s only non-hitting numbers are 4-3 and 4-4, and 4-3 actually makes White’s 5-point, rendering the blot on the 11-point somewhat useless!

Here’s a quick rule of thumb: a move like 13/11 is excellent when you have an anchor somewhere, so the blot on the 11-point is a useful builder immediately. It’s not so useful when a hitting contest is about to ensue on the other side of the board. As long as the battle for Black’s bar-point is unresolved, a blot on the 11-point is really just an extra target. Play the simple 23/16 instead and try to escape a checker.