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Problem of the Week #155: Solution
12-17-2012
, 10:13 AM
Problem of the Week #155: Solution
(a) Cash game, center cube.
Should Black double? Should White take if doubled?
(b) Assume Black doubles and White takes. Black to play
(b1) 55
(b2) 33
(b3) 53
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) Cube action?
Problem 155 is a more or less common middle game position with some interesting move choices coming up. First, however, Black has to decide if he wants to double or not.
Let’s start by looking at the elements in our standard position-race-threat matrix.
Position: Black has some clear assets here. He has an anchor, and White doesn’t. White is on the bar, which is a plus for Black. Black has a 4-point block, White has only three points in front of Black’s anchor.
On the negative side, White has a better home board, with three points to Black’s two. In addition, White has spares on his midpoint, while Black’s midpoint is stripped. On balance, we have an edge for Black, but not a huge edge.
Race: Black leads 140 to 149, with plenty of contact. Small edge to Black.
Threats: Black has a few numbers to make a 5-prime: 31, 41, 43, and some small doubles. If he can fill in another point in his board and White doesn’t anchor, Black could develop a blitz. That constitutes a few threats, but not a lot of threats.
The takeaway from all this is that Black has an edge in all three areas, so he should certainly have an initial double. An edge in every area often indicates a pass, but here all the edges are small, so White can squeeze out a take.
Now let’s assume that Black doubles and White takes, and move on to the checker plays.
(b1) Black to play 55. This is an interesting roll because Black has many choices, leading to lots of different game plans. Here’s a quick run-down:
Play #1 -- 8/3(2) 7/2(2). The all-out blitz play, making two inner points.
Play #2 – 13/3(2). A priming play, but one which could turn into a blitz if things go well.
Play #3 – 21/11(2). The connectivity play, keeping a compact formation and leaving no stragglers behind.
Play #4 – 21/16(2) 8/3(2). A little connectivity, a little building.
Play #5 – 21/6 21/16. Creates a nice collection of builders at the cost of leaving a few shots.
If this were double match point and Black’s only goal was to win the game, the clear play would be 21/11(2). That play disengages the anchor, keeps a nicely connected position, and leaves Black sitting on a 29-pip lead in the race with no problems playing upcoming rolls.
All the other plays trade some wins for an increased chance of winning a gammon. The play that gets the most gammon chances is 8/3(2) 7/2(2). Black gets a quick 4-point board, but leaves his other checkers scattered around. At the other extreme is 21/6 21/16, which disengages and gets a nice building structure, at the cost of leaving a few embarrassing shots. The other plays fit in between these two.
Plays that sacrifice some winning chances for extra gammons tend to be harder to evaluate than most. You’re not comparing two similar plays to see which one makes a slightly better structure. Instead you’re measuring apples and oranges. Exactly how much am I giving up in winning chances in these two very dissimilar positions? Exactly what am I getting in extra gammons? Am I getting more than two extra gammons for any extra loss? These are usually tough questions.
Here’s a few rules of thumb that I’ve found work pretty well in these positions. They’re not infallible, but they do help:
Rule 1: If the gammon play doesn’t actually make a point on the defender’s head, go with the DMP play.
Rule 2: Look at the position if the attacker makes the gammon play and the defender anchors. If it’s too hard to bring home, make the DMP play.
Rule 3: The more structure the defender has, the more you want to make the DMP play.
Rule 4: When in doubt, make the DMP play.
A quick scan of this list shows that generally you’ll be playing to win the most games, and that’s right. In the bulk of these problems, the best play to win turns out to be the right choice.
Now let’s go back to our 5-5 play.
By Rule 1, the gammonish plays don’t actually point on White’s head. Play 2 makes a good point, and Play 1 makes two good points, but neither puts a second checker in the air. Rule 1 argues for the positional play, 21/11(2).
For Rule 2, let’s suppose Black makes Play 1 and White then rolls an ace and anchors. How do we like Black’s position? He’s got a couple of loose blots, the 4-point is still open, and Black will have to be moving off the 13-point and 21-point pretty quickly, while White has plenty of spares to move as he improves his position. This will be hard to bring home. Edge to the positional play.
Rule 3 makes an argument for the positional play since White already has plenty of structure – a 3-point board and a nice little block against the 21-point.
With everything arguing for the positional play, Rule 4 doesn’t really apply because there’s not much doubt. Black should play 21/11(2).
