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.