Cash game, Black owns the cube.

White to play 6-2.

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Cash game, White owns the cube.

White to play 3-1.

White has a simple choice in this position: hit with 13/9*, or wait and make a point with 15/12 13/12. Last time we looked at some choices between hitting a blot or making a point in the context of early game play. This position occurs much later in the game, but, as it turns out, the very same principles are still useful. Let’s again list the criteria we explained last time, and see how they apply to this position.

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Center cube. Money game. White on move.

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

White seems to be doing pretty well in this position. He has a 4-point board, while Black as yet has no new home board points made. Black doesn’t have an anchor yet. White can hit on the 4-point with 18 numbers (all 4s, 3-1, 2-2, 1-1, 6-3, and 3-3.) He has a few more numbers to hit on the 1-point, although that’s certainly not his top choice. White leads by a whopping 38 pips in the race. Looks like White’s concrete assets and threats combine to give him a good double. Can Black even take this? Over the board, a lot of players would drop almost instantly.

Before we pass final judgment on this cube, let’s alter the position just a little bit:

Position A: White on roll.

We’ve moved White’s spare on the 3-point back to the 6-point, where it’s active, and we moved the third checker on the 8-point back to the midpoint. White has lost 8 pips in the race, but his checkers are now where they belong and his position is much stronger.

Position A is a strong double for White and a clear pass for Black. (By the way, it’s not remotely close to being too good to double.) Our original position, by contrast, is also a good double but a clear take. White has threats, but he also has a number of bad rolls, and even when he rolls well to start, his checkers aren’t sufficiently well-positioned to follow up.

Now let’s look at the two positions a little more closely. Position A is what I like to call a balanced position. Given the underlying structure, White’s spares are well-placed and effective. Our original position is unbalanced; here White’s spares are in the wrong places. The spare on the 3-point is mostly useless. The extra spare on the 8-point doesn’t do much, and the broken midpoint is costly in both the long and short term.

The difference between balanced and unbalanced positions is visually pretty clear, but the real difference shows up when we examine White’s bad rolls. (The good rolls will play well anyway.) Let’s list White’s worst rolls and see how they play in both the original position and Position A.

6-6: In the original position, this is a disaster; White is forced to play 13/1* 8/2(2), killing two checkers. In Position A, this is a very good roll; White makes the 1-point.

5-5: In the original, this is another awful roll; White switches with 6/1*(2) and plays 13/3, killing a checker. It’s not as bad in Position A, where White plays 6/1* 13/8 13/3.

6-5: In the original, White kills a checker with 13/2. In A, he plays 6/1* 13/7, much better.

6-2: White plays 3/1* 13/7 in the original. In A, he plays 23/15 because he owns the midpoint, rather than having a blot there. Big edge to A.

6-1: In the original, White makes the 7-point, but gives up control of the outfield. In A, he gets to play 23/16 as before. Another big edge for A.

5-3: In the original, he plays 13/8 with either 24/21 or 23/20. In A, he again takes advantage of owning the midpoint by playing 23/15. Huge edge to A.

5-2: Same story. In the original he plays either 13/6 or 13/8 23/21. In A, he gets to play 23/16. Another big edge to A.

5-1: In the original he plays 13/8 23/22. In A he plays the much stronger 6/1* 2/1.

3-2: In the original he gets to play 3/1* 23/20, activating the checker on the 3-point. In A he plays the massively stronger double-hit.

2-1: In the original he plays 3/1* 2/1 as above, activating a bad checker. In A he gets to play 6/4* 23/22, hitting on the more important point.

As this listing shows, the difference between the standard-looking position in A and the inferior position in the original isn’t slight; it’s actually huge. A lot of players look quickly at the original position and actually “see” something more like A. But the exact placement of all the spares matter, and it especially matters in the case of the bad rolls. In tough cube decisions, try to pay at least a glancing impression as to how concrete rolls actually play, rather than get caught up in forming a general sense of the position.

Cash game. Center cube. White on move.

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

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

These two positions show a couple of very typical middle game doubles. In each case we’re six to eight moves into the game, one side has finally grabbed a noticeable advantage, and now they’re thinking about turning the cube. Double? Take? What’s right?

Let’s start with the doubling question. The best general guide to early/middle game doubles of this sort came years ago from Joe Sylvester. (Joe was one of the titans of backgammon in the 1980s and 1990s, and he won the first World Cup in 1988. Today he’s somewhat inactive.) Joe recommended looking at three features of the position: the race, the structure, and threats. His rule was the following: if you have an edge in at least two of these three, then you have a double.

With this idea in mind, how’s White doing in Position (a)?

> White leads in the race, 133 to 149, a 16-pip lead.

> White has a better structure, with a 4-point block, his 4, 5, and 6-points already made, and good distribution. Black lacks his 4-point and 5-point and has a big stack on his 6-point.

> White has plenty of immediate threats. Twos hit the blot in Black’s board, 6-1, 6-3, and 3-1 make a 5-point prime, and 6-4 points on the 2-point. White’s edge is threatening to get much bigger next turn.

With an edge in every department, Sylvester’s rule suggests White should have a strong double in Position (a), and in fact he does.

Now let’s look at Position (b).

> White leads in the race, 134 to 162, a 28-pip lead.

> White has a better structure, with four points made in front of Black’s anchor. In addition, Black has three men back on his 23-point, which is weak. Black also has no inner board yet, which is also weak. Here the issue is not so much that White is strong, but that Black’s pretty weak.

> White has no particular threats. True, 6-1 makes his 5-point, and a few numbers will run his back checker into the outfield. But that’s more the sort of background threat noise that’s present in every position.

Here, we can say that White has an edge in two out of the three criteria. Again, he has a solid double.

Now, what about the take/drop question? Here I’ve got my own rule. I ask myself three quick questions. If the answer to the first and third questions is ‘yes’, and the answer to the second question is ‘no’ I’m pretty sure I’ve got a take. If not, then I’ll look at the position more closely. My questions are:

> Do I have an anchor?

> Does my opponent have a 5-prime?

> Is there still contact on both sides of the board?

Take a look at Problem 1 and Problem 2. In both cases Black has an anchor, in both cases White hasn’t yet built a 5-prime, and in both cases we still have contact on the other side. With all these conditions in place, it’s hard (although not impossible) for Black to be a 3-to-1 underdog in the game. In both positions, Black’s best guess should be that he probably has a take. And in fact, rollouts show that’s the correct action.

Both positions: Cash game. Center cube. White on move.

(a) White to play 5-4.

(b) White to play 6-2.

In Problem 140A, White has no way to safety the blot on his 16-point. In fact, he can’t avoid creating a second blot as well. He has a few reasonable plays: 13/4, 16/11 13/9, 16/11 6/2, 13/8 13/9, and 6/1* 13/9. None of these plays look terribly strong. How should he decide among them?

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