(b2) Black to play 3-3. This roll poses a whole new set of problems. The best play to win the gammon is clearly 7/1*(2). But the DMP play isn’t as clear as before. At DMP, two game plans dominate: the running game, because races don’t win many gammons and are relatively easy to bring home, and the priming game, because if you can build a full prime and break your opponent’s timing you become a huge favorite. Here we have one good candidate for each type – 21/15(2) for the running game and 13/4 7/4 for the priming game. What’s right?
In a matchup between 21/15(2) and 13/4 7/4, making the 4-point dominates. Making the prime is almost as good for the win as running (74% versus 75.4%, according to rollouts), but since it actually makes an inner-board point, it’s hugely better for winning gammons (31% gammons versus 16.4%).
What about the choice between 7/1*(2) and 13/4 7/4? Here Rule 1 favors the blitzing play (which now points on White’s head), but Rules 2 and 3 still favor the more positional approach. (White has plenty of structure and Black’s position is widely spread out if White ever anchors.) And of course, Rule 4 says to break ties in favor of the DMP play. So 13/4 7/4 is the winner.
Incidentally, there’s an in-between play with 3-3 which isn’t bad: 21/18(2) 13/10(2). It tightens up Black’s position a bit, and creates some more numbers to make a 5-prime. But since it doesn’t make a new inner point, it’s not very gammonish, and it won’t be that easy to get off the 18-point once White anchors, so making the 4-point still comes out on top.
(b3) Black to play 5-3. Another roll, another set of problems. This time the gammonish play is 7/2 5/2, making another inside point. But the play gobbles up a couple of builders and leaves the 3-point and 4-point still open, so it doesn’t inspire confidence.
The running play for DMP is the simple 21/13, which cleanly preserves the racing lead and leaves Black with only the problem of escaping the back checker.
The priming play for DMP is 13/8 13/10, which leaves Black in pretty good shape, with four builders to make the 4-point.
If we look back at our four rules, all of them argue against 7/2 5/2 and in favor of a DMP play. In this case the two DMP plays are a photo finish. Rollouts show that running to the 13-point wins about 2.5% more games, but bringing two men down wins about 5% more gammons, making the two plays about equivalent. Give yourself credit for either choice.
Solution: (a) Double and take.
(b1) 21/11(2)
(b2) 13/4 7/4
(b3) Either 21/13 or 13/8 13/10 is OK
(a) Cash game, center cube.
Should Black double? Should White take if doubled?
(b) Assume Black doubles and White takes. Black to play
(b1) 55
(b2) 33
(b3) 53
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) Cube action?
Problem 155 is a more or less common middle game position with some interesting move choices coming up. First, however, Black has to decide if he wants to double or not.
Let’s start by looking at the elements in our standard position-race-threat matrix.
Position: Black has some clear assets here. He has an anchor, and White doesn’t. White is on the bar, which is a plus for Black. Black has a 4-point block, White has only three points in front of Black’s anchor.
On the negative side, White has a better home board, with three points to Black’s two. In addition, White has spares on his midpoint, while Black’s midpoint is stripped. On balance, we have an edge for Black, but not a huge edge.
Race: Black leads 140 to 149, with plenty of contact. Small edge to Black.
Threats: Black has a few numbers to make a 5-prime: 31, 41, 43, and some small doubles. If he can fill in another point in his board and White doesn’t anchor, Black could develop a blitz. That constitutes a few threats, but not a lot of threats.
The takeaway from all this is that Black has an edge in all three areas, so he should certainly have an initial double. An edge in every area often indicates a pass, but here all the edges are small, so White can squeeze out a take.
Now let’s assume that Black doubles and White takes, and move on to the checker plays.
(b1) Black to play 55. This is an interesting roll because Black has many choices, leading to lots of different game plans. Here’s a quick run-down:
Play #1 -- 8/3(2) 7/2(2). The all-out blitz play, making two inner points.
Play #2 – 13/3(2). A priming play, but one which could turn into a blitz if things go well.
Play #3 – 21/11(2). The connectivity play, keeping a compact formation and leaving no stragglers behind.
Play #4 – 21/16(2) 8/3(2). A little connectivity, a little building.
Play #5 – 21/6 21/16. Creates a nice collection of builders at the cost of leaving a few shots.
If this were double match point and Black’s only goal was to win the game, the clear play would be 21/11(2). That play disengages the anchor, keeps a nicely connected position, and leaves Black sitting on a 29-pip lead in the race with no problems playing upcoming rolls.
