Part (a): How should Black play a 4-2?
Part (b). How should Black play 6-2?
Let’s start with Part (a): How should Black play a 4-2?
There are two clear candidates here; make your own 4-point, or your opponent’s 5-point (your 20-point). Anything else is a waste of a great shot. But which point should we pick?
These early game point versus point problems can usually be solved by asking yourself three key questions.
First, which point is intrinsically more important?
Second, how do the particular circumstances of the position affect the absolute value of the point?
Third, what’s the degree of difficulty for making each point?
We’ll start with the intrinsic value of the points. This is pretty easy to determine. The most valuable points in the early going are the two 5-points, closely followed by the 4-points and the bar-points, which are about equal. Other points are much weaker than these key blocking points. Only considering intrinsic value, the White 5-point (your 20-point) is the top choice.
Now we have to look and see how the actual position we’re in affects the value of the points. This part requires more judgment.
On Black’s side of the board, not much has changed from the starting position. Black has moved a builder from the 13-point to the 8-point, giving him a little better diversification than he had before. White is still anchored on Black’s 1-point. All in all, Black’s 4-point is just about as valuable as on the opening roll.
But on White’s side of the board, the position has changed a lot. First, White has actually made an inner board point. That means an anchor, any anchor, is more important than it used to be, because any attack that White launches is now more likely to be successful.
In addition, however, the point White has made is his 4-point. With the 4-point made, White’s 5-point becomes even more valuable (for both sides) because of the strength of the 4-5-6 structure. Back in the 1970s, Paul Magriel, in his classic book Backgammon, labeled the 5-point the “Golden Point”, signifying its importance in the opening. While the 5-point is the best point to have in the early going, its power can be mostly neutralized if the opponent then makes the 4-point anchor. But the combination of the 4-point, 5-point, and 6-point, which I like to call the Golden Structure, is a real game-changer. Whoever makes that structure in the early game is on the verge of a powerful double. Even anchoring on the 3-point in front of the structure merely allows the defender to hang on in a clearly inferior position. The only road to equality is hopping the structure entirely and anchoring on the bar-point, and that will be hard to do.
Conclusion: White’s 5-point has risen in important, while Black’s 4-point hasn’t changed much. Edge to making the anchor with 24/20 22/20.
Finally, we have to consider degree of difficulty. How hard is it to make a good anchor, compared to the difficulty of making blocking points? This question almost always favors making the anchor.
Right now Black has one non-double (4-2) that makes the 20-point, and another one (6-4) that makes the almost equally valuable bar-point. On his side of the board, he currently has six rolls (3-1, 4-2, and 6-1) that make a good blocking point. But that number will grow dramatically as soon as he adds even a single builder in his outfield. Pull a checker from the midpoint to the 9-point, for example, and Black will suddenly have nine non-doubles working on those points (6-1, 6-2, 2-1, 3-1, 4-1, 4-3, 4-2, 5-2, and 5-4). Add in his doubles, and Black becomes a favorite to make a key blocking point, each turn!
Meanwhile, his chances of making a good anchor won’t get bigger, because unless he gets hit, he can’t add any new checkers to his anchor-making list. Upshot: good anchors are much harder to make than good blocking points, so your desire to make them is greater.
Part (a) Solution
All three considerations point clearly to 24/20 22/20 as the best play with a 4-2. When in doubt between an anchor and a blocking point, make the anchor!
Now on to Part (b). How should Black play 6-2?
The lesson here is much the same as in Part (a). Anchors are good. Period. True, the 22-point is certainly not the best anchor, but it’s the only anchor available. As we’ve just seen, the 20-point and bar-point anchors are hard to get, so when you’re under pressure you’re happy to take what’s available.
Having played 24/22, the best six is obviously 13/7. The bar-point is much stronger than the 2-point, so you slot the bar.
Of the plays that don’t make the anchor, the best is 22/16 13/11, simply because it moves a checker into the outfield and tries to keep out of trouble, which is a very good idea when your opponent has a better home board and you don’t have an anchor. Black has a few too many blots after this play, but White has to throw a four to really hurt him.
Several plays here are outright blunders: 13/5, 24/18 22/20, and 24/18 13/11.
The first play (13/5) violates a good general rule: Don’t slot while your back checkers are split. When you slot a point, you’re hoping for your opponent to miss so you can cover next turn. If your back checkers are split, your opponent will attack you there if he doesn’t hit your slot, and you’ll have to get in from the bar before you can try to cover.
The other two plays (24/18 24/22 and 24/18 13/11) violate a different rule: Don’t leave your back checkers sitting on points your opponent really wants to make. Violate this rule and your opponent will just start hitting everything in sight, while you scramble to survive. The exception (sort of) to this rule is the split on the opening roll with a play like 24/20 or 24/18. If your opponent is in the starting position, he doesn’t have quite enough ammunition in place to really hurt you. But once he starts making points, you’re in danger. Either keep your blots safely tucked away back on the 24, 23, or 22-points, or run for safety in the outfield, but don’t dawdle on the target range.
Part (b) Solution