This article originally appeared in the October 2000 issue of GammOnLine.|
Thank you to Kit Woolsey for his kind permission to reproduce it here.
Let's start with a letter I got from a friend:
"Dear Hank. I lost a tournament match last night. My opponent was bad, but gosh was he lucky. Look at this position:
I redoubled to 4, and can you believe he took? Of course he went on to win the game and the match."
It didn't seem like a hard problem, and it's not. The point isn't that Blue has an easy take, but that I took the time to analyze it in Snowie and find that White wins the game 55.9% of the time. (Not a double ordinarily but a double at this match score.)
A couple of weeks later I was playing a money game when this position game up:
Is this a double? Well clearly I have a lot of market losers. I have to be thinking about doubling. What are my winning chances? I don't know. But here is how I reasoned it.
"I remember the other position was 56% win chances. I know my position here is better because I have a checker on the 4-point instead of the 5. My opponent's position is a little worse. In the other position he had 6 rolls to get off in one shake (3-3, 4-4, 5-5, 6-6, and 6-5) and in this one he has only 5. True there are some times in the other position that he doesn't get off in 2 rolls, but many of those won't matter because I'll have been redoubled out when I didn't get off in two shakes. So I must be somewhat better off than 55.9%. The one extra roll he doesn't get off adds 3%. Moving the checker from the 6 to the 5, a few percent more. I'm not sure just what my chances arebut I'm pretty sure they're good enough to double.
Most games have strategies that are determined by rules. Bridge players are familiar with the "rule" that you need 26 points to bid a game. Monopoly players know to never make a deal with an opponent with enough money to build houses that are more valuable than what you can build. These games have decisions points, reference points.
Backgammon does also, but they are much less a part of beginning and intermediate literature than in other games. Bridge players learn the 26-point rule in their second or third lesson. Reference positions are just as important a part of learning backgammon. In this article we will discuss the general idea of reference positions. We will not try to give reference positions for all different situations. Those are adequately covered in other literature. What we will try to do is to give readers of this article the tools to use them.
Consider this very common position:
Most players will instinctively realize that the correct play here is 6-4 6-1. Blue's primary goal is safety, not speed. Even an immediate 6-6 by White still leaves him a solid favorite.
Now change the position:
Blue surely should have the idea that he cannot afford the luxury of taking no checkers off. He trails by 3 crossovers and needs to take some moderate risks in the race to get all his checkers off. The safe play leaves no shots next turn, while 5-off 5-3 leaves shots with both 5-1 and 6-1 (assuming White does not enter and get out of Blue's home board).
A bit of experimentation with Snowie reveals that the borderline between the safe play and the slighly risky play comes when White has 4 checkers off. At that point, White needs 15 crossovers and Blue needs 12.
It is certainly not practical to try to memorize every possible backgammon position that arises. But this fairly common one can be generalized to a lot of other situations. And so it seems reasonable to commit to memory the idea that "I will play safe in breaking up a closed board when I am leading by at least 3 crossovers. When leading by less, or trailing, I will look to take checkers off if I can do so with moderate risk." This rule will cover a wide variety of situations.
In effect, we are creating a reference positiona position that shows the borderline between taking two actions. A double/no double, a take/pass, an aggressive/safe play.
I am not going to try to present a whole catalog of reference positions in this article. The point of this article is not to present reference positions, but just to emphasize their value. There are many backgammon books on the market for intermediate to advanced players that present and solve common backgammon problems.
But there is a tendency to read books like this with the wrong view. Without a doubt, there is value in learning the positions that appear in the books, and in testing your game by seeing how many you can get right. But the real value lies elsewhere.
To my thinking, without a doubt the best way to improve your game from intermediate to advanced is to understand, study, and memorize reference positions. When reading a bookwhen studing a match in Snowiewhen discussing a position with friends or on a message boarddon't just look for the right answer. Look for the features of the position that make it a break-even proposition.
I know that many players hear an expert talk about a position. They hear "That is an easy take"and they say "Well, ok, I trust them, but how do they know that?" The answer is that they know a similar position that is a close take/drop, which is somewhat stronger for the doubling side. By knowing a break-even position, similar positoins can be easily classified.
If you can find these break-even points and remember them, you will have taken a huge step toward improving your game. You will have turned thousands of tough decisions into easy ones.