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Problem of the Week #55: Solution
03-28-2010
, 11:48 AM
Problem of the Week #55: Solution
Cash game, White owns the cube.
Black to play 6-2.
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.
This isn’t a terribly tough problem but it does contain an interesting point.
First, let’s note that all the reasonable plays start with 23/17. Abandoning the checker on the 23-point by playing 17/11 can’t be right in any universe I know about, so let’s play 23/17, then look for the best two. Three candidates quickly appear:
a) 17/15
b) 10/8
c) 8/6
Play (a), 17/15, we have to discard pretty quickly, since it leaves two blots and a triple shot (5s, 3s, and 1s all hit for White, while 3-2, 3-1, and 1-1 are double-hits). As some readers pointed out, none of these hits are decisive, and that’s certainly true. But that’s also true of the blots that Black can leave in the other variations. In addition, the anchor on the 17-point is attacking both White blots, which is a tremendously strong argument for keeping the point.
If Black doesn’t play 17/15, then he has to break one of his outfield points and leave a shot. The obvious break is 10/8, because we have learned from experience that breaking a prime from the back is usually better. But this isn’t really a prime, and after Black breaks a point, he should be able to play for a couple of turns before he has to dismantle another point.
The right play is actually 8/6, for a few reasons.
The first reason is just our old friend duplication. After 8/6, White need fours to hit and fours to button up both outfield blots, so he doesn’t have many good numbers at his disposal.
The second and less important reason is that by breaking the 8-point but retaining the 10-point, Black gets some extra shots if White rolls 4-1, 4-2, or 3-1 and decides to hit. This idea is often a reason for breaking an interior point rather than the back point. Breaking the rear point is often right when Black is bearing home and the rear point is really the rear point; it’s sometimes not right when the whole board is still in play and Black need to keep his army from being disconnected.
The last reason is that Black’s blot is in very little danger because of the presence of the White blots. If White hits with a 4-1, for instance, Black is shooting at three blots. Other hits are equally ineffective. The outfield point on 17 suddenly becomes a tower of strength, protecting the rest of Black’s position.
Solution: 23/17 8/6
Cash game, White owns the cube.
Black to play 6-2.
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.
This isn’t a terribly tough problem but it does contain an interesting point.
First, let’s note that all the reasonable plays start with 23/17. Abandoning the checker on the 23-point by playing 17/11 can’t be right in any universe I know about, so let’s play 23/17, then look for the best two. Three candidates quickly appear:
a) 17/15
b) 10/8
c) 8/6
Play (a), 17/15, we have to discard pretty quickly, since it leaves two blots and a triple shot (5s, 3s, and 1s all hit for White, while 3-2, 3-1, and 1-1 are double-hits). As some readers pointed out, none of these hits are decisive, and that’s certainly true. But that’s also true of the blots that Black can leave in the other variations. In addition, the anchor on the 17-point is attacking both White blots, which is a tremendously strong argument for keeping the point.
If Black doesn’t play 17/15, then he has to break one of his outfield points and leave a shot. The obvious break is 10/8, because we have learned from experience that breaking a prime from the back is usually better. But this isn’t really a prime, and after Black breaks a point, he should be able to play for a couple of turns before he has to dismantle another point.
The right play is actually 8/6, for a few reasons.
The first reason is just our old friend duplication. After 8/6, White need fours to hit and fours to button up both outfield blots, so he doesn’t have many good numbers at his disposal.
The second and less important reason is that by breaking the 8-point but retaining the 10-point, Black gets some extra shots if White rolls 4-1, 4-2, or 3-1 and decides to hit. This idea is often a reason for breaking an interior point rather than the back point. Breaking the rear point is often right when Black is bearing home and the rear point is really the rear point; it’s sometimes not right when the whole board is still in play and Black need to keep his army from being disconnected.
The last reason is that Black’s blot is in very little danger because of the presence of the White blots. If White hits with a 4-1, for instance, Black is shooting at three blots. Other hits are equally ineffective. The outfield point on 17 suddenly becomes a tower of strength, protecting the rest of Black’s position.
Solution: 23/17 8/6
