By L.H. Madsen
| Going through some of my online backgammon matches, I found quite a few errors involving a choice between pointing or hitting in early and middle game positions. They were too many and too big. So I decided to analyze some of the positions, along with a few I picked up elsewhere. I played around with each position, to get a feel for what was going on. What follows is my thoughts about some of the more illustrative positions. They are not always particular close or difficult problems; I picked the ones I thought was most valuable for learning purposes.
All of the positions are rolled out with GNUBG, mostly 1296 trials (some close plays more, some clear plays less) at 0-ply checker play, cubeful with a 2-ply cube and no truncation.
Here we go:
| Position 1a
|| Position 1b
| In the first two contrasting positions Black has the option of either hitting or making an advanced anchor. With a 5-4 making the anchor is right by a lot, but with 4-3 it is the other way around: hitting is very correct. The difference between the right and the wrong play is quite big, about 0.07 in both cases. Why such a big change in what seems to be similar plays?
The first thing to realize is that the 20-point is really a much better point than the 21-point here. If Black uses his 4-3 to anchor on the 21, and then for some reason were allowed to slide his anchor to the 20-point, the gain in equity would be a healthy 0.13. I think the reason for the big difference here, is that the 21-point looks a lot weaker if White ever manages to make his 5-point, which he have a good chance to do at some point during the game.
Second, the value of hitting is not all that great, since Black does not yet have any offence. Suppose Black hits with 5-4 and White enters quitely, without doing anything special, say, with a 6-4. Now Black is hoping for a four to make the anchor or a good attacking number, and the hit hasn’t really gained him anything, except for a not too meaningful racing lead. And hitting does leave Black vulnerable to a few jokers, 1-1, 2-2, 3-3 plus a couple of fly shots.
So what really is going on is that if Black has the option of making an excellent point, he should do so instead of hitting. The 20-point fits the bill, the 21-point does not. The strategic value of the 20-point dominates the tactical value of hitting.
| Position 1c
|| Position 1d
| If Black has a stronger offensive position, like in diagram 1c, the hit goes way up in value, of course. Now, the tactic advantages of hitting are really great. Still the choice is relatively close, with the hit probably winning partly due to cube considerations; for instance Black probably has a nice initial double (easy take, though) if White should happen to fan. If Black anchors it’s harder to find a quick cube.
Owning the barpoint, however, is not enough to make hitting correct with a 5-4. The bar point is not nearly as strong as the 4-point, so Black should definitely play bar/20 24/20 in diagram 1d.
| Position 2a
|| Position 2b
| Again, Black has a choice of making a nice poing or hitting. In position 2a the hit looks a bit lose to me, but in fact the rollouts has it too close to call compared to making the 5-point. After making the 5-point Black is in a clear second place no matter what White rolls, but hitting does open the posibility of a turnaround, should White roll one of his 15 missing numbers. The bottom line is that Black has a pretty close decision here.
If, however, the alternative to hitting is the less strong 4-point, as in position 2b, the hit is clear. Again, it’s the quality of the point that decides if the hit is worth it. And the difference between making the 5- and the 4-point is bigger than you might think: After pointing in 2a Black would lose about 0.1 equity if he were to slide his 5-point to the 4-point. The same is true for position 2b, the 5-point is about 0.1 better than the 4-point.
| Position 3a
|| Position 3b
| I position 3a Black has a similar decision between hitting in White’s outfield and making his own 5-point. The way to hit here is 23/14*. There’s no real reason to leave extra return shot and complications when Black is a clear favorit, possibly approaching a good double. So the choice in positon 3a is between 23/14* and 11/5 8/5.
The hit is probably correct by a small amount, perhaps around 0.02 better than making the 5-point.
If Black’s back checkers were a bit more split, as in position 3b, the pointing play would be clearly correct (compared to hitting with 24/15*). The reason is not so much that the hit leaves more returns than in 3a. The real reason why pointing is a much better play in 3b than in 3a, is than Black’s back checkers are better placed, so there’s less of a reason to get them going. They are better placed because the checker on the 22-point can escape directly with a 6.
To see how important this factor is, consider that after making the 5-point Black is almost 0.1 better off in 3b than in 3a, while after hitting the two positins are roughly equal for Black. That’s how important that little extra split is.
Another significant reason why the pointing play is a close second in 3a and clear winner in 3b, is that White’s back checkers are split. It they were both on the 24-point Black would not be threatening a later attack, and the pointing play would lose value. In fact, hitting would then be much better in both 3a and 3b.
