Two Plus Two Forums
Sports and Games
Chess and Other Board Games
Backgammon Forum hosted by Bill Robertie.
Problem of the Week #97: Solution
03-01-2011
, 03:54 PM
Problem of the Week #97: Solution
Cash game, center cube. Black on roll.
Black to play 3-2.
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.
In Problem 97, Black has two choices: he can enter and hit on the 5-point, or he can enter and make the anchor on the 22-point. To hit or not to hit: what’s right?
The 5-point is a strong point. In the abstract, it’s the best point there is, so hitting to make the 5-point later is often a good idea. But making an anchor is a good idea too, and very often correct. If we could only do one of these good things, we’d do it. But here we can do either but not both, so we have to pick and choose.
These choices in the opening are rarely easy. Some writers try to make them seems easy, with comments like “Making the 5-point can’t be wrong” or “When in doubt, hit”. When you see remarks that those, remember that writers have deadlines, and a broad (and wrong) generalization is quicker than a carefully reasoned analysis complete with counter-examples. (And yes, I’ve done this myself. Mea culpa.)
In reality, these decisions can’t be made in the abstract. They hinge on multiple features of the position, all of which must be carefully weighed together to make a good judgment. Let’s list the features that come into play in Problem 97.
Features that favor hitting.
(1) The strength of the point. The more important the point, the more you want to fight for it. In the opening, the two 5-points are the most important points on the board. Strong argument for hitting with 8/5*.
(2) The strength of your opponent’s inner board. The weaker your opponent’s inner board, the more inclined you are to hit. Here White has no inner board. Good argument for hitting.
(3) Your opponent’s threats. The more your opponent is threatening to do next turn, the more you want to hit and take away half his roll. Here White has many rolls that make one 5-point or the other. Strong argument for hitting.
(4) Your opponent’s structure. By “structure” here I mean features like blots, stacked points, and stripped points. Weak structures take time to repair, and hitting removes some of that time by taking away half a roll. White’s blots on the 10-point and 11-point coupled with his stack on the 6-point provide a strong argument for hitting.
Features that favor making the anchor.
(1) The strength of your inner board. The stronger your board, the more you want to hit, as your opponent may dance. Here you have no inner board. Good argument for making the anchor.
(2) The likelihood of getting hit back if you hit. After playing Bar/23 8/5*, White has 25 numbers that hit back: everything except 6-1, 6-2, 6-3, 6-4, 6-6, and 2-1. That’s a good argument for not hitting.
The preponderance of positional factors favors the natural play of hitting. The 5-point is very important, White’s board is weak, and White’s rolls all play very well if Black doesn’t hit. Not surprisingly, rollouts back up the hitting play by a solid margin.
To see the position more clearly, however, let’s make a couple of small changes and see what happens.
Position 97a: Black to play 3-2.
In Position 97a, we’ve given White his 5-point and eliminated the stack on his 6-point. Not only is White’s board stronger, but White’s blots are somewhat less vulnerable, and his structure is vastly improved. In addition, White has fewer threats (since he’s already made his 5-point) and thus your need to hit is less. Apart from the importance of Black’s 5-point itself, all the factors in favor of hitting are reduced, and now making the 22-point anchor is the only reasonable play, while hitting is just a blunder.
Position 97b: Black to play 3-2.
In Position 97b, we made only one small change: we left the inner boards alone and instead connected White’s two outfield blots on the 10-point. This modification changes only two of the features that affect our desire to hit: White has fewer threats, so we have less need to hit, and White’s overall structure is better, making him less inconvenienced by a hit, which in turn also reduces our desire to hit. The effect is less dramatic than in 97a, but it’s enough; making the anchor with Bar/22 24/22 still becomes correct by a small amount.
These three position illustrate a key point about opening play: you must consider the position as a whole. The 5-point is important (very important in fact), but its importance isn’t the only factor driving a hit-or-no-hit decision. You have to look at all the checkers, and see just what they’re trying to do and how they interrelate to each other. Ostensibly similar positions can have very different answers.
