Backgammon is all about odds. The best play is only the best play when it gives you better odds of winning the game or match than any other play. A double or take is only right if statistically you come out ahead by doubling or taking.
The top players in the game all know this. They all use this approach to winning. Every single one of them. And now, since we have excellent computer programs that can play out a game for us millions of times and assure us which play or decision is statistically right, there is little argument about right and wrong, even amongst the top players who used to have completely different approaches to elements of the game 20 years ago.
So if you want to become one of the best players in the world, the path is simple: learn the odds.
But here's the problem. The odds are complicated. It's not that difficult to figure out your odds of getting hit or hitting a blot (loose checker) on any given playthere are only 36 possible rolls of the dice and you can count shots on your fingers and toes if you need to. But when you start calculating the odds of winning or losing a game or match when you make one play vs. another, and then add in the value of winning or losing possible gammons and backgammons, and then factor in the comparative differences in score if you or your opponent win, the odds get far too complicated for all but the most agile at math. And even if you happen to be a great mathematician, it takes years of study to learn the match equity tables and even more years to be able to look at a given backgammon position and estimate the odds of winning and losing and gammons and backgammons.
Now, I don't want to discourage you. It is possible to learn it all and become an expert. I have shown some of the world's best players very complicated positions and seen them look at a position and do some quick calculations and estimate numbers that turned out to be within a couple of percentage points of the computer rollouts. Top players are not always right, but they are usually pretty close. But even they are doing a lot of estimating and rounding-off in their heads to come up with the numbers, and they also have two other tools that help them with the decisions. First, because they have been playing so long, they have seen and studied just about every possible position and situation there is, and second, because they have incredible memories, they usually remember pretty well what the odds are for a given type of situation, and they might even remember playing from this situation many times and remember how it usually turned out. They have hundreds of reference positions in their head to call on to get them close to the odds before they even have to start doing calculations.
But what about the rest of us? What about those of us that have not played 25 years, have not spent thousands of hours studying the numbers and positions, and might not happen to have the math expertise and memory skills of the experts? What can we do to improve our game and play well?
My best advice to you is to try to play pretty backgammon. In addition to a mathematical approach to the game, there is also an aesthetic approach. It is possible to play excellent backgammon without calculating numbers and odds in your head constantly, simply by playing moves that look more appealing than others.
Of course, in order to make the best looking moves, you do need to learn what constitutes the definition of beauty in a backgammon game. Unfortunately, in backgammon, beauty is not in the eye of the beholder. The definition of a beautiful game or position just happens to be the one that gives you the highest odds. But instead of calculating the odds, you come to the same conclusion based on the looks of the position.
Making points in a row is what experts call a pretty position. A six prime is the most beautiful looking position in backgammon, and a six prime with your opponent's checkers on the bar, and his inner board destroyed is the Mona Lisa of backgammon. So you strive to create a Mona Lisa, and if you can't do that, if you can't make a 6-prime, you try to make a 5-prime. And if you can't make a 5-prime, you strive to make a 4-prime. And so on.
A pretty game is one where you have made your 5-point, and an even prettier game is one where you have made your 5 point and your bar point, and if you toss in the 4 point as well, and several of your opponents checkers on the bar or behind your prime, it becomes a beautiful game or position.
Conversely, an ugly game is one where you leave a lot of blots around the board. And ugly game is where you have points made that are not together, but separated by several spaces. An ugly game is one where you have many checkers stacked on one or two points. An ugly game is inflexible in that you have the fewest possibilities of rolls to safely and productively advance your position.
If the particular combination of rolls do not allow you to make a pretty game, then use those rolls to make sure your opponent's game cannot become pretty. He can't make his 5 point if you make his 5 point. He can't close you out if you make an anchor in his inner board. He can't make much of a prime if you make his bar point. So another kind of pretty game is one that makes sure your opponent's game can't get pretty.
Holding several points in your opponent's inner board, with good timing and with your own inner board preserved is another kind of pretty game. And as I said, it not only looks pretty, but if you run the position through the computer programs you'll find that even though you are way behind in the pip count, you can easily be a favorite to win the game or match with a good enough back game.
Please do not think I am advocating that players do not need to learn and study the odds. If you want to improve your game, you must do the math. But along the way, you can use aesthetics to augment your skills. The more you play, the more you will learn what kind of positions tend to win you the most games and the most gammons, and you will start associating those positions with beauty.
In backgammon, as in life, we should always strive for beauty.