Two Plus Two Forums
Sports and Games
Chess and Other Board Games
Backgammon Forum hosted by Bill Robertie.
Problem of the Week #49: Solution
02-14-2010
, 11:52 PM
Problem of the Week #49: Solution
Center cube. Black on move.
Should Black double? If he doubles, should White take, drop, or beaver?
Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.
Black seems to be doing pretty well in Problem 49. He has a 4-point board, while White as yet has no new home board points made. White doesn’t have an anchor yet. Black 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. Black leads by a whopping 38 pips in the race. Looks like Black’s concrete assets and threats combine to give him a good double. Can White 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:
Problem 49a: Black on roll.
We’ve moved Black’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. Black has lost 8 pips in the race, but his checkers are now where they belong and his position is much stronger.
Position 49a is a strong double for Black and a clear pass for White. (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. Black 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 49a is what I like to call a balanced position. Given the underlying structure, Black’s spares are well-placed and effective. Our original position is unbalanced; here Black’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 Black’s bad rolls. (The good rolls will play well anyway.) Let’s list Black’s worst rolls in Position 49, and see how they play in both 49 and 49a.
6-6: In the original position, this is a disaster; Black is forced to play 13/1* 8/2(2), killing two checkers. In 49a, this is a very good roll; Black makes the 1-point.
5-5: In the original, this is another awful roll; Black switches with 6/1*(2) and plays 13/3, killing a checker. It’s not as bad in 49a, where Black plays 6/1* 13/8 13/3.
6-5: In 49, Black kills a checker with 13/2. In 49a, he plays 6/1* 13/7, much better.
6-2: Black plays 3/1* 13/7 in 49. In 49a, he plays 23/15 because he owns the midpoint, rather than having a blot there. Big edge to 49a.
6-1: In 49, Black makes the 7-point, but gives up control of the outfield. In 49a, he gets to play 23/16 as before. Another big edge for 49a.
5-3: In 49, he plays 13/8 with either 24/21 or 23/20. In 49a, he again takes advantage of owning the midpoint by playing 23/15. Huge edge to 49a.
5-2: Same story. In 49 he plays either 13/6 or 13/8 23/21. In 40a, he gets to play 23/16. Another big edge to 49a.
5-1: In 49 he plays 13/8 23/22. In 49a he plays the much stronger 6/1* 2/1.
3-2: In 49 he gets to play 3/1* 23/20, activating the checker on the 3-point. In 49a he plays the massively stronger double-hit.
2-1: In 49 he plays 3/1* 2/1 as above, activating a bad checker. In 49a 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 49a and the inferior position in 49 isn’t slight; it’s actually huge. A lot of players look quickly at the original position and actually “see” something more like 49a. 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.
Solution: Black should double, and White should take.
Center cube. Black on move.
Should Black double? If he doubles, should White take, drop, or beaver?
Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.
Black seems to be doing pretty well in Problem 49. He has a 4-point board, while White as yet has no new home board points made. White doesn’t have an anchor yet. Black 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. Black leads by a whopping 38 pips in the race. Looks like Black’s concrete assets and threats combine to give him a good double. Can White 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:
Problem 49a: Black on roll.
We’ve moved Black’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. Black has lost 8 pips in the race, but his checkers are now where they belong and his position is much stronger.
Position 49a is a strong double for Black and a clear pass for White. (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. Black 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 49a is what I like to call a balanced position. Given the underlying structure, Black’s spares are well-placed and effective. Our original position is unbalanced; here Black’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 Black’s bad rolls. (The good rolls will play well anyway.) Let’s list Black’s worst rolls in Position 49, and see how they play in both 49 and 49a.
6-6: In the original position, this is a disaster; Black is forced to play 13/1* 8/2(2), killing two checkers. In 49a, this is a very good roll; Black makes the 1-point.
5-5: In the original, this is another awful roll; Black switches with 6/1*(2) and plays 13/3, killing a checker. It’s not as bad in 49a, where Black plays 6/1* 13/8 13/3.
6-5: In 49, Black kills a checker with 13/2. In 49a, he plays 6/1* 13/7, much better.
6-2: Black plays 3/1* 13/7 in 49. In 49a, he plays 23/15 because he owns the midpoint, rather than having a blot there. Big edge to 49a.
6-1: In 49, Black makes the 7-point, but gives up control of the outfield. In 49a, he gets to play 23/16 as before. Another big edge for 49a.
5-3: In 49, he plays 13/8 with either 24/21 or 23/20. In 49a, he again takes advantage of owning the midpoint by playing 23/15. Huge edge to 49a.
5-2: Same story. In 49 he plays either 13/6 or 13/8 23/21. In 40a, he gets to play 23/16. Another big edge to 49a.
5-1: In 49 he plays 13/8 23/22. In 49a he plays the much stronger 6/1* 2/1.
3-2: In 49 he gets to play 3/1* 23/20, activating the checker on the 3-point. In 49a he plays the massively stronger double-hit.
2-1: In 49 he plays 3/1* 2/1 as above, activating a bad checker. In 49a 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 49a and the inferior position in 49 isn’t slight; it’s actually huge. A lot of players look quickly at the original position and actually “see” something more like 49a. 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.
Solution: Black should double, and White should take.