All the other plays trade some wins for an increased chance of winning a gammon. The play that gets the most gammon chances is 8/3(2) 7/2(2). Black gets a quick 4-point board, but leaves his other checkers scattered around. At the other extreme is 21/6 21/16, which disengages and gets a nice building structure, at the cost of leaving a few embarrassing shots. The other plays fit in between these two.
Plays that sacrifice some winning chances for extra gammons tend to be harder to evaluate than most. You’re not comparing two similar plays to see which one makes a slightly better structure. Instead you’re measuring apples and oranges. Exactly how much am I giving up in winning chances in these two very dissimilar positions? Exactly what am I getting in extra gammons? Am I getting more than two extra gammons for any extra loss? These are usually tough questions.
Here’s a few rules of thumb that I’ve found work pretty well in these positions. They’re not infallible, but they do help:
Rule 1: If the gammon play doesn’t actually make a point on the defender’s head, go with the DMP play.
Rule 2: Look at the position if the attacker makes the gammon play and the defender anchors. If it’s too hard to bring home, make the DMP play.
Rule 3: The more structure the defender has, the more you want to make the DMP play.
Rule 4: When in doubt, make the DMP play.
A quick scan of this list shows that generally you’ll be playing to win the most games, and that’s right. In the bulk of these problems, the best play to win turns out to be the right choice.
Now let’s go back to our 5-5 play.
By Rule 1, the gammonish plays don’t actually point on White’s head. Play 2 makes a good point, and Play 1 makes two good points, but neither puts a second checker in the air. Rule 1 argues for the positional play, 21/11(2).
For Rule 2, let’s suppose Black makes Play 1 and White then rolls an ace and anchors. How do we like Black’s position? He’s got a couple of loose blots, the 4-point is still open, and Black will have to be moving off the 13-point and 21-point pretty quickly, while White has plenty of spares to move as he improves his position. This will be hard to bring home. Edge to the positional play.
Rule 3 makes an argument for the positional play since White already has plenty of structure – a 3-point board and a nice little block against the 21-point.
With everything arguing for the positional play, Rule 4 doesn’t really apply because there’s not much doubt. Black should play 21/11(2).
(b2) Black to play 3-3. This roll poses a whole new set of problems. The best play to win the gammon is clearly 7/1*(2). But the DMP play isn’t as clear as before. At DMP, two game plans dominate: the running game, because races don’t win many gammons and are relatively easy to bring home, and the priming game, because if you can build a full prime and break your opponent’s timing you become a huge favorite. Here we have one good candidate for each type – 21/15(2) for the running game and 13/4 7/4 for the priming game. What’s right?
In a matchup between 21/15(2) and 13/4 7/4, making the 4-point dominates. Making the prime is almost as good for the win as running (74% versus 75.4%, according to rollouts), but since it actually makes an inner-board point, it’s hugely better for winning gammons (31% gammons versus 16.4%).
What about the choice between 7/1*(2) and 13/4 7/4? Here Rule 1 favors the blitzing play (which now points on White’s head), but Rules 2 and 3 still favor the more positional approach. (White has plenty of structure and Black’s position is widely spread out if White ever anchors.) And of course, Rule 4 says to break ties in favor of the DMP play. So 13/4 7/4 is the winner.
Incidentally, there’s an in-between play with 3-3 which isn’t bad: 21/18(2) 13/10(2). It tightens up Black’s position a bit, and creates some more numbers to make a 5-prime. But since it doesn’t make a new inner point, it’s not very gammonish, and it won’t be that easy to get off the 18-point once White anchors, so making the 4-point still comes out on top.
(b3) Black to play 5-3. Another roll, another set of problems. This time the gammonish play is 7/2 5/2, making another inside point. But the play gobbles up a couple of builders and leaves the 3-point and 4-point still open, so it doesn’t inspire confidence.
The running play for DMP is the simple 21/13, which cleanly preserves the racing lead and leaves Black with only the problem of escaping the back checker.
The priming play for DMP is 13/8 13/10, which leaves Black in pretty good shape, with four builders to make the 4-point.
If we look back at our four rules, all of them argue against 7/2 5/2 and in favor of a DMP play. In this case the two DMP plays are a photo finish. Rollouts show that running to the 13-point wins about 2.5% more games, but bringing two men down wins about 5% more gammons, making the two plays about equivalent. Give yourself credit for either choice.
Solution: (a) Double and take.
(b1) 21/11(2)
(b2) 13/4 7/4
(b3) Either 21/13 or 13/8 13/10 is OK
