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Problem of the Week #61: Solution
05-10-2010
, 09:54 AM
Problem of the Week #61: May 2
Cash game, center cube.
Should Black double? If he doubles, should White take or drop?
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.
A key idea in understanding the proper use of the doubling cube on a practical level is that of the “benchmark” position. A benchmark cube situation is a position where one of the decisions (doubling or taking) is a toss-up, while the other is completely clear. Properly understanding a benchmark position is very useful since it unlocks the key to many related positions. Just compare your actual position to the benchmark, spot what the relevant differences, and you should be able to make a good cube decision over the board. Better players are aware of hundreds of good benchmarks, so they can make their over-the-board decisions quickly and accurately.
Problem 61 shows an excellent benchmark position. White started the game with a 5-1, splitting his back men, and Black responded with a 4-4, making two inner-board points. (Not best, by the way; making the 20-point and the 9-point is better, with a more enduring positional edge.) White then danced, and Black is now contemplating a double.
A long Snowie rollout indicated that the double/no double decision was completely marginal, with only a 0.001 difference between the two plays. If doubling is theoretically marginal, then taking is, of course, hugely correct. Dropping is a mistake costing almost one-third of a point. (As a practical matter, this means that doubling is mandatory, since it theoretically costs nothing and might prompt a huge blunder on your opponent’s part.)
Once we recognize #61 as a benchmark position for early blitzes where Black has made a couple of points and White has a checker on the bar plus a blot in White’s board, we can use it to analyze related positions. For instance, take a look at Position 61a:
Position 61a: Should Black double? Should White take?
In this case, White again opened with a 5-1 but this time Black responded with a 5-5, making two inner points. (The correct play in this case.) Again, Black is thinking about doubling. Let’s compare the two positions and see what we should do.
First, we note that if our benchmark position was a trivially easy take for White, this must be also. The two positions just aren’t different enough to swing this to a pass. So we’re certain White should take, and now we’ll look at the double.
This new position differs from our benchmark in two ways, one favoring Black, the other favoring White. The factor favoring Black is tactical, the factor favoring White is strategic.
Black is favored because he has two numbers to hit White’s last blot (sixes and fours) instead of just one number (fives) in the benchmark position. The extra direct shot means that Black has a slightly better chance of closing White out.
White is favored because Black’s two inner board points are deeper, and the ace-point is in fact behind White’s blot. As a result, when White does anchor Black will have some checkers out of play, so his alternative game plan of priming White isn’t nearly as strong. In our benchmark position, all Black’s checkers are still in front of White’s blot, so if a blitz doesn’t work, Black still has chances of building a prime.
Which feature is more important? In fact, Black completes a closeout less than 30% of the time in either position, so the long-term aspects of the position matter most. In Position 61, Black can play quietly for the prime, taking chances only when he rolls very well. In 61a, he has to go for the closeout, but he stands somewhat poorly whenever White survives. Black is actually substantially worse off in 61a, so the theoretically correct play there is no double. (The correct play over the board against anyone but a top player is to double, for the same reason as before; many players are afraid of blitz positions and will pass them without much thought.)
Solution: The double/no double decision is a tossup; if doubled, White should take.
Cash game, center cube.
Should Black double? If he doubles, should White take or drop?
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.
A key idea in understanding the proper use of the doubling cube on a practical level is that of the “benchmark” position. A benchmark cube situation is a position where one of the decisions (doubling or taking) is a toss-up, while the other is completely clear. Properly understanding a benchmark position is very useful since it unlocks the key to many related positions. Just compare your actual position to the benchmark, spot what the relevant differences, and you should be able to make a good cube decision over the board. Better players are aware of hundreds of good benchmarks, so they can make their over-the-board decisions quickly and accurately.
Problem 61 shows an excellent benchmark position. White started the game with a 5-1, splitting his back men, and Black responded with a 4-4, making two inner-board points. (Not best, by the way; making the 20-point and the 9-point is better, with a more enduring positional edge.) White then danced, and Black is now contemplating a double.
A long Snowie rollout indicated that the double/no double decision was completely marginal, with only a 0.001 difference between the two plays. If doubling is theoretically marginal, then taking is, of course, hugely correct. Dropping is a mistake costing almost one-third of a point. (As a practical matter, this means that doubling is mandatory, since it theoretically costs nothing and might prompt a huge blunder on your opponent’s part.)
Once we recognize #61 as a benchmark position for early blitzes where Black has made a couple of points and White has a checker on the bar plus a blot in White’s board, we can use it to analyze related positions. For instance, take a look at Position 61a:
Position 61a: Should Black double? Should White take?
In this case, White again opened with a 5-1 but this time Black responded with a 5-5, making two inner points. (The correct play in this case.) Again, Black is thinking about doubling. Let’s compare the two positions and see what we should do.
First, we note that if our benchmark position was a trivially easy take for White, this must be also. The two positions just aren’t different enough to swing this to a pass. So we’re certain White should take, and now we’ll look at the double.
This new position differs from our benchmark in two ways, one favoring Black, the other favoring White. The factor favoring Black is tactical, the factor favoring White is strategic.
Black is favored because he has two numbers to hit White’s last blot (sixes and fours) instead of just one number (fives) in the benchmark position. The extra direct shot means that Black has a slightly better chance of closing White out.
White is favored because Black’s two inner board points are deeper, and the ace-point is in fact behind White’s blot. As a result, when White does anchor Black will have some checkers out of play, so his alternative game plan of priming White isn’t nearly as strong. In our benchmark position, all Black’s checkers are still in front of White’s blot, so if a blitz doesn’t work, Black still has chances of building a prime.
Which feature is more important? In fact, Black completes a closeout less than 30% of the time in either position, so the long-term aspects of the position matter most. In Position 61, Black can play quietly for the prime, taking chances only when he rolls very well. In 61a, he has to go for the closeout, but he stands somewhat poorly whenever White survives. Black is actually substantially worse off in 61a, so the theoretically correct play there is no double. (The correct play over the board against anyone but a top player is to double, for the same reason as before; many players are afraid of blitz positions and will pass them without much thought.)
Solution: The double/no double decision is a tossup; if doubled, White should take.
