"Dear Hank. I lost a tournament match last night. My opponent was bad,but gosh was he lucky. Look at this position:

13 10

White 0 7 point match Blue 4

I redoubled to 4, and can you believe he took? Of course he went on to winthe game and the match."

It didn't seem like a hard problem, and it's not. The point isn't thatBlue has an easy take, but that I took the time to analyze it in Snowie andfind that White wins the game 55.9% of the time. (Not a double ordinarilybut a double at this match score.)

A couple of weeks later I was playing a money game when this position game up:

12 6

White money game Blue

Is this a double?Well clearly I have a lot of market losers. I have to be thinking aboutdoubling. What are my winning chances? I don't know. But here is how Ireasoned it.

"I remember the other position was 56% win chances. I know my positionhere 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 6rolls to get off in one shake (3-3, 4-4, 5-5, 6-6, and 6-5) and in this onehe has only 5. True there are some times in the other position that hedoesn't get off in 2 rolls, but many of those won't matter because I'llhave been redoubled out when I didn't get off in two shakes. So I must besomewhat better off than 55.9%. The one extra roll he doesn't get off adds3%. Moving the checker from the 6 to the 5, a few percent more. I'm notsure just what my chances are - but I'm pretty sure they're good enough todouble.

Most games have strategies that are determined by rules. Bridge playersare 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 enoughmoney 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 andintermediate literature than in other games. Bridge players learn the26-point rule in their second or third lesson. Reference positions arejust as important a part of learning backgammon. In this article we willdiscuss the general idea of reference positions. We will not try to givereference positions for all different situations. Those are adequatelycovered in other literature. What we will try to do is to give readers ofthis article the tools to use them.

Consider this very common position:

78 42

White money game Blue

Most players will instinctively realize that the correct play here is 6-46-1. Blue's primary goal is safety, not speed. Even an immediate 6-6 byWhite still leaves him a solid favorite.

Now change the position:

37 42

White money game Blue

Blue surely should have the idea that he cannot afford the luxury of takingno checkers off. He trails by 3 crossovers and needs to take somemoderate risks in the race to get all his checkers off. The safe playleaves no shots next turn, while 5-off 5-3 leaves shots with both 5-1 and6-1 (assuming White does not enter and get out of Blue's home board).

A bit of experimentation with Snowie reveals that the borderline betweenthe Safe Play and the slighly risky play comes when White has 4 checkersoff. At that point, White needs 15 crossovers and Blue needs 12.

It is certainly not practical to try to memorize every possible backgammonposition that arises. But this fairly common one can be generalized to alot of other situations. And so it seems reasonable to commit to memorythe idea that "I will play safe in breaking up a closed board when I amleading by at least 3 crossovers. When leading by less, or trailing, Iwill look to take checkers off if I can do so with moderate risk." Thisrule will cover a wide variety of situations.

In effect, we are creating a reference position - a position thatshows the borderline between taking two actions. A double/no double, atake/pass, an aggressive/safe play.

I am not going to try to present a whole catalog of reference positions inthis article. The point of this article is not to present referencepositions, but just to emphasize their value. There are many backgammonbooks on the market for intermediate to advanced players that present andsolve 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 inthe 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 fromintermediate to advanced is to understand, study, and memorize referencepositions. When reading a book - when studing a match in Snowie - whendiscussing a position with friends or on a message board - don't just lookfor the right answer. Look for the features of the position that make it abreak-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 dothey know that?" The answer is that they know a similar position that is aclose take/drop, which is somewhat stronger for the doubling side. Byknowing a break-even position, similar positoins can be easily classified.

If you can find these break-even points and remember them, you will havetaken a huge step toward improving your game. You will have turnedthousands of tough decisions into easy ones.