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Problem of the Week #9: Solution
05-10-2009
, 08:57 PM
Problem of the Week #9: Solution
Cash game, center cube. Black to play 4-3.
This position is from a match played some years ago in Monte Carlo. The opponents were two former World Champions: Paul Magriel (Black) and Philip Marmorstein of Germany (White). (It was early in a long match and the score had no bearing on the play, so I’ve turned it into a cash game problem.)
The players are involved in what’s called a mutual holding game, where both sides have an advanced anchor. Black leads by 17 pips in the race, 124 to 141. With the 4-3, Magriel decided it was a good time to break his anchor by 18/11, relying on the duplication of sixes and White’s awkward home board. Was he correct? If not, what’s a better plan and why?
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In a mutual holding game, both sides secure an advanced anchor early in the game. Once that occurs, strategy becomes pretty simple. Each side hopes to roll a big double, allowing them to take a lead in the race while swinging the anchor around the board. Since big doubles are rare, this variation doesn’t usually happen. Instead, both players hold their anchor while filling their home board with the remaining spare checkers and waiting. This phase of the game is easy to play.
Eventually, players run out of spare checkers and start to face some tough decisions. Do I run off my anchor now or wait? Do I save a 6 in the outfield, or break my home board? If I get a shot, can I double? These decisions are always challenging, and a large body of theory has developed on this part of the game.
Problem 9 is more unusual, however. We’re still in an early phase of the holding game, and both sides have spares to play. The “normal” play here would be either 7/3 7/4 or 6/2 4/1, leaving no shots and waiting for the next roll. Over the board, I would expect to see one of those choices made 90% of the time.
Paul Magriel, however, is a brilliant and creative player, and found an interesting idea. White’s home board is weak and difficult to improve quickly. Black will be ahead in the race by 24 pips after this roll. Might this not be the time to break the anchor, especially since he can duplicate sixes in the process? After some thought, Magriel played the unusual 18/11!
The idea is clear and clever. Sixes are duplicated, and if White misses, Black has a reasonable chance to consolidate and play a one-way holding game with a considerable racing advantage.
Ingenious and clever to be sure, but in backgammon, ingenious and clever isn’t the same as correct. Let’s look at the play a little more closely. In particular, let’s think about the real value of duplication.
Duplication is a nice tactical idea which, however, can be overused. It’s most often a guide to the correct play in two common situations.
The first situation occurs when you’re stuck with two blots floating around the board, and you have to find the right places for them. If you can duplicate your opponent’s hitting numbers, say by arranging your blots so he needs a three to hit in one place and a three to hit in another place, then you’ve almost certainly found the best play. Note that in this case you had no choice about leaving the blots; you were going to have blots no matter what play you made. Duplication just allowed you to arrange the blots in the safest possible way.
The second situation occurs when your opponent badly needs a number on one side of the board (say a four to make an advanced anchor) and you can slot a point you’d like to make, giving him a four to hit on the other side of the board. Now you’re leaving an extra blot, but the cost of this extra blot is very small, because your opponent could have used the hitting number to great advantage elsewhere.
Note that in these two cases, duplication isn’t really a goal, like building points or hitting blots; instead it’s a shorthand way of either counting shots (the first situation), or discounting the value of shots (the second situation).
Problem 9 represents a third type of situation, one where you actually break a point you didn’t have to break, relying on duplication to lessen the danger. When the game from which this position was taken occurred, this idea was very much in the air. Now, however, theory has advanced to the point where we can say that such positions are extremely rare, and require very unusual circumstances to be correct.
This position actually illustrates pretty clearly the problems with this approach. True, 18/11 duplicates sixes. Very nice. But now let’s go a step further and actually count the number of very good rolls White has. We’ll define a ‘good roll’ as one which either hits a blot and makes the 5-point, or one which hits two blots. The result is a little surprising.
White rolls that hit and make the 5-point (11): 6-2, 6-3, 1-2, 1-3, 1-1, 2-2, 3-3.
White rolls that hit two men (3): 6-6, 6-1.
