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.

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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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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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.

Cash game. Center cube. White on roll.

Position (a): White to play 5-1.

Position (b): White to play 5-1.

In the opening, plays that hit blots or make key points tend to easily dominate all other maneuvering plays. Interesting choices, however, arise when both plays are available. Do you hit, or do you make a point?

Five simple rules guide most of these plays.

(1) The stronger your inner board, the more you want to hit and the less you need to make an additional point.

(2) The better the point you can make, the more you want to make it.

(3) If you can make a point while unstacking, your desire to hit goes down.

(4) If you have to break a good anchor to hit, your desire to hit goes down.

(5) If you have a vulnerable, exposed blot, your desire to hit goes up.

These two positions illustrate the relative importance of rules (4) and (5). Note that in both parts of this problem, points (1) through (3) all suggest making the 5-point as the better play. White has a weak inner board, the 5-point is the best point available, and he can make the 5-point while also unstacking the 6-point.

In part (a), the decisive criterion is that White now has a great anchor on Black’s 4-point, and to hit, he’d have to break that anchor. So making the 5-point is clear, and in fact every hitting play is just a blunder.

In part (b), however, the picture changes. Now White has no anchor, so hitting doesn’t cost him an asset. In addition, making the 5-point now leaves the checker on the 21-point exposed to nine pointing numbers (11, 22, 44, 54, 52, and 42) plus some annoying double-hits (23, 43, 53). In addition, Black gets great diversification because his escaping numbers (all sixes) don’t duplicate his other good numbers. Hitting becomes essential for White both to gain ground in the race and to protect his otherwise vulnerable blots. In fact, making the 5-point now becomes a blunder!

After hitting in part (b), how should White play the ace? The right play is 16/15, because it duplicates Black’s threes: Black now needs threes to hit in the outfield and threes to anchor.

Cash game. Center cube. White on roll.

Part (a): Should White double? If White doubles, should Black take, drop, or beaver?

Part (b): Should White double? If White doubles, should Black take, drop, or beaver?

When contemplating a middle game double, don’t make the mistake of looking only at your position. Remember to look just as carefully at the weaknesses in your opponent’s position. It may be his weakness, rather than your strength, that gives you a good double.

Part (a) is a perfect case in point. White has escaped his back checkers and built a little structure, while Black has grabbed your 5-point. In most positions of this general type, White’s advantages wouldn’t even add up to an initial double. But now look at Black’s position:

> His back men are split and vulnerable to potential blitzing rolls like 66, 55, and 44, both now and on subsequent rolls. If his two back checkers were anchored on the 23-point or the 22-point, the position wouldn’t be a double.

> His front position is still chaotic and will be for a couple of turns. If he had a small 4-prime or even a good board with, say, the 4-point and 5-point made, he’d have a threat to contain any checker hit on the next couple of turns, and White wouldn’t have a double.

But with both these weaknesses, Black’s game is toothless enough so that White has a very solid double. Black still has a clear take of course.

In Part (b), White is off to a decent start. He’s got a good defensive anchor, while on the offensive side he has – well – something. He’s got some great points slotted, and next turn he might actually cover one or two of them.

The key to the position is not White’s game but Black’s. While White has something, Black has a bit less than nothing. No points, just blots. Something versus nothing is a good prescription for an early double, especially if the defender doesn’t have an anchor. Without an anchor, there will always be variations where things go terribly wrong and White’s messy position turns into a powerful blitz. Did you stop to guess what White’s cubeless gammon chances were in Part (b)? If you did, did you realize they’re over 25%? Numbers like that almost always guarantee not just an initial double, but a strong and mandatory initial double. White’s checkers aren’t just passive slots. They’re also potential attackers, which can be activated by a single good sequence. Couple that with a rock-solid defensive anchor, and White has a great double.

Clear take, of course. There are plenty of variations where things don’t go so well and Black recovers quickly.