This article originally appeared in the October 2002 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
The main feature which makes backgammon different from a game such as chess
is the uncertainty due to the dice rolls. Unlike chess, you can't plan ahead
exactly what is going to happen. There are 21 different possible dice
rolls at every turn, and each of these rolls leads to different positions.
Since we can't tell what is going to be rolled, we try to choose our plays so as to maximize the number of good rolls for our side and minimize the number of good rolls for the opponent. The latter can often be accomplished by duplication. If a number is of use for the opponent in two places, then he can't do everything he wants to do unless he is fortunate enough to roll doubles.
Let's look at a simple example:
Blue would like to make his four point, but it isn't worth the risk of slotting it. This is a mutual holding game with a close race, and Blue loses a lot of ground if White hits. The cost of this is more than the gain from making the four point. Blue should simply play 13/6 and await developments.
However, change the position to:
This is a different story. White needs aces very badly on his side of the board to cover the blot on the five point. Here, Blue should slot with 13/10, 8/4. White can hit with an ace; in fact he probably will choose to so in preference to making his five point since the gain in the race is very important and Blue might not hit back. However, White doesn't gain all that much from the hit, since using the ace to make his five point would have been a big improvement also. Of course if White doesn't roll an ace, Blue will be happy he slotted the four point because he can use that point and will be a big favorite to cover it next roll.
The key to this type if duplication is that the opponent must need the duplicated number very badly in two places. If he only needs it moderately in one place while it would be of huge value for him elsewhere, then the duplication isn't so valuable.
I have seen players play 13/9, 4/3 in this type of position, justifying their play by saying that they were duplicating White's fours. It is true that White can use fours on both sides of the board, but the value of these fours is quite different. It would be convenient for White to make his bar point with a four, but that is far from vital. White gains a ton if he hits the shot, sending a third checker back while gaining in the race and escaping one of his back checkers. In addition, making the nine point isn't vital for Blue. Blue should simply play 13/8 and await developments. This sort of slotting play is duplication for duplication's sake.
When the opponent is on the bar, there is often good opportunity to make use of duplication. If your opponent rolls anything with a six he will need to enter with the other number and then play a six, so you don't want to leave him good return sixes. Similarly, if he rolls something with an ace he would usually prefer to enter with the higher number rather than the ace. By making the middle numbers be his otherwise good numbers, you effectively duplicate his good numbes.
Blue would like to anchor on White's bar point, and this is a good time to continue to develop while White is on the bar. Despite this, Blue is better off playing 23/18*, 18/16 instead of 23/18*, 13/11. The key is the duplication. Blue doesn't want to give White good aces and sixes. After 23/18*, 18/16 White can't hit with 6-2 and 6-4, and if White rolls 1-2 or 1-4 he can hit but he winds up with three checkers on Blue's ace point. As an added bonus for B/18*, 18/16, the outfield checker is six pips away from the blot on Blue's ten point, so if White rolls a 6-4 to hit that blot Blue will have a return six all ready.
The most obvious use of duplication comes when you are forced to leave multiple shots. If you can position your checkers so your opponent has the same number to hit in both places, you have cut down on his good rolls.
Blue must play 16/11, 5/4, duplicating White's fours. Getting hit is fatal, and this gives White fewer hitting rolls than 16/10 or 16/15, 16/11. The latter two plays give White direct fours and threes to hit with, while 16/11, 5/4 leaves White only direct fours plus a few indirect shots. This use of duplication is very valuable when safety is the main criterion for the play as it is here. Usually it isn't even necessary to count the actual shot numbers. Simply let duplication do the work for you.
Duplication can come in very handy in priming battles, where a player needs a specific number to leap or get to the edge of a prime. In this sort of position, proper use of duplication may cut down his good numbers.
Blue could play 21/14, which would leave fewer shots and get closer to home. However, this doesn't take proper advantage of duplication. White has very good sixes anyway. If White can spring his back checker, the race is close enough so he is a serious contender. The proper play is 21/15, 7/6, duplicating White's sixes. Now White must roll a six to stay in the game. If Blue plays 21/14, White is in the game if he rolls either a five or a six.
It is very easy to overdo the duplication concept. For example, make a small change in this last example:
This time Blue should play 21/14. It is true that White can use a six to leap a back checker, but this doesn't help him all that much. Blue should simply leave fewer shots and get closer to home.
There is another interesting feature to this position. One might think it could be right to hang back on the 15 point, since that doesn't give White the hit and leap 6-5 number which would be very helpful to White. This is conpensated for by the fact that White might roll boxes. If Blue is on the 15 point and White rolls boxes, White becomes an instant favorite.
The above is an example of how duplication can blow up in ones face if the opponent rolls doubles of the number which has been duplicated. We have all seen this happen, and when it does we just say: See, duplication strikes again. However, when it is the only thing which can really go wrong, one chould be concerned about those devestating doubles when duplicating the enemy's numbers.
It might seem instinctive to play 22/13, which minimizes shot numbers, duplicates White's aces, gets closer to home, and saves pips for the priming battle in case White hits. Despite all these factors, Blue should play 22/16, 7/4. The reason is entirely because of the threat of 1-1. If Blue plays 22-13, 1-1 is such a huge number for White -- hitting, making the five point, and splitting to the edge of Blue's prime. This would give White a real chance to win the game frontwards. If Blue plays 22/16, 7/4 and White hits, Blue is still going to remain a substantial favorite
Combination numbers can be duplicated just the same as single numbers. The idea is exactly the same -- minimize the number of good rolls for your opponent.
It looks natural to play 12/11, 12/6. Moving the blot to the 11 point both reduces White's shot numbers from six (5-4, 6-3, 6-5) to five (6-4, 6-2, 4-4), as well as gets closer to home so the checker is more likely to be able to get safe next turn. A look at the other side of the board shows that this is the wrong play. 6-5 and 6-3 are already great rolls for White, since they make his five point. 6-4, 6-2, and 4-4 are nothing special on White's side of the board. Therefore, it is correct to stay back on the 12 point and play 12/5. This play gives White fewer good numbers, since some of the hits are duplicated with making the five point. The bots are very good at picking up on this sort of duplication, with their uncanny ability to look ahead at all the possible upcoming dice rolls and evaluate them in an instant. Quite often I have been surprised by a bot recommendation until I looked closer and saw that there was a duplication factor involved which I hadn't seen.
One must be careful using duplication. It is important not to fall into the trap of duplicating for duplication's sake, creating good rolls for the opponent when it is not necessary. It is also vital to stick with the logical themes for the position. For example:
A player could choose to play 13/7, arguing that White has several good sixes anyway so his sixes are duplicated. That argument might be sound in other positions, but it doesn't hold up here. Blue has the racing lead and the stronger inner board. He loses that racing lead if White hits, and White will be on his way toward escaping a back checker. In addition, Blue's racing lead translates into favorable timing for White. If the timing remains the way it is, White will be the favorite in a priming battle. Blue's focus should be on getting his back checkers in motion before White is able to build up a strong board, not on slotting the offensive bar point. 24/23, 13/8 is the play which is thematic to the position. If it were White who was ahead in the race then the slot would have a lot going for it, but in this position the split is the proper thematic play.