The purpose of the Backgammon game is to bear your checkers off faster than your opponent. In order to do that, you need first to move them in the inner table (or inner board).
In the figure we see the starting configuration for a backgammon game. This is the “left” configuration, and we play with the black checkers. A board has 24 points. The first six (numbered from 1 to 6) designate the inner table and the last six (numbered from 19 to 24) designate the base area. We start moving the checkers clockwise from point 24 to point 1.
The purpose of the backgammon game is to move our checkers from the base area to the inner table, according to the backgammon rules. Once all checkers (15) are in the inner table, we start bearing them off. Winner is the player who bears them off faster than the opponent.
Our goal is not to hit our opponent, but to move our checkers to the inner table as soon as possible. Therefore, during the game we strive to move the two checkers away from point 1 and closer to point 19.
Next, we want to capture point 20 and then point 18. By blocking those two positions we prevent the opponent from running away. If the opponent does not have any checkers in his/her point 1, then there is no need to capture point 18. But, we do need to own point 20, so that we can give him/her a hard time to re-enter the board, if we hit him/her. Then, we want to capture point 5, as that will ease the movement of the two checkers at point 1.
It is better to move the checkers away from point 1 than to hit the opponent. Of course, we move them to a safe position, and not to a point that our opponent can easily hit them. (Read the article on outcome of rolling dice for this)
Finally, it is better to capture an empty space than to hit our opponent. Because, that will help us to move the checkers that are left behind safer to the inner table. Of course, this greatly depends on the way that the checkers are laid out on the board. For example, if it is not possible to hit the opponent, then our only goal is to move the checkers as fast as possible to the inner table.
Enjoy the game!