Two Plus Two Forums
Sports and Games
Chess and Other Board Games
Backgammon Forum hosted by Bill Robertie.
Problem of the Week #78: Solution
10-11-2010
, 01:14 PM
Problem of the Week #78: Solution
Cash game, Center cube. Black on roll.
(a) Should Black double? Should White take if doubled?
(b) Assume Black doubles and White takes. Black to play
3-1
4-1
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.
We’ve talked before about the important of reference positions to understanding proper cube action. Problem 78 is another example of this idea.
A reference position is simply a prototypical position that captures a lot of information in a single example. By building a solid library of well-chosen reference positions, we can compare the real position we’re facing to a related example from our mental reference library, and make a better judgment than we would have made by analyzing the position from scratch.
When using reference positions, it’s important to recall the position exactly, rather than relying on a vague impression of the position. In backgammon, small changes in the position can have a big effect on the evaluation, and Position 78 illustrates this idea perfectly.
The reference position I’d be referring to in this situation is the well-known position after White opens with a 6-4 and runs, Black responds with 5-5, making two inner points, and White dances. Here’s that position:
Position 78a: First Blitz Reference Position
If you remember this position precisely (which is easy to do because it comes from just a three-move sequence) then you’ll have no problem with our starting position. Position 78a is a clear double and an easy take. Position 78 differs in three ways: Black has an extra builder on the 7-point, Black has an extra shot at White’s blot on the 10-point (13 hitting numbers versus 11 if the blot is on the 11-point), and White has an extra blot on his own 9-point.
These might look like modest changes, but they’re not. To see why, let’s count Black’s numbers in each position that either (a) make an inner-board point or (b) hit a second checker. In the reference position (78a) Black has 17 numbers that do one of these things: all twos plus 3-1, 6-4, 1-1, and 4-4. In our actual problem position, however, Black has 26 numbers that do at least one of these things: all threes plus 2-1, 4-2, 6-4, 5-4, 6-5, 6-2, 1-1, 2-2, and 4-4. In other words, Black has gone from having less than half of his numbers playing very well to nearly three-quarters, a huge improvement.
Not only does Black have more good numbers in our actual position, but his good numbers are much better than in the reference position because of the presence of the second White blot. As a typical example, if Black throws 6-2 and plays 24/16*, he now has two checkers up in the air plus a double shot at White’s loose checker on his 10-point, which is a better result than he can achieve in the reference position.
In short, if we can remember our reference position clearly, it’s easy to see that Problem 78 is much stronger for Black, and in fact the correct evaluation is double and drop.
What happens, however, if our reference position isn’t an exact position but just a slightly hazy concept? In that case, our mental process might sound like this: “Hmm – blitzing here – I know this position, my opponent’s rolled double fives and I’m on the bar – he’s shooting at a blot – double and easy take. I take!”
If you remember that small changes to a position can make big changes in the evaluation, then you’ll see the value of remembering specific positions, rather than vague concepts.
In addition to Position 78a above, there are two other blitz reference positions that I think are crucial to remember clearly. One is the position after splitting to the bar with a 6-2 and getting blitzed:
Position 78b: White played 6-2, splitting to the bar; Black rolled 5-5 and White danced.
This position is an optimal double for Black, and White’s decision to take or drop is very close, with dropping probably slightly better in a cash game against a first-class opponent.
The other good reference position is a 3-3 blitz:
Position 78c: White played 4-3, splitting to the 20-point; Black rolled 3-3 and White fanned.
This is a clear double and a clear take, although the take is closer than in 78a. White loses about 0.9 points by taking.
(b) Black to play 3-1 and 4-1 in our original position.
The two checker play problems are pretty simple, but each has an important point worth noting.
With the 3-1, hitting with 13/10* 24/23 is the best play by a pretty wide margin. Hitting with 13/10*/9 trails in second place, and making the 5-point is a blunder. In normal early game positions, where both sides have a couple of men back, making the 5-point often trumps hitting in the outfield. In a blitz position, however, hitting in the outfield is usually better than making an inner-board point. In addition to putting a second man on the bar, hitting brings a fourth builder into play for both the 4-point and the 5-point, while splitting in back creates some new hitting numbers at the blot on White’s 9-point. That’s a lot of good things.
Making the 5-point is structurally nice but gobbles up most of Black’s builders in the process. If White then enters, he’ll usually safety his blot on the 10-point, and Black will have to struggle to make new progress.
The other roll, 4-1, is one of Black’s worst shots, a swing and a miss. Players have a tendency in blitz positions to overplay things when they roll a really bad number, almost as though they’re in a big rush to keep the game on the road they think it should go. You might, for instance, see someone make a play like 13/9 24/23 here, spreading out blots in the hope that White fans again and now he’s a huge favorite to hit or make another point.
But spreading out the blots when your opponent has only one man on the bar is often just a bad idea. Remember that the blitz isn’t your only game plan for winning. After a sequence like 5-5 and a fan, you not only have blitzing chances, you’re also way ahead in the race. Sometimes the dice demand that you shelve one game plan for now and switch back to another. In this case, the 4-1 play requires you to downplay the blitz and give yourself a better chance to just win the race. The right idea is the simple 24/20 8/7, buttoning up and getting the back men moving. If White fans again, you’ll still have lots of chances to restart the blitz; otherwise you’ve put yourself in a pretty good position to simply convert your racing advantage.
Solution:
(a) Black should double and White should pass.
