Maybe not exactly one of the backgammon rules but certainly, most important: The object of Backgammon is for each player to bring all his men into his home board, and then to bear them off the board. The first player to get all his men off the board is the winner.
Each player casts one die. The player with the higher number makes the first move, using the two numbers cast by his die and his opponent's. In the event that both players roll the same number, it is a standoff and each rolls another die to determine the first move. In the event of subsequent ties, this process is repeated until the dice turn up different numbers. (In some games, players double the unit stake automatically every time they cast the same number; others limit the automatic doubles to one. In tournament play, there is no such thing as an automatic double.)
Each player's turn consists of the roll of two dice. He then moves one or more men in accordance with the numbers cast. Assume he rolls 4-2. He may move one man six spaces, or one man four spaces and another man two spaces. Bear in mind that, when moving a single man for the total shown by the two dice, you are actually making two moves with the one man---each move according to the number shown on one of the dice.
If the same number appears on both dice, for example, 2-2 or 3-3 (known as doublets), the caster is entitled to four moves instead of two. Thus, if he rolls 3-3, he can move up to four men, but each move must consist of three spaces.
The players throw and play alternately throughout the game, except in the case where a player cannot make a legal move and therefore forfeits his turn.
A player makes a point by positioning two or more of his men on it. He then ``owns'' that point, and his opponent can neither come to rest on that point nor touch down on it when taking the combined total of his dice with one man.
A player who has made six consecutive points has completed a prime. An opposing man trapped behind a prime cannot move past, for it cannot be moved more than six spaces at a time---the largest number on a die.
A single man on a point is called a blot. If you move a man onto an opponent's blot, or touch down on it in the process of moving the combined total of your cast, the blot is hit, removed from the board and placed on the bar.
A man that has been hit must re-enter in the opposing home table. A player may not make any move until such time as he has brought the man on the bar back into play. Re-entry is made on a point equivalent to the number of one of the dice cast, providing that point is not owned by the opponent.
A Player who has made all six points in his home board is said to have a closed board. If the opponent has any men on the bar, he will not be able to re-enter it since there is no vacant point in his adversary;s home board. Therefore, he forfeits his rolls, and continues to do so until such time as the player has to open up a point in his home board, thus providing a point of rentry. It should be noted, the he doesn't loses his turn, as he still retains the ability to double his opponent before any of his opponents rolls, assuming the cube is centered or on his side.
Many beginners do not know that but this is a very important backgammon rule: A player is compelled to take his complete move if there is any way for him to do so. If he can take either of the numbers but not both, he must take the higher number if possible, the lower if not.
Once a player has brought all his men into his home board, he can commence bearing off. Men borne off the board are not re-entered into play. The player who bears off all his men first is the winner. A player may not bear off men while he has a man on the bar, or outside his home board. Thus if, in the process of bearing off, a player leaves a blot and it is hit by his opponent, he must first re-enter the man in his opponents home board, and bring it round the board into his own home board before he can continue the bearing off process.
In bearing off, you remove men from the points corresponding to the numbers on the dice cast. However, you are not compelled to remove a man. You may, if you can, move a man inside your home board a number of spaces equivalent to the number of a die.
If you roll a number higher than the highest point on which you have a man, you may apply that number to your highest occupied point. Thus, if you roll 6-3 and your 6-point has already been cleared but you have men on your 5-point, you may use your 6 to remove a man from your 5-point.
In some cases it may be advantageous to play the smaller die first before applying the higher die to your highest point (See Compulsory Move). For example, suppose you have one checker on your 5 point, and two checkers on your 2 point. Your opponent has a checker on the ace (one point) and on the bar. You roll 6-3. You may play the 3 to the 2 point then the 6 to bear a checker off the 2 point leaving your opponent no shots (no blots for the opponent to hit). The alternative, using the 6-3 to bear checkers off both the 5 and 2 points, would leave your opponent 20 out of 36 ways to hit your remaining blot.
If you bear off all 15 of your men before your opponent has borne off a single man, you win a gammon, or double game.
If you bear off all 15 of your men before your opponent has borne off a single man, and he still has one or more men in your home board or on the bar, you win a backgammon or a triple game.
It is customary to cast your dice in your right-hand board. Both dice must come to rest completely flat in that board. If one die crosses the bar into the other table, or jumps off the board, or does not come to rest flat, or ends up resting on one of the men, the dice are ``cocked'' and the whole throw, using both dice, must be retaken. Anyway, it is not something you should worry about when playing backgammon online...