Despite the duplication, White has 14 rolls, or almost 40% of his total rolls, that do something very good immediately. But Black has still more problems after this roll. Suppose, for instance, White rolls a constructive non-hitter, something like 5-3, which makes his 5-point. How likely is Black to leave another shot (or two)?
The answer may surprise you. Black is about 70% to leave a shot on the next roll! Here’s the count.
Black rolls that leave two blots (1): 6-6.
Black rolls that leave one blot (25): 6-5, 6-4, 6-3, 6-2, 6-1, 5-1, 4-2, 4-1, 3-2, 3-1, 2-1, 3-3, 2-2, 1-1.
With that count, we can pretty much dismiss 18/11 as a play. So what’s left? Do we have to play safe, or is there yet another idea to try?
The safe play of clearing the 7-point is OK, roughly on a par with 18/11. Black avoids trouble on this roll but, as you might expect, gets squeezed off the 18-point fairly quickly. The right play involves a completely different idea and is incredibly hard to find over the board. It’s the surprising 13/6!
The idea behind the move is to take a small immediate risk to buy a lot of time. It leaves White only three hit and cover numbers (3-1 and 4-4). By breaking the midpoint in relative safety, however, Black creates a lot of spares. If missed, he can now freely move the blot on the midpoint, the two spares on his 6-point, and the four checkers on his 7-point and 8-point. While he moves these checkers, he can wait for a double that will let him move off the 18-point, or a weird roll from White that somehow changes the nature of the position.
What makes this play particularly hard to find is that it’s an in-between move. It doesn’t try to solve the immediate problem in a bold and direct manner (18/11) and it doesn’t simply play safe and wait (7/3 7/4). Instead, it incurs a small immediate risk which then buys a lot of time. We humans tend to look for moves that are direct solutions. If those fail, we naturally fall back on plays that are completely safe. Positions where in-between plays actually have the highest equity are difficult for us to handle.
I used this position for a long time in one of the problem sets that I gave to pupils. Over the years, about a hundred pupils looked at this problem, and no one ever found the correct play over the board, making this one of the most deceptively difficult middle game positions of which I’m aware.
Solution: 13/6.
Cash game, center cube. Black to play 4-3.
This position is from a match played some years ago in Monte Carlo. The opponents were two former World Champions: Paul Magriel (Black) and Philip Marmorstein of Germany (White). (It was early in a long match and the score had no bearing on the play, so I’ve turned it into a cash game problem.)
The players are involved in what’s called a mutual holding game, where both sides have an advanced anchor. Black leads by 17 pips in the race, 124 to 141. With the 4-3, Magriel decided it was a good time to break his anchor by 18/11, relying on the duplication of sixes and White’s awkward home board. Was he correct? If not, what’s a better plan and why?
-------------------------
In a mutual holding game, both sides secure an advanced anchor early in the game. Once that occurs, strategy becomes pretty simple. Each side hopes to roll a big double, allowing them to take a lead in the race while swinging the anchor around the board. Since big doubles are rare, this variation doesn’t usually happen. Instead, both players hold their anchor while filling their home board with the remaining spare checkers and waiting. This phase of the game is easy to play.
Eventually, players run out of spare checkers and start to face some tough decisions. Do I run off my anchor now or wait? Do I save a 6 in the outfield, or break my home board? If I get a shot, can I double? These decisions are always challenging, and a large body of theory has developed on this part of the game.
Problem 9 is more unusual, however. We’re still in an early phase of the holding game, and both sides have spares to play. The “normal” play here would be either 7/3 7/4 or 6/2 4/1, leaving no shots and waiting for the next roll. Over the board, I would expect to see one of those choices made 90% of the time.
Paul Magriel, however, is a brilliant and creative player, and found an interesting idea. White’s home board is weak and difficult to improve quickly. Black will be ahead in the race by 24 pips after this roll. Might this not be the time to break the anchor, especially since he can duplicate sixes in the process? After some thought, Magriel played the unusual 18/11!
The idea is clear and clever. Sixes are duplicated, and if White misses, Black has a reasonable chance to consolidate and play a one-way holding game with a considerable racing advantage.