(b) 3-1: play 13/10* 24/23.
(b) 4-1: play 24/20 8/7.
Cash game, Center cube. Black on roll.
(a) Should Black double? Should White take if doubled?
(b) Assume Black doubles and White takes. Black to play
3-1
4-1
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.
We’ve talked before about the important of reference positions to understanding proper cube action. Problem 78 is another example of this idea.
A reference position is simply a prototypical position that captures a lot of information in a single example. By building a solid library of well-chosen reference positions, we can compare the real position we’re facing to a related example from our mental reference library, and make a better judgment than we would have made by analyzing the position from scratch.
When using reference positions, it’s important to recall the position exactly, rather than relying on a vague impression of the position. In backgammon, small changes in the position can have a big effect on the evaluation, and Position 78 illustrates this idea perfectly.
The reference position I’d be referring to in this situation is the well-known position after White opens with a 6-4 and runs, Black responds with 5-5, making two inner points, and White dances. Here’s that position:
Position 78a: First Blitz Reference Position
If you remember this position precisely (which is easy to do because it comes from just a three-move sequence) then you’ll have no problem with our starting position. Position 78a is a clear double and an easy take. Position 78 differs in three ways: Black has an extra builder on the 7-point, Black has an extra shot at White’s blot on the 10-point (13 hitting numbers versus 11 if the blot is on the 11-point), and White has an extra blot on his own 9-point.
These might look like modest changes, but they’re not. To see why, let’s count Black’s numbers in each position that either (a) make an inner-board point or (b) hit a second checker. In the reference position (78a) Black has 17 numbers that do one of these things: all twos plus 3-1, 6-4, 1-1, and 4-4. In our actual problem position, however, Black has 26 numbers that do at least one of these things: all threes plus 2-1, 4-2, 6-4, 5-4, 6-5, 6-2, 1-1, 2-2, and 4-4. In other words, Black has gone from having less than half of his numbers playing very well to nearly three-quarters, a huge improvement.
Not only does Black have more good numbers in our actual position, but his good numbers are much better than in the reference position because of the presence of the second White blot. As a typical example, if Black throws 6-2 and plays 24/16*, he now has two checkers up in the air plus a double shot at White’s loose checker on his 10-point, which is a better result than he can achieve in the reference position.
In short, if we can remember our reference position clearly, it’s easy to see that Problem 78 is much stronger for Black, and in fact the correct evaluation is double and drop.
What happens, however, if our reference position isn’t an exact position but just a slightly hazy concept? In that case, our mental process might sound like this: “Hmm – blitzing here – I know this position, my opponent’s rolled double fives and I’m on the bar – he’s shooting at a blot – double and easy take. I take!”
If you remember that small changes to a position can make big changes in the evaluation, then you’ll see the value of remembering specific positions, rather than vague concepts.
In addition to Position 78a above, there are two other blitz reference positions that I think are crucial to remember clearly. One is the position after splitting to the bar with a 6-2 and getting blitzed:
Position 78b: White played 6-2, splitting to the bar; Black rolled 5-5 and White danced.
This position is an optimal double for Black, and White’s decision to take or drop is very close, with dropping probably slightly better in a cash game against a first-class opponent.
The other good reference position is a 3-3 blitz:
Position 78c: White played 4-3, splitting to the 20-point; Black rolled 3-3 and White fanned.
This is a clear double and a clear take, although the take is closer than in 78a. White loses about 0.9 points by taking.
(b) Black to play 3-1 and 4-1 in our original position.
The two checker play problems are pretty simple, but each has an important point worth noting.
With the 3-1, hitting with 13/10* 24/23 is the best play by a pretty wide margin. Hitting with 13/10*/9 trails in second place, and making the 5-point is a blunder. In normal early game positions, where both sides have a couple of men back, making the 5-point often trumps hitting in the outfield. In a blitz position, however, hitting in the outfield is usually better than making an inner-board point. In addition to putting a second man on the bar, hitting brings a fourth builder into play for both the 4-point and the 5-point, while splitting in back creates some new hitting numbers at the blot on White’s 9-point. That’s a lot of good things.
Making the 5-point is structurally nice but gobbles up most of Black’s builders in the process. If White then enters, he’ll usually safety his blot on the 10-point, and Black will have to struggle to make new progress.
The other roll, 4-1, is one of Black’s worst shots, a swing and a miss. Players have a tendency in blitz positions to overplay things when they roll a really bad number, almost as though they’re in a big rush to keep the game on the road they think it should go. You might, for instance, see someone make a play like 13/9 24/23 here, spreading out blots in the hope that White fans again and now he’s a huge favorite to hit or make another point.
But spreading out the blots when your opponent has only one man on the bar is often just a bad idea. Remember that the blitz isn’t your only game plan for winning. After a sequence like 5-5 and a fan, you not only have blitzing chances, you’re also way ahead in the race. Sometimes the dice demand that you shelve one game plan for now and switch back to another. In this case, the 4-1 play requires you to downplay the blitz and give yourself a better chance to just win the race. The right idea is the simple 24/20 8/7, buttoning up and getting the back men moving. If White fans again, you’ll still have lots of chances to restart the blitz; otherwise you’ve put yourself in a pretty good position to simply convert your racing advantage.
Solution:
(a) Black should double and White should pass.
(b) 3-1: play 13/10* 24/23.
(b) 4-1: play 24/20 8/7.
10-16-2010
, 06:09 PM