Solution: Bar/23 8/5*
Cash game, center cube. Black on roll.
Black to play 3-2.
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.
In Problem 97, Black has two choices: he can enter and hit on the 5-point, or he can enter and make the anchor on the 22-point. To hit or not to hit: what’s right?
The 5-point is a strong point. In the abstract, it’s the best point there is, so hitting to make the 5-point later is often a good idea. But making an anchor is a good idea too, and very often correct. If we could only do one of these good things, we’d do it. But here we can do either but not both, so we have to pick and choose.
These choices in the opening are rarely easy. Some writers try to make them seems easy, with comments like “Making the 5-point can’t be wrong” or “When in doubt, hit”. When you see remarks that those, remember that writers have deadlines, and a broad (and wrong) generalization is quicker than a carefully reasoned analysis complete with counter-examples. (And yes, I’ve done this myself. Mea culpa.)
In reality, these decisions can’t be made in the abstract. They hinge on multiple features of the position, all of which must be carefully weighed together to make a good judgment. Let’s list the features that come into play in Problem 97.
Features that favor hitting.
(1) The strength of the point. The more important the point, the more you want to fight for it. In the opening, the two 5-points are the most important points on the board. Strong argument for hitting with 8/5*.
(2) The strength of your opponent’s inner board. The weaker your opponent’s inner board, the more inclined you are to hit. Here White has no inner board. Good argument for hitting.
(3) Your opponent’s threats. The more your opponent is threatening to do next turn, the more you want to hit and take away half his roll. Here White has many rolls that make one 5-point or the other. Strong argument for hitting.
(4) Your opponent’s structure. By “structure” here I mean features like blots, stacked points, and stripped points. Weak structures take time to repair, and hitting removes some of that time by taking away half a roll. White’s blots on the 10-point and 11-point coupled with his stack on the 6-point provide a strong argument for hitting.
Features that favor making the anchor.
(1) The strength of your inner board. The stronger your board, the more you want to hit, as your opponent may dance. Here you have no inner board. Good argument for making the anchor.
(2) The likelihood of getting hit back if you hit. After playing Bar/23 8/5*, White has 25 numbers that hit back: everything except 6-1, 6-2, 6-3, 6-4, 6-6, and 2-1. That’s a good argument for not hitting.
The preponderance of positional factors favors the natural play of hitting. The 5-point is very important, White’s board is weak, and White’s rolls all play very well if Black doesn’t hit. Not surprisingly, rollouts back up the hitting play by a solid margin.
To see the position more clearly, however, let’s make a couple of small changes and see what happens.
Position 97a: Black to play 3-2.
In Position 97a, we’ve given White his 5-point and eliminated the stack on his 6-point. Not only is White’s board stronger, but White’s blots are somewhat less vulnerable, and his structure is vastly improved. In addition, White has fewer threats (since he’s already made his 5-point) and thus your need to hit is less. Apart from the importance of Black’s 5-point itself, all the factors in favor of hitting are reduced, and now making the 22-point anchor is the only reasonable play, while hitting is just a blunder.
Position 97b: Black to play 3-2.
In Position 97b, we made only one small change: we left the inner boards alone and instead connected White’s two outfield blots on the 10-point. This modification changes only two of the features that affect our desire to hit: White has fewer threats, so we have less need to hit, and White’s overall structure is better, making him less inconvenienced by a hit, which in turn also reduces our desire to hit. The effect is less dramatic than in 97a, but it’s enough; making the anchor with Bar/22 24/22 still becomes correct by a small amount.
These three position illustrate a key point about opening play: you must consider the position as a whole. The 5-point is important (very important in fact), but its importance isn’t the only factor driving a hit-or-no-hit decision. You have to look at all the checkers, and see just what they’re trying to do and how they interrelate to each other. Ostensibly similar positions can have very different answers.
Solution: Bar/23 8/5*
