What is Duplication?
When you must expose more than one blot but you have a choice of where to leave your blots, you often want to minimize shots. You can always count the number of shots left by each play, but sometimes you can spare yourself this effort by applying the concept of duplication.
When the numbers which your opponent can use to hit each blot are the same, his good rolls are said to be duplicated. When the same numbers hit more than one blot, fewer numbers hit any blot at all, and you have minimized shots, without counting rolls laboriously.
Sometimes the best play is the one which minimizes shots, of course, but sometimes you must use other criteria. Some shots are worse than others, depending on where you get hit or from where your opponent must hit you. In some positions, you may actually prefer to get hit. And you must often consider how useful a blot is on the point where you leave it if your opponent doesn’t hit.
Duplication, however, applies even when you have only one blot. In deciding where to leave that blot, examine the rolls your opponent can use to hit. Can he use the same numbers elsewhere on the board? To make a key point? To enter from the bar? To leap a prime, or move to the edge of it? If so, you have duplicated his numbers.
He will have to choose among two or more useful plays with the rolls that contain those numbers: If one of his alternatives is more important to him than hitting your blot, then, in effect, duplication has made that blot immune to hitting. And many rolls which do not contain the duplicated numbers may be entirely useless to your opponent.
What is Diversification?
You may not often get a chance to duplicate your opponent’s rolls, for you cannot control which numbers let him do other things than hit your blots. But you can often control which of your own numbers play constructively. Just as duplicating your opponent’s good rolls helps you, so also duplicating your own good rolls harms you. The opposite of duplication is diversification. Duplicate your opponent’s good numbers but diversify your own.
Black to play 5-2.
Black must enter, bar/20, with the 5, but may play the 2 in any of three ways: (a) 20/18; (b) 9/7; or (c) 3/1 (better than the very similar 4/2 because it preserves a playable 3).
- Play (a) lets white hit with direct 1’s, 3’s, and 6’s, plus 2-2, 2-4, and 4-4 — 31 rolls in all.
- Play (b) lets white hit with 1’s and 3’s, plus 2-2, 2-6, and 4-4 — 24 rolls in all.
- Play (c) lets white hit with 3’s, plus 1-1, 1-2, 2-2, 2-6, and 4-4 — only 18 rolls.
As this enumeration shows, play (c), which duplicates white’s 3’s by placing black’s blots the same 3 pips away from white’s hitters, yields the fewest shots by far. The concept of duplication saves you the work of counting.
Notice also that duplication reduces the number of rolls which hit two blots. Play (c) risks a double hit only on white’s 3-3, whereas play (b) permits double hits on 1-1 and 3-1, and play (a) permists double hits on 1-1, 3-1, and 6-3.
Black to play 6-1.
Here black has only one legal 6, 16/10, and he is forced to leave a single blot. He has a choice of aces 16/15 or 10/9 (slightly better than 6/5). 16/15 minimizes shots (there are 15 direct and indirect 4’s but only 14 direct and indirect 3’s).
Despite the one extra shot, however, 10/9 is the right ace, for it duplicates the 4’s White needs to cover the vulnerable blot on his four point. After 16/9, only 4’s work well for white. After 16/10, 16/15, both 3’s (to hit) and 4’s (to cover) work well.