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Problem of the Week #12: Solution
06-01-2009
, 10:17 AM
Problem of the Week #12: Solution
Cash game, center cube. Black on roll.
(a) Should Black double?
(b) If doubled, should White take, drop, or beaver?
----------------------------
Early game doubles cover a wide variety of positions, but in general they can be spotted by analyzing three key aspects of the game: race, position, and threats. Many years ago, Joe Sylvester (a very great player in the 80s and 90s, now somewhat inactive) coined a simple rule: if you’re ahead in two out of three of these aspects, you have a double. Your opponent may or may not have a take. Let’s evaluate these three features of Problem 12 and see what they tell us.
The Race. This is pretty simple. Black leads 149 to 173. He’s up by 24 pips, a solid advantage. There’s plenty of contact left, but 24 pips is a big edge.
The Position. Black is ahead on both sides of the board, although not by much in either case. Defensively, he has a modest anchor, which is certainly better than being on the bar with no anchor. Offensively, he has his 5-point, while White has nothing.
Threats. Black is a little lacking in this area. His doubles are very strong, of course, but that’s true of almost all early game positions. What we’re looking for here are powerful non-doubles, and there really aren’t many of those, beyond the obvious 6-2 and 6-3 rolls.
Our scoring gives Black an edge in two out of three areas, so by Sylvester’s criteria Black has a double. And in fact that’s right: Black should double. What’s a little more surprising is that the double is extremely strong and in fact White has only a narrow take.
Some of our respondents sensibly asked “Why is it a take at all, given that White has absolutely no position?” Good question. The answer is simply that the gap between Black’s strengths and White’s weaknesses isn’t great enough yet to make it a pass. White will very likely enter from the bar next turn, and as soon as he does, he’ll start to construct his position. Each point that he makes will give him more and more counterplay. While he’s certainly an underdog, he’s not yet a huge underdog.
At the start of my backgammon career, I used to routinely pass early doubles when I didn’t have much of a position. To learn more about these positions, I started doing manual rollouts, where I would play out a position a hundred times or so and record the results. Compared to computer rollouts, manual rollouts have a couple of big disadvantages: they’re much less accurate, and they take a long time. But they compensate with one big advantage: they give you a picture of the actual flow of the game, and you get a sense of just how likely (or unlikely) it is that a game will take a certain course.
One of the first lessons I learned was this: the fewer points made, the less likely that a game will go any particular way. In Problem 12, for instance, Black has only made his 5-point, and his opponent’s 3-point. Once White enters, the game will have a chance to flow in a lot of different directions. White might make Black’s bar-point and play a holding game. Or White might be forced into a backgame. Or Black might run from his anchor and then get blitzed. All of these variations are unlikely in themselves, but together they amass a considerable amount of equity, enough to give White a thin take.
Why is the take thin? The answer, simply, is because White’s position is so weak to start. Compared to the starting position, White has actually gone into reverse. He’s moved a checker from his 24-point to the bar, and from his 8-point to his 13-point, making his midpoint stack worse.
One last point before we leave the problem. Not doubling here is an easy error to make over the board. Black’s position doesn’t easily fit any of the usual categories. It’s not a blitz, it’s not a prime, and in fact Black doesn’t have a lot of threats beyond making an additional point with a few numbers. In a game played at normal speed over the board, we tend to rely on obvious visual cues (“Am I way ahead in the race?” “Do I have lots of threats?”) to tell us to think carefully about a double. This position lacks most of those cues. Black seems to lack immediate threats, and since both sides have two men back, he isn’t obviously well up in the race. Presented as a problem, it’s relatively easy to break the position down and decide logically that Black must be a solid favorite. Over the board, this is an easy double to let slip by.
Solution: Black doubles, White should take.
Cash game, center cube. Black on roll.
(a) Should Black double?
(b) If doubled, should White take, drop, or beaver?
----------------------------
Early game doubles cover a wide variety of positions, but in general they can be spotted by analyzing three key aspects of the game: race, position, and threats. Many years ago, Joe Sylvester (a very great player in the 80s and 90s, now somewhat inactive) coined a simple rule: if you’re ahead in two out of three of these aspects, you have a double. Your opponent may or may not have a take. Let’s evaluate these three features of Problem 12 and see what they tell us.
The Race. This is pretty simple. Black leads 149 to 173. He’s up by 24 pips, a solid advantage. There’s plenty of contact left, but 24 pips is a big edge.
The Position. Black is ahead on both sides of the board, although not by much in either case. Defensively, he has a modest anchor, which is certainly better than being on the bar with no anchor. Offensively, he has his 5-point, while White has nothing.
Threats. Black is a little lacking in this area. His doubles are very strong, of course, but that’s true of almost all early game positions. What we’re looking for here are powerful non-doubles, and there really aren’t many of those, beyond the obvious 6-2 and 6-3 rolls.
Our scoring gives Black an edge in two out of three areas, so by Sylvester’s criteria Black has a double. And in fact that’s right: Black should double. What’s a little more surprising is that the double is extremely strong and in fact White has only a narrow take.
Some of our respondents sensibly asked “Why is it a take at all, given that White has absolutely no position?” Good question. The answer is simply that the gap between Black’s strengths and White’s weaknesses isn’t great enough yet to make it a pass. White will very likely enter from the bar next turn, and as soon as he does, he’ll start to construct his position. Each point that he makes will give him more and more counterplay. While he’s certainly an underdog, he’s not yet a huge underdog.
At the start of my backgammon career, I used to routinely pass early doubles when I didn’t have much of a position. To learn more about these positions, I started doing manual rollouts, where I would play out a position a hundred times or so and record the results. Compared to computer rollouts, manual rollouts have a couple of big disadvantages: they’re much less accurate, and they take a long time. But they compensate with one big advantage: they give you a picture of the actual flow of the game, and you get a sense of just how likely (or unlikely) it is that a game will take a certain course.
One of the first lessons I learned was this: the fewer points made, the less likely that a game will go any particular way. In Problem 12, for instance, Black has only made his 5-point, and his opponent’s 3-point. Once White enters, the game will have a chance to flow in a lot of different directions. White might make Black’s bar-point and play a holding game. Or White might be forced into a backgame. Or Black might run from his anchor and then get blitzed. All of these variations are unlikely in themselves, but together they amass a considerable amount of equity, enough to give White a thin take.
Why is the take thin? The answer, simply, is because White’s position is so weak to start. Compared to the starting position, White has actually gone into reverse. He’s moved a checker from his 24-point to the bar, and from his 8-point to his 13-point, making his midpoint stack worse.
One last point before we leave the problem. Not doubling here is an easy error to make over the board. Black’s position doesn’t easily fit any of the usual categories. It’s not a blitz, it’s not a prime, and in fact Black doesn’t have a lot of threats beyond making an additional point with a few numbers. In a game played at normal speed over the board, we tend to rely on obvious visual cues (“Am I way ahead in the race?” “Do I have lots of threats?”) to tell us to think carefully about a double. This position lacks most of those cues. Black seems to lack immediate threats, and since both sides have two men back, he isn’t obviously well up in the race. Presented as a problem, it’s relatively easy to break the position down and decide logically that Black must be a solid favorite. Over the board, this is an easy double to let slip by.
Solution: Black doubles, White should take.
