The Crawford Rule makes a big difference in some situations. Suppose that Black leads you 14-12 in a match up to 15 and that this is the Crawford game, i.e. Black reached 14 points on the previous game so you cannot double him this game. You have much the better of the game and have a chance of winning a double game. Normally you are prepared to take some risks in order to try and win a gammon, especially when you are behind. But in this case that would be quite wrong. If you win this game, you are going to be able to double Black immediately in the next game. Therefore it makes very little difference whether the score after this game is 14-13 in Black's favour or 14-all. The only difference is that if it is 14-13 he does have a free drop. But that is a small advantage and you are certainly not justified in taking any significant risk of losing the game, and with it the match, to prevent him getting it. The same principle applies whenever the Crawford game is being played and you need an odd number of points to win the match. If Black were leading you 14-4, for instance, in a match to 15, the only advantage of winning a double game would be to deprive him of his free drop. Once you get to 5 points, you only need five single games, or three single and one double, or one single and two double, and that is also what you need if you reach 6 points.
But remember that all this only applies when you need an odd number of points to win the match. If you need an even number, then a gammon is a great advantage and you should try hard for it.
The other side of the coin is also important. When you are leading, and the Crawford game is being played, then if Black needs an odd number of points for the match you need not be afraid of losing a gammon. So you can take any risk to give yourself the best chance of winning, as long as you are careful not to lose a triple game.
Suppose that you are within 1 point of winning the match but have a big lead. The Crawford game has been played and Black is going to double you at the beginning of each game. It's annoying, and you may feel that you have to accept the double every time rather than give away an easy point at such an early stage. You are wrong! If the number of points which Black needs to take him to victory is an even number, you can refuse one double without improving his chances at all. To take an example, suppose you are leading by 14 points to 9 in a match up to 15. Black doubles you at his first opportunity, i.e. after your first move. If you accept the double, Black will need (with the doubling cube at 2) to win three single games or one single game and one gammon. If you refuse the double, the score will be 14 points to 10, and, assuming you now do accept any double which Black gives you, he will still need three single games or one single game and one gammon. So the point which you have given him by dropping one double does not help him. You have a 'free drop'. Of course, a second point would help him because once he gets to 11 he only needs two single games or one gammon. So the lesson is that when Black needs an even number of points to win, and you are within one point of winning, you should drop a double if Black already has a significant advantage when he doubles. If he happens to start the game with a 3-1 as the first move, you would obviously be right to refuse the double. If Black is only one point behind you, needing just two points to win the match, you refuse his double if you think he has any advantage at all, for now there is going to be only one game left anyway, and it's better to have the match depend on the next game where the chances are equal. If he is a long way behind, and starts with a number which gives him a small advantage, e.g. 6-5, you may accept a double because you cannot lose the match unless there are several more games, in which case there is likely to be one where he starts with a more serious advantage, so that you will want to drop the double in that game. Remember you have only one free drop.