Here are two closely related positions which illustrate an idea called diversification, which is the opposite of duplication. Duplication enables us to reduce our opponent’s good shots by moving so that the same number works for him in different parts of the board. Diversification increases our own good shots by giving us different numbers working in separate parts of the board. It’s a quick and useful tool that will generally point to good plays.
(a) Money game, Black owns a 2-cube.
White to play 1-1.
(b) Money game, Black owns a 2-cube.
White to play 1-1.
Problem (a) shows the idea in its simplest form. With two of his aces, White will of course play 2/1*(2), knocking out Black’s chance at an ace-point game and buying some more time to release his back checkers. Now he has to decide how to arrange his remaining spares. On Black’s side of the board, White needs fours and fives to escape, so on his side of the board, he’ll try to give himself different numbers to attack the open 2-point.
Notice that if he plays 8/6 with his last two aces, he’ll need fours and fives to hit on the deuce point (assuming Black enters with a checker). Those are the same numbers he needs on the other side of the board, so in effect he’s duplicated his own good numbers — not the right idea.
A better play is 7/5 with his two aces. That gives him sixes and threes to hit on the 2-point, different numbers from those he needs to escape. By making different numbers work on different sides of the board, you maximize the chance that your next roll will accomplish something.
Position (b) shows a more difficult situation. This time White needs fives and sixes to escape instead of fours and fives. Now we have to think a little.
After the mandatory 2/1*(2), White can play 7/5, giving himself sixes and threes aiming at the 2-point, or 8/6, giving himself fives and fours. Since he needs fives and sixes on the other side of the board, either play duplicates a number: 7/5 duplicates his sixes, and 8/6 duplicates his fives. But notice that the duplication isn’t equal: White needs two fives to escape his back checkers, but only one six. Since White will always prefer escaping to hitting (because escaping is harder, and you always do what’s harder first), he won’t hit with a five until he’s first thrown two fives to escape. That makes leaving a five to hit less useful than leaving a six to hit, so the right play is once again 7/5.
