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Problem of the Week #34: Solution
11-01-2009
, 03:29 PM
Problem of the Week #34: Solution
Cash game. White owns the cube. Black on move.
Black to play 3-3.
Black’s off to a good start in Problem 34. He’s already made a three-point board, whereas White hasn’t yet made a new point, and he hit a blot, leaving him 17 pips ahead in the race. White is still scrambling to make an anchor. Last turn Black offered an aggressive double, and White quite reasonably took.
Now Black throws one of his best shots, 3-3, and has three game plans:
(a) The consolidation play with 14/8 13/10(2), leaving him firmly in control with a nice edge, or
(b) Consolidation plus a little attack with 24/21 14/8 6/3*, or
(c) All-out blitz with either 13/4*/1* or 13/4* 6/3*.
What’s the right idea?
Here’s the general approach for handling these sorts of positions. If your opponent has no structure, and the cube has already been turned (activating gammons), then the blitz dominates any safe game plan. If the blitz fails, Black will just drop back into a holding game where he holds a slight edge. If he makes one of the solid plays, he’ll reach those holding games anyway since almost all of White’s rolls will anchor somewhere. He’ll be slightly better off if he goes for the holding game right away, because of his racing lead, but the difference is small. But if the blitz succeeds, he wins a gammon right away, and with the cube already turned, that’s a quick four points and a huge swing.
As White acquires more structure, the blitz drops in value. If we alter White’s position and give him his 5-point (as though he had rolled a 3-1 at some point), then the blitz plays are only slightly superior to the consolidating plays. If we give White two extra points, say the 5-point and the 3-point, then the blitz plays become pretty big errors and the consolidating plays becomes correct. (There’s very little difference between Play (a) and Play (b) no matter what structure White has.)
So we’re blitzing. Next question: what’s the right way to blitz?
What makes this problem especially interesting is that Black has two distinct ways to blitz: the obvious 13/4*/1* and the apparently riskier 13/4* 6/3*. Problems with two plausible blitzing moves are rare, but we can choose between them by noticing that the double-hit gives Black a new winning idea. If Black hits on the 1-point and White then throws a three and anchors immediately, White’s achieved his holding game. But if Black double-hits and White throws an ace, he’s only managed to get an ace-point game, which is a much weaker position.
The double-hit with 13/4* 6/3* also obeys one of the key rules of good backgammon: play to keep your checkers in front of your opponent, rather than moving behind him. The two blitz plays are much superior to any non-blitzing play, and the double-hit is slightly the better of the two.
Solution: 13/4* 6/3*
Cash game. White owns the cube. Black on move.
Black to play 3-3.
Black’s off to a good start in Problem 34. He’s already made a three-point board, whereas White hasn’t yet made a new point, and he hit a blot, leaving him 17 pips ahead in the race. White is still scrambling to make an anchor. Last turn Black offered an aggressive double, and White quite reasonably took.
Now Black throws one of his best shots, 3-3, and has three game plans:
(a) The consolidation play with 14/8 13/10(2), leaving him firmly in control with a nice edge, or
(b) Consolidation plus a little attack with 24/21 14/8 6/3*, or
(c) All-out blitz with either 13/4*/1* or 13/4* 6/3*.
What’s the right idea?
Here’s the general approach for handling these sorts of positions. If your opponent has no structure, and the cube has already been turned (activating gammons), then the blitz dominates any safe game plan. If the blitz fails, Black will just drop back into a holding game where he holds a slight edge. If he makes one of the solid plays, he’ll reach those holding games anyway since almost all of White’s rolls will anchor somewhere. He’ll be slightly better off if he goes for the holding game right away, because of his racing lead, but the difference is small. But if the blitz succeeds, he wins a gammon right away, and with the cube already turned, that’s a quick four points and a huge swing.
As White acquires more structure, the blitz drops in value. If we alter White’s position and give him his 5-point (as though he had rolled a 3-1 at some point), then the blitz plays are only slightly superior to the consolidating plays. If we give White two extra points, say the 5-point and the 3-point, then the blitz plays become pretty big errors and the consolidating plays becomes correct. (There’s very little difference between Play (a) and Play (b) no matter what structure White has.)
So we’re blitzing. Next question: what’s the right way to blitz?
What makes this problem especially interesting is that Black has two distinct ways to blitz: the obvious 13/4*/1* and the apparently riskier 13/4* 6/3*. Problems with two plausible blitzing moves are rare, but we can choose between them by noticing that the double-hit gives Black a new winning idea. If Black hits on the 1-point and White then throws a three and anchors immediately, White’s achieved his holding game. But if Black double-hits and White throws an ace, he’s only managed to get an ace-point game, which is a much weaker position.
The double-hit with 13/4* 6/3* also obeys one of the key rules of good backgammon: play to keep your checkers in front of your opponent, rather than moving behind him. The two blitz plays are much superior to any non-blitzing play, and the double-hit is slightly the better of the two.
Solution: 13/4* 6/3*
