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Problem of the Week #11: Solution
05-25-2009
, 10:56 PM
Problem of the Week #11: Solution
Cash game, center cube. Black to play 6-1.
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Problem 11 is a somewhat unusual position. We have a roughly balanced middle game, in which both sides have moderately strong home boards. White has only one man back, and as a result Black trails in the pip count by 15 pips (136 to 121).
Black’s roll, 6-1, is awkward since he has no great six. Moving off the midpoint leaves a shot. Moving off the 24-point creates two blots and breaks his defensive anchor. The only sensible play that involves moving from the 7-point or 8-point is the loose hit, 8/1*, which doesn’t accomplish much. Nonetheless, Black does have to pick one choice from this unappetizing situation.
The right play is the counter-intuitive 13/7 6/5, slotting the 5-point. While slotting plays themselves are not uncommon, one of the preconditions of a good slotting play is that no other blots are left around the board. The reason is simple: if your opponent fails to hit the slotted checker, you want the maximum opportunity to cover the slot next turn. Other blots allow your opponent to hit in other places, reducing the count of cover numbers for your slot. The opening adage “Don’t slot while split” is a simple reminder of this principle.
Despite the extra blot, however, Black’s should still go ahead and slot his 5-point with 13/7 6/5, leaving White fours and ones to hit. The arguments for the slotting play are threefold.
> The slot gives Black a chance to build a full prime, while alternatives don’t ever lead to a very strong position.
> There is a significant amount of duplication after 13/7 6/5, so Black’s actual risk is less than first appears.
> Black’s alternatives are very weak.
Let’s look at these three arguments one at a time.
Building a full prime. After 13/7 6/5, a White miss followed by a Black cover can give Black a full (6-point) prime. White has 20 hits (all fours and ones) and 16 misses, so he’s only a slight favorite to hit. If White misses, Black can cover with twos and eights, building a 6-prime, or threes, which build a 5-prime. At the very least, Black can pick up his blot on the midpoint, leaving White with only fours to hit on his second turn.
Building the prime is very significant. For instance, after the sequence: Black 6-1 (13/7 6/5) and White 3-2 (13/8), Black is almost a 2-1 favorite in the position. He doesn’t quite have a double, but he’s close.
Duplication. Most middle game slotting plays hinge on at least some partial duplication of the opponent’s useful numbers. Position 11 is typical in this respect. After 13/7 6/5 White needs fours and ones to hit, but these numbers are already useful elsewhere. Note that 6-4 and 4-2 make White’s 2-point, while 4-4 and 5-4 hop White’s last back checker. In addition, 6-1 and 3-1 make White’s bar-point and 5-point respectively. Although White will in fact hit with all these numbers of Black slots, the fact that the numbers play usefully on the other side of the board makes the cost of each hit considerably less.
Weak alternatives. If Black doesn’t slot, his remaining plays are 13/6, 8/1*, and 24/18 24/23. Let’s look at each one.
13/6 leaves a blot on the midpoint anyway, but contains no threat. Even if White rolls a poor number (3-2 or 5-3, for example), Black isn’t prepared to capitalize on it.
8/1* is all downside. It leaves 15 shots (all aces plus 6-2 and 5-3) compared to 20 shots for 13/7 6/5, so it is a slightly safer play. But where’s the upside? Slotting the 5-point at least leaves Black threatening to make a 6-prime. Hitting on the one-point leaves Black threatening – to make the one-point! Not an even trade. This is the worst of the reasonable possibilities.
With 24/18 24/23, Black simply spreads his arms and says “Please – kill me now!” Fully half of White’s numbers now at least hit two checkers (6-6, 3-3, 2-2, 1-1, 6-5, 6-4, 6-2, 6-1, 5-1, 4-1, and 2-1. White will at least have some moderately tough decisions. With 6-2, for instance, should he make the 2-point or hit two men? (The double-hit is slightly stronger.) But abandoning your defenses like this is suicidal and must be dismissed quickly.
Slotting the 5-point is an unusual play, but if conditions are right, it can be best. Here the threat, the duplication, and the absence of good alternatives combine to move slotting to the top of the list.
