Winning Chances
Throughout this site, I have talked as though it is possible for a player to look at a position and just know what his chances of winning and losing are. Of course, in real life that's not possible unless you let a computer play out the game thousands of times. The top players do not try to calculate their chances down to the third decimal place. But unless you have a framework for making decisions about checker plays and cube decisions, you can't make informed choices. It's better to say "I should take this double if my winning chances are at least 25% - now, do I think they're that good" - than to say "I know I'm losing, but I have no idea whether to take or not."
Sometimes, of course, you can know exactly. Say you have two checkers on your ace-point and your opponent has two checkers left, on his 5 and 2 points. He doubles. He has 19 rolls to get both checkers off out of 36, for a 53% chance to win - you take. Suppose they're on the 5 and 1 points. 23 good rolls - 64%. You still take. Suppose they're on the 4 and 1 points. Now he has 29 good rolls, or 80%. Time to drop.
But in most cases you can only estimate. The better your ability to estimate - the better you'll do at backgammon.