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Problem of the Week #67: Solution
06-20-2010
, 10:24 AM
Problem of the Week #67: Solution
Cash game, center cube.
Black to play 4-2.
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.
ANNOUNCEMENT: I’ll be taking a vacation until July 16th, so this will be the last problem for a few weeks. Problem 68 will be posted on Sunday, July 18th.
If you understood the logic behind Problem 66, you should have no trouble with Problem 67, although the two positions belong to different categories. Problem 66 was what I call a “One Man Back” position, where the issue was to move up in the board and try to get into a race, or stay back and wait for a better chance later. Problem 67 belongs in a category I call “Split or Something Else”, where one choice is to split the back checkers and go for an anchor, while the other choice is something different, like making an offensive point, bringing down builders, or just waiting. In this case Play A is splitting with 24/20 13/11, while Play B is to wait with 13/7, gobbling up some of Black’s timing in the process.
The merits of the two plays seem pretty clear. Splitting looks like the high risk, high reward play, while staying back maintains the status quo while waiting for a better chance to move up.
The key question you need to ask in these positions is a simple one: If I move up and get pointed on, how much worse off am I than if I had stayed back and White had made the point anyway? In Problem 66, we saw that getting pointed on was hardly any worse at all than staying back and having White make the point. Is that true in Problem 67 as well?
Actually, the result here is even more surprising. If Black knew that White’s next roll would be 6-2, making the 5-point, he would still be better off splitting! This seems startlingly counter-intuitive to most players, but if we drill down into some of the variations, we can see the logic.
1) After White makes the five-point, the only great rolls for Black are those which let him anchor on White’s 4-point. If Black has two checkers back on the 24-point, only one number accomplishes this (3-3). If Black has a checker on the bar, he can make the 4-point with two numbers (4-3 and 3-4).
2) Black’s big numbers (6-6, 5-5, and 6-5) are very bad if Black has to play them while sitting on the 24-point, since they ruin his timing. If Black is in the air, he dances with these numbers, which improves his position considerably. Remember that Black’s 4-prime is a huge asset in this position (his only asset, in fact), and once that goes he’s toast.
3) Once White makes the 5-point, Black needs to be advancing to White’s 4-point. He has more ways to get to the 4-point if he’s on the bar (all fours plus 2-3, 1-3, and 2-2) than if both checkers are on the 24-point (all threes plus 1-2).
In short, after Black plays 13/7 and White rolls 6-2, Black (on roll) is about 30% to win, while after 24/20 13/11 followed by a 6-2 from White, Black is about 34% to win! By splitting, Black isn’t actually taking on extra risk for a big reward. The play is essentially risk-free, since it’s both trying to establish an anchor while preserving timing on the other side of the board. In this sense the play has a connection to a lot of back game situations, where the back game player can leave blots freely, knowing that he’s better off both when the blots get hit and when they don’t get hit.
The last point to notice about the position is the cube action. It’s no double and easy take after either play. Black’s 4-point prime is a huge asset, giving White plenty of work to do on both sides of the board.
Solution: 24/20 13/11
Cash game, center cube.
Black to play 4-2.
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.
ANNOUNCEMENT: I’ll be taking a vacation until July 16th, so this will be the last problem for a few weeks. Problem 68 will be posted on Sunday, July 18th.
If you understood the logic behind Problem 66, you should have no trouble with Problem 67, although the two positions belong to different categories. Problem 66 was what I call a “One Man Back” position, where the issue was to move up in the board and try to get into a race, or stay back and wait for a better chance later. Problem 67 belongs in a category I call “Split or Something Else”, where one choice is to split the back checkers and go for an anchor, while the other choice is something different, like making an offensive point, bringing down builders, or just waiting. In this case Play A is splitting with 24/20 13/11, while Play B is to wait with 13/7, gobbling up some of Black’s timing in the process.
The merits of the two plays seem pretty clear. Splitting looks like the high risk, high reward play, while staying back maintains the status quo while waiting for a better chance to move up.
The key question you need to ask in these positions is a simple one: If I move up and get pointed on, how much worse off am I than if I had stayed back and White had made the point anyway? In Problem 66, we saw that getting pointed on was hardly any worse at all than staying back and having White make the point. Is that true in Problem 67 as well?
Actually, the result here is even more surprising. If Black knew that White’s next roll would be 6-2, making the 5-point, he would still be better off splitting! This seems startlingly counter-intuitive to most players, but if we drill down into some of the variations, we can see the logic.
1) After White makes the five-point, the only great rolls for Black are those which let him anchor on White’s 4-point. If Black has two checkers back on the 24-point, only one number accomplishes this (3-3). If Black has a checker on the bar, he can make the 4-point with two numbers (4-3 and 3-4).
2) Black’s big numbers (6-6, 5-5, and 6-5) are very bad if Black has to play them while sitting on the 24-point, since they ruin his timing. If Black is in the air, he dances with these numbers, which improves his position considerably. Remember that Black’s 4-prime is a huge asset in this position (his only asset, in fact), and once that goes he’s toast.
3) Once White makes the 5-point, Black needs to be advancing to White’s 4-point. He has more ways to get to the 4-point if he’s on the bar (all fours plus 2-3, 1-3, and 2-2) than if both checkers are on the 24-point (all threes plus 1-2).
In short, after Black plays 13/7 and White rolls 6-2, Black (on roll) is about 30% to win, while after 24/20 13/11 followed by a 6-2 from White, Black is about 34% to win! By splitting, Black isn’t actually taking on extra risk for a big reward. The play is essentially risk-free, since it’s both trying to establish an anchor while preserving timing on the other side of the board. In this sense the play has a connection to a lot of back game situations, where the back game player can leave blots freely, knowing that he’s better off both when the blots get hit and when they don’t get hit.
The last point to notice about the position is the cube action. It’s no double and easy take after either play. Black’s 4-point prime is a huge asset, giving White plenty of work to do on both sides of the board.
Solution: 24/20 13/11
