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Problem of the Week #28: Solution
09-20-2009
, 03:13 PM
Problem of the Week #28: Solution
Cash game. Center cube. Black on move.
Part (a): Black to play 2-1.
Part (b): Black to play 6-5.
We’ve talked a little in previous problems about proto-backgames, those transitional positions that lie between ‘normal’ backgammon and true backgames. Here are our first couple of examples of proto-backgame positions, so let’s pause for a bit and discuss just what each side is trying to do.
Proto-backgames are defined by two key conditions. First, one or both players have several men back in their opponent’s inner board. In Problems 28(a) and 28(b), both sides have extra men back; White has five men back and Black has three. In addition, both sides will have blocking positions, but neither side will have a strong prime yet. ‘Strong’ in this context means a five or six-point prime; four points in a row are good, but not quite enough to really control your opponent’s back checkers.
In a proto-backgame, both sides have the same overarching goal: build a five-point prime and force your opponent to play a true backgame. The closer you get to your goal, the bigger your edge. In Position 28(a), Black has a clear advantage (although nothing close to a doubling advantage) because he’s well ahead in the race, and the priming positions are about the same on both sides. In Position 28(b), the game is about even; Black still leads in the race, but White now has a better prime.
So we know the strategic goal is to build a prime. But what are we looking to do tactically, to get us closer to our goal? In general, we’re looking to do the following things from turn to turn:
(1) Kill no checkers. This is really the First Commandment of backgame and proto-backgame play. In this context, a ‘killed’ checker is any checker that moves deeper into your board than your opponent’s front anchor. In Position 28(a), for instance, Black doesn’t want to move any checker to his 1-point or 2-point, since those points are behind White’s anchor on the 3-point. Good players obey this rule religiously in complex position, while weak players are constantly distracted by the lure of making a deep inner-board point. In Position 28(a), Black will eagerly make the bar-point and will fight hard for the 4-point, because those points are in front of White’s anchor. But he will at all costs avoid moving down to the 1 and 2-points.
(2) Make new blocking points whenever you can. This is pretty obvious. You’ll never have a lot of rolls on any turn to make a new blocking point, so when you can it will probably take precedence over anything else.
(3) Circulate checkers into the outfield. The outfield is the real battleground in proto-backgames. When you move into your opponent’s outfield, you accomplish several good things. First, you jump over his blocking position, which reduces the chance that you’ll get stuck in his inner board with some later awkward shot. Second, you create builders for new priming points of your own, since checkers in his outfield bear on your outfield. Third, you put pressure on your opponent; by controlling the outfield first, you may prevent him from moving out.
With these goals in mind, Problems 28(a) and 28(b) become fairly easy positions.
In Position 28(a), Black should play Bar/24 6/4*. The checkers on the 6-point have no function now other than to make the 4-point. The 4-point is clearly the most important point on the board right now, since making it will not only give Black his best possible home board, but, by pushing White back, will make it harder for White’s checkers to get into the outfield.
The safe play Bar/23 22/21, favored by a couple of respondents, allows White to grab Black’s 4-point without a fight, after which Black’s two checkers on the 6-point have nothing to do for awhile. That’s bad. Black only has 15 checkers, and he’ll need 10 of them to make a five-prime. Everybody has to keep working! Allowing White to grab the 4-point effectively kills the checkers on the 6-point.
The right idea in 28(b) is 21/15 21/16! Black doesn’t want to get stuck behind White’s little prime, and the outfield is currently up for grabs, so Black moves there first. Note that although White has a lot of hits, the hits cost White the midpoint. That’s a big concession, effectively isolating White’s rear checkers from the rest of his army, so Black really doesn’t fear being hit. Notice in addition that the alternatives are very weak. Playing 13/2* kills a checker and strips the midpoint, and 13/7 6/1* does the same thing in a different way. Running with one checker by 21/10 looks safer, but allows White to hit with a six without making a positional concession.
Solutions:
Part (a): Bar/24 6/4*.
