In particular, consider a match to 3 where you are trailing 1-0. Your opponent doubles, and you take. You should always turn the cube on your next roll. What do you have to lose? If you lose this game you lose the match, so why not be sure to win the match if you win the game?
Owning the cube is worth something. By "owning" I mean, having the right to double but your oppoent doesn't. Suppose your opponent is on roll with checkers on his 5 and 6 points. You have 3 checkers on your 4 point. Your chances of winning the game, if neither player has doubled, are zero. He should double, and you should drop. If, however, he's doubled, and you've taken, you still have about a 14% chance to win the game. So don't double with a small lead.
At the same time, don't wait until the game is iced. Consider the position in the previous paragraph. If you are the player with two checkers on, double. Why give your opponent a free chance to get lucky? And if he happens to (wrongly) take, be happy! And if he takes and you lose the game, well, that's the luck factor in backgammon.
I'm not saying that it's easy to determine what your win percentages are. In a racing position, most experts pretty much know, but other positions are far more complex. But you have to know the guidelines. I've noticed one thing. Playing on the zone, I usually won't double unless I have a stronger advantage than I would against a real-life player I thought was as good as I am. I don't want to give an opponent too much chance to get lucky and get two points, when hopefully I can grind him down. What that means is that it is almost never right to accept a double I give. But time and again players take my doubles.
A somewhat crude guideline for doubling in long races (at least 60 pips remaining) is that the player on roll should have about an 8% lead to double, and you can take when up to about 12% behind. So if you have 70 pips left and your opponent has 76, you have enough to double. He should take if he has about 76 to 78 pips left, and drop if he has 79 or more. Of course, these are guidelines. If your checkers are well-spaced, rather than being stacked on one point, that makes you more apt to double or take, and vice versa.
Always double when it can't cost! Suppose you are down 2-0 in a match to 3. You win the next game, the Crawford game, and are now down 2-1. There is no reason not to double on your first roll of the next game! If you lose the game, so what? Losing 4-1 and losing 3-1 are the same thing. But this way, if you win the game, you win the match.
I've heard some players say, "I want to wait until I have a big advantage, maybe I'll get my opponent to drop." But this can't be right. Consider this.
Suppose you reach a point where you are even 90% likely to win the game! Say you double and your opponent drops. The score is now 2-2 and you have a 50% chance to win the match. But suppose you had already doubled. You now have a 90% chance to win the match, because this game decides it!
There is another situation where this concept comes into play. Suppose you are trailing 1-0 in a match to 3 and your opponent doubles. Let's say you decide to take. Redouble right away! If you lose the game you lose the match, so why not set yourself up to win the match?
Another great resource is to get one of the computer backgammon programs. If you're serious about your game, there is no alternative to not having one (Especially that there are very strong and free programs now).
When bearing off, if you can take checkers off with both your dice, just take them off. About 99.99% of the time that is better than trying to "smooth out your distribution." Just take 'em off.
If you are going to lose the match if your opponent wins the game at the current cube value, and you are able to double, then do. You have absolutely nothing to lose.
Early in the game, try to avoid putting checkers on low points. It restricts your options later in the game. Sometimes it is right, but if you have a decent alternative, try not to put checkers on your 1- and 2-points too early.
When you are positioning your checkers to bear off and there is no chance of hitting or being hit, the best strategy is not an even distribution. A bigger stack on the 6-point, sloping down to the 4 or 3, is best. Your goal is to get the most use of your later rolls - to not have to use a 5 or 6 to bear off from the 4-point, for example. This downward-sloping formation is the best to avoid wasting pips.
If you are playing a 2-point match, or have reached a score where both players need 2 points to win (like 1-1 in a 3-point match, or 3-3 in a 5-point match) it is usually right to double at your first opportunity. If you are playing a significantly stronger player, you should double when you have any advantage, no matter how slight. Your opponent will surely double later if he obtains the advantage, but you may not realize later on when it's correct to double. Don't be afraid to turn it into what is essentially a one-point match.