Summing up, the pointing play is right in 3b because 1) it makes an excellent point, 2) Black has little reason to move his back checkers, and 3) because it puts preassure on White to roll well or be attacked. If any of these were not true, hitting would be best.
| Position 3c
|| Position 3d
|Position 3c and 3d illustrates the point about White’s split back checkers. Position 3c is quite easy, especially knowing what the right play in 3b is. The pointing play of 11/5 7/5 is hugely correct, since Black can make a good point while picking up the blot at his barpoint. However, if those white checkers were not split, that would make a big difference. Just one pip backward for White to reach position 3d, and suddenly hitting is right by a lot (about 0.07). There are fewer return hits and White can no longer be attacked inside Black’s home board, after he makes his 5-point. Pointing in 3c is worth about 0.61 but only about 0.47 in 3d. The difference is due to extra gammons and lots of quick cubes in the next few rolls.|
| Position 4a
|| Position 4b
|Sometimes you have to hit or be hit. Position 4a, 4b and 4c illustrate this principle. In position 4a Black’s best play by far is to make his 5-point, 11/5 6/5. This creates a strong, offensive position and makes it dangerous for White to hit lose. In position 4b, on the other hand, Black is under attack from three White builders, and that makes all the difference in the world. Now hitting is the play, and the best way to do that is 21/15 11/10. (Right by about 0.03 over 11/5 6/5).|
| Position 4c
|Position 4c appears similar, again Black is under attack if he doesn’t hit. This time, however, the tactical considerations are a bit different, and pointing is probably slightly better. The reason is, I think, that there’s a bigger swing on White’s pointing numbers in 4b: 6-4 and 6-2 play awful from the bar, while the corresponding numbers of 2-1 and 4-1 in 4c play much better. So when the hit works it gains more in 4b than in 4c.|
| Position 5a
|| Position 5b
| In position 5a Black has a close decision. The incentive to hit is there, since Black is likely to face a strong prime next turn if he doesn’t hit now. On the other hand hitting does leave White even money to hit back, which could be fatal. The 5-point is strong, and Black would have about an even game after making it. The bottom line is that pointing is probably right by a modest amount, perhaps in the order of 0.02.
In position 5b Black is not nearly as vulnerable after hitting, and that swings the decision. Hitting is now clearly correct (by about 0.13). This can be seen by noting that the position after point is worth about the same for Black in 5a and 5b, but after hitting 5b is a lot stronger than 5a.
| Position 5c
|| Position 5d
| In position 5c hitting is again correct, but for a different reason. Hitting is still dangerous and leaves Black just as vulnerable as in 5a, but this time the pointing alternative is not as promising because White is at the edge of the prime. Also, Black is now an underdog and has more incentive to take chances. The gain if White should happen to dance is bigger in 5c than in 5a.
In 5d hitting is even more right than in 5c. The pointing play is still not so effective, and Black does not have that extra blot to worry about, so the hit is a standout.
| Position 6a
|| Position 6b
| Position 6a and 6b provides an interesting set for comparison. Black can hit the fleeing checker, or he can make an inner board point.
The alternative to hitting is to make the 5-point. Even though that leaves a more stacked position, the 5-point is distinctively stronger than the 4-point, and there may be opportunities for unstacking later.
Whatever the right play is, it might appear that it’s the same in the two positions. If there is a difference, maybe hitting is slightly right in 6a and slightly wrong in 6b, since the blot is closer to home in 6a. Actually it’s the other way around! In 6a pointing is right, and in 6b hitting is right. The reason is, that White is better diversified in 6b, so there’s more to gain by hitting. This took me quite some time to realize, and it required a roll-by-roll-analysis.
In 6b, after Black points, White has 22 quiet non-doubles that make a new point and save the blot on the 15-point. In 6a the, corresponding number of rolls is only 18. In addition, in 6b White has a few super rolls that doesn’t exits to the same degree in 6a, namely 63 and 44. So all in all White, if left alone, has quite a few extra good rolls in 6b than in 6a. That’s enough to make a measurable difference. Hitting is slightly wrong in 6a and slightly right in 6b.
It’s hard, for me at least, to find plays like this that depends mostly on immediate, numerical aspects of a position.
| Position 6c
|| Position 6d
| In position 6c Black is a lot better off than in 6a (by as much as 0.5) with the 4-point made and smoother position. The made 4-point makes both hitting and pointing a lot stronger. The net effect is that it is probably still correct to hit, by a small margin.
Position 6d is a bit different. The spare on the 8-point is now stacked on the 7-point, and the alternative to hitting is to make the 4-point. It is correct, by a clear margin, to make the 4-point, even though it’s not as strong as the 5-point. Compared to 6a hitting is weaker, because it’s harder to follow up by making inner board points. Since Black is not in such a great shape to make points, he should do so now that he has rolled a nice pointing roll.
Concluding, it’s hard to put down any solid rule of thumb, that doesn’t have lots of exceptions. When deciding between hitting and pointing it’s important to consider:
2) The need to hit, in order to cut down on opponents attacking chances or other threats (like priming).
3) If a play does two good things, like escaping while hitting, or pointing while picking up blots, that’s a strong argument for that play.
4) The follow-up. One play or the other may be easier to follow up, by attacking or by making new points. A stacked position calls for a point making play, since points are hard to come by. An anchor-less opponent may also indicate a point making play, with a later attack in mind.
5) Occasionally the right play simply depends on the number of constructive rolls your opponent has, if left alone. In otherwise close decisions, it may pay to take a long and hard look at how specific rolls play, and if joker control might be an issue.
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