Ingenious and clever to be sure, but in backgammon, ingenious and clever isn’t the same as correct. Let’s look at the play a little more closely. In particular, let’s think about the real value of duplication.
Duplication is a nice tactical idea which, however, can be overused. It’s most often a guide to the correct play in two common situations.
The first situation occurs when you’re stuck with two blots floating around the board, and you have to find the right places for them. If you can duplicate your opponent’s hitting numbers, say by arranging your blots so he needs a three to hit in one place and a three to hit in another place, then you’ve almost certainly found the best play. Note that in this case you had no choice about leaving the blots; you were going to have blots no matter what play you made. Duplication just allowed you to arrange the blots in the safest possible way.
The second situation occurs when your opponent badly needs a number on one side of the board (say a four to make an advanced anchor) and you can slot a point you’d like to make, giving him a four to hit on the other side of the board. Now you’re leaving an extra blot, but the cost of this extra blot is very small, because your opponent could have used the hitting number to great advantage elsewhere.
Note that in these two cases, duplication isn’t really a goal, like building points or hitting blots; instead it’s a shorthand way of either counting shots (the first situation), or discounting the value of shots (the second situation).
Problem 9 represents a third type of situation, one where you actually break a point you didn’t have to break, relying on duplication to lessen the danger. When the game from which this position was taken occurred, this idea was very much in the air. Now, however, theory has advanced to the point where we can say that such positions are extremely rare, and require very unusual circumstances to be correct.
This position actually illustrates pretty clearly the problems with this approach. True, 18/11 duplicates sixes. Very nice. But now let’s go a step further and actually count the number of very good rolls White has. We’ll define a ‘good roll’ as one which either hits a blot and makes the 5-point, or one which hits two blots. The result is a little surprising.
White rolls that hit and make the 5-point (11): 6-2, 6-3, 1-2, 1-3, 1-1, 2-2, 3-3.
White rolls that hit two men (3): 6-6, 6-1.
Despite the duplication, White has 14 rolls, or almost 40% of his total rolls, that do something very good immediately. But Black has still more problems after this roll. Suppose, for instance, White rolls a constructive non-hitter, something like 5-3, which makes his 5-point. How likely is Black to leave another shot (or two)?
The answer may surprise you. Black is about 70% to leave a shot on the next roll! Here’s the count.
Black rolls that leave two blots (1): 6-6.
Black rolls that leave one blot (25): 6-5, 6-4, 6-3, 6-2, 6-1, 5-1, 4-2, 4-1, 3-2, 3-1, 2-1, 3-3, 2-2, 1-1.
With that count, we can pretty much dismiss 18/11 as a play. So what’s left? Do we have to play safe, or is there yet another idea to try?
The safe play of clearing the 7-point is OK, roughly on a par with 18/11. Black avoids trouble on this roll but, as you might expect, gets squeezed off the 18-point fairly quickly. The right play involves a completely different idea and is incredibly hard to find over the board. It’s the surprising 13/6!
The idea behind the move is to take a small immediate risk to buy a lot of time. It leaves White only three hit and cover numbers (3-1 and 4-4). By breaking the midpoint in relative safety, however, Black creates a lot of spares. If missed, he can now freely move the blot on the midpoint, the two spares on his 6-point, and the four checkers on his 7-point and 8-point. While he moves these checkers, he can wait for a double that will let him move off the 18-point, or a weird roll from White that somehow changes the nature of the position.
What makes this play particularly hard to find is that it’s an in-between move. It doesn’t try to solve the immediate problem in a bold and direct manner (18/11) and it doesn’t simply play safe and wait (7/3 7/4). Instead, it incurs a small immediate risk which then buys a lot of time. We humans tend to look for moves that are direct solutions. If those fail, we naturally fall back on plays that are completely safe. Positions where in-between plays actually have the highest equity are difficult for us to handle.
I used this position for a long time in one of the problem sets that I gave to pupils. Over the years, about a hundred pupils looked at this problem, and no one ever found the correct play over the board, making this one of the most deceptively difficult middle game positions of which I’m aware.
Solution: 13/6.
