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Problem of the Week #113: Solution
07-27-2011
, 11:46 AM
Problem of the Week #113: Solution
Cash game. Center cube. Black on roll.
Should Black double? Should White take if doubled?
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.
Problem 113 shows a common sort of early game position. Black made his 5-point early on while White countered with his 4-point. Black has just hit White on his 4-point, and White fanned. The dance gives Black a chance to think about turning the cube. Should he? Let’s see.
We like to evaluate these early doubles with the Race – Position – Threat (RPT) method. Evaluate who’s ahead in each category, and if Black has an edge in two out of three, he probably has a double and White probably has a take. If Black leads in all three, White often has to pass.
The race here is pretty easy: White has a checker in the air, and Black has a solid lead of 17 pips, 153 to 170.
The position and the threat categories actually merge in this problem. If Black covers his 4-point, then he has a solid edge in position. But his only real threat in the position is to cover the 4-point, which he’s likely to do. We can say that he either has a positional edge with no threat, or a big threat but no current edge. (Note that White’s blot on his 10-point is pretty safe, as almost all the numbers that hit would be properly used to cover the 4-point. Black’s only hitting number is actually 5-3.)
With the positional edge hinging on the execution of the threat, we can’t really give Black a 3 on the RPT score. Scoring him a solid 2 looks more like it, in which case White most likely has a take and Black probably has a double. As most of our readers correctly saw, White’s take is pretty easy here. Mostly Black covers his 4-point and White enters, after which the game goes on. White has the worst of it but his game is solid with no actual positional weaknesses. Black will have two checkers to escape, and he’ll be unlikely to make his bar-point anytime soon, so White should be able to generate plenty of counterplay for the rest of the game.
How strong is Black’s double? That’s actually the more interesting question. A good double requires some market losers, and Black has a few here. If he covers, say with a 6-3, and White then fans, the position will be double and drop. He’s got a total of 26 cover numbers, after which White fans 25% of the time, making a total of about 18% market-losing chances. That might sound like a lot, but it’s not really that impressive because no sequence leads to a huge market loss. After Black covers with a 6-3 and White fans, for instance, Black loses his market by only about 0.15 ppg. A cover sequence that breaks the 8-point is even weaker. After 4-1 (played 8/4 6/5) followed by dancing, Black loses his market by only about 0.05 ppg. So while Black has a few market losers, hardly any are really crushing. That’s discouraging, because when we double, we’d like to see a few sequences where our equity shoots way up into the “pass” category.
In fact, rollouts indicate that a double here is a completely marginal decision – doesn’t gain anything, doesn’t lose anything. That result in itself, however, makes this a very valuable benchmark position. Since it’s not an uncommon sort of structure, committing it to memory is very useful; anything better than this for Black is a clear double, anything worse is a clear no double. Most serious players are familiar with a collection of take/pass benchmarks, but double/no double benchmarks are just as valuable.
Knowing that it’s a marginal decision, I would as a practical matter double over the board. There’s always some chance my opponent will pass, which is an enormous gain for me, and if he takes I’ve lost nothing.
Solution: marginal double/no double for Black; easy take for White.
Cash game. Center cube. Black on roll.
Should Black double? Should White take if doubled?
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.
Problem 113 shows a common sort of early game position. Black made his 5-point early on while White countered with his 4-point. Black has just hit White on his 4-point, and White fanned. The dance gives Black a chance to think about turning the cube. Should he? Let’s see.
We like to evaluate these early doubles with the Race – Position – Threat (RPT) method. Evaluate who’s ahead in each category, and if Black has an edge in two out of three, he probably has a double and White probably has a take. If Black leads in all three, White often has to pass.
The race here is pretty easy: White has a checker in the air, and Black has a solid lead of 17 pips, 153 to 170.
The position and the threat categories actually merge in this problem. If Black covers his 4-point, then he has a solid edge in position. But his only real threat in the position is to cover the 4-point, which he’s likely to do. We can say that he either has a positional edge with no threat, or a big threat but no current edge. (Note that White’s blot on his 10-point is pretty safe, as almost all the numbers that hit would be properly used to cover the 4-point. Black’s only hitting number is actually 5-3.)
With the positional edge hinging on the execution of the threat, we can’t really give Black a 3 on the RPT score. Scoring him a solid 2 looks more like it, in which case White most likely has a take and Black probably has a double. As most of our readers correctly saw, White’s take is pretty easy here. Mostly Black covers his 4-point and White enters, after which the game goes on. White has the worst of it but his game is solid with no actual positional weaknesses. Black will have two checkers to escape, and he’ll be unlikely to make his bar-point anytime soon, so White should be able to generate plenty of counterplay for the rest of the game.
How strong is Black’s double? That’s actually the more interesting question. A good double requires some market losers, and Black has a few here. If he covers, say with a 6-3, and White then fans, the position will be double and drop. He’s got a total of 26 cover numbers, after which White fans 25% of the time, making a total of about 18% market-losing chances. That might sound like a lot, but it’s not really that impressive because no sequence leads to a huge market loss. After Black covers with a 6-3 and White fans, for instance, Black loses his market by only about 0.15 ppg. A cover sequence that breaks the 8-point is even weaker. After 4-1 (played 8/4 6/5) followed by dancing, Black loses his market by only about 0.05 ppg. So while Black has a few market losers, hardly any are really crushing. That’s discouraging, because when we double, we’d like to see a few sequences where our equity shoots way up into the “pass” category.
In fact, rollouts indicate that a double here is a completely marginal decision – doesn’t gain anything, doesn’t lose anything. That result in itself, however, makes this a very valuable benchmark position. Since it’s not an uncommon sort of structure, committing it to memory is very useful; anything better than this for Black is a clear double, anything worse is a clear no double. Most serious players are familiar with a collection of take/pass benchmarks, but double/no double benchmarks are just as valuable.
Knowing that it’s a marginal decision, I would as a practical matter double over the board. There’s always some chance my opponent will pass, which is an enormous gain for me, and if he takes I’ve lost nothing.
Solution: marginal double/no double for Black; easy take for White.