Solution: 13/7 6/5.
Cash game, center cube. Black to play 6-1.
--------------------
Problem 11 is a somewhat unusual position. We have a roughly balanced middle game, in which both sides have moderately strong home boards. White has only one man back, and as a result Black trails in the pip count by 15 pips (136 to 121).
Black’s roll, 6-1, is awkward since he has no great six. Moving off the midpoint leaves a shot. Moving off the 24-point creates two blots and breaks his defensive anchor. The only sensible play that involves moving from the 7-point or 8-point is the loose hit, 8/1*, which doesn’t accomplish much. Nonetheless, Black does have to pick one choice from this unappetizing situation.
The right play is the counter-intuitive 13/7 6/5, slotting the 5-point. While slotting plays themselves are not uncommon, one of the preconditions of a good slotting play is that no other blots are left around the board. The reason is simple: if your opponent fails to hit the slotted checker, you want the maximum opportunity to cover the slot next turn. Other blots allow your opponent to hit in other places, reducing the count of cover numbers for your slot. The opening adage “Don’t slot while split” is a simple reminder of this principle.
Despite the extra blot, however, Black’s should still go ahead and slot his 5-point with 13/7 6/5, leaving White fours and ones to hit. The arguments for the slotting play are threefold.
> The slot gives Black a chance to build a full prime, while alternatives don’t ever lead to a very strong position.
> There is a significant amount of duplication after 13/7 6/5, so Black’s actual risk is less than first appears.
> Black’s alternatives are very weak.
Let’s look at these three arguments one at a time.
Building a full prime. After 13/7 6/5, a White miss followed by a Black cover can give Black a full (6-point) prime. White has 20 hits (all fours and ones) and 16 misses, so he’s only a slight favorite to hit. If White misses, Black can cover with twos and eights, building a 6-prime, or threes, which build a 5-prime. At the very least, Black can pick up his blot on the midpoint, leaving White with only fours to hit on his second turn.
Building the prime is very significant. For instance, after the sequence: Black 6-1 (13/7 6/5) and White 3-2 (13/8), Black is almost a 2-1 favorite in the position. He doesn’t quite have a double, but he’s close.
Duplication. Most middle game slotting plays hinge on at least some partial duplication of the opponent’s useful numbers. Position 11 is typical in this respect. After 13/7 6/5 White needs fours and ones to hit, but these numbers are already useful elsewhere. Note that 6-4 and 4-2 make White’s 2-point, while 4-4 and 5-4 hop White’s last back checker. In addition, 6-1 and 3-1 make White’s bar-point and 5-point respectively. Although White will in fact hit with all these numbers of Black slots, the fact that the numbers play usefully on the other side of the board makes the cost of each hit considerably less.
Weak alternatives. If Black doesn’t slot, his remaining plays are 13/6, 8/1*, and 24/18 24/23. Let’s look at each one.
13/6 leaves a blot on the midpoint anyway, but contains no threat. Even if White rolls a poor number (3-2 or 5-3, for example), Black isn’t prepared to capitalize on it.
8/1* is all downside. It leaves 15 shots (all aces plus 6-2 and 5-3) compared to 20 shots for 13/7 6/5, so it is a slightly safer play. But where’s the upside? Slotting the 5-point at least leaves Black threatening to make a 6-prime. Hitting on the one-point leaves Black threatening – to make the one-point! Not an even trade. This is the worst of the reasonable possibilities.
With 24/18 24/23, Black simply spreads his arms and says “Please – kill me now!” Fully half of White’s numbers now at least hit two checkers (6-6, 3-3, 2-2, 1-1, 6-5, 6-4, 6-2, 6-1, 5-1, 4-1, and 2-1. White will at least have some moderately tough decisions. With 6-2, for instance, should he make the 2-point or hit two men? (The double-hit is slightly stronger.) But abandoning your defenses like this is suicidal and must be dismissed quickly.
Slotting the 5-point is an unusual play, but if conditions are right, it can be best. Here the threat, the duplication, and the absence of good alternatives combine to move slotting to the top of the list.
Solution: 13/7 6/5.