Part (b): 21/15 21/16.
Cash game. Center cube. Black on move.
Part (a): Black to play 2-1.
Part (b): Black to play 6-5.
We’ve talked a little in previous problems about proto-backgames, those transitional positions that lie between ‘normal’ backgammon and true backgames. Here are our first couple of examples of proto-backgame positions, so let’s pause for a bit and discuss just what each side is trying to do.
Proto-backgames are defined by two key conditions. First, one or both players have several men back in their opponent’s inner board. In Problems 28(a) and 28(b), both sides have extra men back; White has five men back and Black has three. In addition, both sides will have blocking positions, but neither side will have a strong prime yet. ‘Strong’ in this context means a five or six-point prime; four points in a row are good, but not quite enough to really control your opponent’s back checkers.
In a proto-backgame, both sides have the same overarching goal: build a five-point prime and force your opponent to play a true backgame. The closer you get to your goal, the bigger your edge. In Position 28(a), Black has a clear advantage (although nothing close to a doubling advantage) because he’s well ahead in the race, and the priming positions are about the same on both sides. In Position 28(b), the game is about even; Black still leads in the race, but White now has a better prime.
So we know the strategic goal is to build a prime. But what are we looking to do tactically, to get us closer to our goal? In general, we’re looking to do the following things from turn to turn:
(1) Kill no checkers. This is really the First Commandment of backgame and proto-backgame play. In this context, a ‘killed’ checker is any checker that moves deeper into your board than your opponent’s front anchor. In Position 28(a), for instance, Black doesn’t want to move any checker to his 1-point or 2-point, since those points are behind White’s anchor on the 3-point. Good players obey this rule religiously in complex position, while weak players are constantly distracted by the lure of making a deep inner-board point. In Position 28(a), Black will eagerly make the bar-point and will fight hard for the 4-point, because those points are in front of White’s anchor. But he will at all costs avoid moving down to the 1 and 2-points.
(2) Make new blocking points whenever you can. This is pretty obvious. You’ll never have a lot of rolls on any turn to make a new blocking point, so when you can it will probably take precedence over anything else.
(3) Circulate checkers into the outfield. The outfield is the real battleground in proto-backgames. When you move into your opponent’s outfield, you accomplish several good things. First, you jump over his blocking position, which reduces the chance that you’ll get stuck in his inner board with some later awkward shot. Second, you create builders for new priming points of your own, since checkers in his outfield bear on your outfield. Third, you put pressure on your opponent; by controlling the outfield first, you may prevent him from moving out.
With these goals in mind, Problems 28(a) and 28(b) become fairly easy positions.
In Position 28(a), Black should play Bar/24 6/4*. The checkers on the 6-point have no function now other than to make the 4-point. The 4-point is clearly the most important point on the board right now, since making it will not only give Black his best possible home board, but, by pushing White back, will make it harder for White’s checkers to get into the outfield.
The safe play Bar/23 22/21, favored by a couple of respondents, allows White to grab Black’s 4-point without a fight, after which Black’s two checkers on the 6-point have nothing to do for awhile. That’s bad. Black only has 15 checkers, and he’ll need 10 of them to make a five-prime. Everybody has to keep working! Allowing White to grab the 4-point effectively kills the checkers on the 6-point.
The right idea in 28(b) is 21/15 21/16! Black doesn’t want to get stuck behind White’s little prime, and the outfield is currently up for grabs, so Black moves there first. Note that although White has a lot of hits, the hits cost White the midpoint. That’s a big concession, effectively isolating White’s rear checkers from the rest of his army, so Black really doesn’t fear being hit. Notice in addition that the alternatives are very weak. Playing 13/2* kills a checker and strips the midpoint, and 13/7 6/1* does the same thing in a different way. Running with one checker by 21/10 looks safer, but allows White to hit with a six without making a positional concession.
Solutions:
Part (a): Bar/24 6/4*.
Part (b): 21/15 21/16.
