8.1.0.6

Backgammon Rules

Backgammon is a race game. Two players, the black player and the white player, take turns rolling dice and moving move their pieces, called checkers, around the board but in opposite directions. The first player to get all of their pieces to their home wins the game.

1The Board

Here is the board, without any pieces on it:

The alternating tan-colored triangles are called points and each piece that is on play rests on a point. Each point can be empty or, if it has checkers on it, they must all be of the same color.

The player’s checkers move in opposite directions past each other. The black player’s pieces that are on the upper row of points move to the left and, when they reach the left-most one, they move around the corner and continue to the left-most point on the lower row of points, where they move to the right. The white player’s pieces move in a similar fashion, but reversed, going left along the lower row to the end and then to the right along the upper row.

The final quadrant that each player traverses is called the home board. For the black player, that is the bottom right quadrant and for the white player, it is the upper right quadrant.

In backgammon discussion elsewhere, the points are numbered according the perspective of the player whose checkers are being considered; in this class we exclusively use the perspective of the black player to number the points.

The points are numbered according to the perspective of the black player. Each point’s number indicates the distance that a checker on that point has to travel before it leaves the board.

The dark brown region in middle of the board is called the bar and logically it counts as being one spot before the furthest spot from a player’s home board. So, for the black player, pieces on the bar are logically just past the white home board in the sense that moving forward by one from the bar for the black player would put them on the point numbered 24.

2The Initial Checker Placement

When the game starts, the players’ checkers are placed on specific points, as shown in this board.

3Taking a Turn and Ending the Game

The turns alternate between the players. On each players turn, the player starts by rolling a pair of dice (except the first turn which is slightly special as discussed below). The result of the dice determine the distance the player may move their checkers, where the number of pips showing on the die determine the number of points that some checker may move by. That is, if a player rolls a 2 and a 4, then the player moves one checker by 2 and one by 4 (these may be the same checker), although there are a number of special cases the restrict a checker’s movement, as discussed in the following sections.

Doubles are a special case, where the player behaves as if four dice were rolled, each with the same number that appeared in the doubles. Once the player has moved, if all of their checkers are off the board, they win. Otherwise, it is the other player’s turn.

Before the first turn, each player rolls just one die. The player with the higher number goes first and that player uses the two numbers that were rolled to make their move. If the numbers are the same, no player takes the first turn and the players again each roll one die to determine who goes first. (Accordingly, it is impossible to roll doubles on the first move.)

4Normal Movement

When none of a player’s checkers are on the bar and at least one of the player’s checkers is not in their home board, the player’s legal moves are governed by the rules in this section. Specifically, the following bullet points must all be followed:

• Each die roll must correspond to a checker that moves across the corresponding number of points (although the same checker may consume multiple dice via multiple moves).

• A checker may not land on a point that is occupied by two or more of the opponent’s checkers. Such a point is called a made point for the player that has the multiple checkers on the point. (The act of moving that results in a made point is called making a point.)

• If a checker lands on a point occupied by exactly one of the opponents checkers (this single checker is called a blot), the blot is moved to the bar. The act of moving the blot to the bar is called bopping.

• No checker may move off of the board when the rules in this section are in force (although only a portion of a player’s turn may be governed by the normal movement rules in this section as the player’s first die may be used to move the last checker into the home board).

5Moving with a Checker on the Bar

When a player has one (or more) checker(s) on the bar, the player must move one of checkers off of the bar as the first action they take. If it is not possible to move a remaining checker off of the board (because the opponent has made points on all of the place where the otherwise-legal die rolls would go), the player forfeits any remaining dice.

Note that if a player has more than one checker on the bar and they move one off, they are still in the state of having a checker on the bar (so they must move another one off before doing anything else).

6Moving with All of the Checkers in the Home Board

When all of the checkers are in the home board, a player may begin moving pieces off of the board. Each checker must move off of the board by an exact roll, as if moving to an imaginary point one past the last point on the board, with one exception. That exception is when the value of the die is larger than the distance for any remaining checker to that imaginary point. In that case, the die roll may be consumed by one of the player’s checkers that is furthest away from the imaginary point.

7Using all of the Dice

A player is required to use all of the dice, if possible. Of course, in the general case, there are situations where it is not possible for a player to use all of the dice that were rolled and in that situation, the player forfeits some of the dice, simply by not moving a corresponding checker.

There is one subtle point, however: if it is possible to use all of the dice, the player must do so. For example, consider this board with the die roll shown.

If the black player takes the 2 with the checker on the 12 point, then it is not possible to use the die that rolled a 4. But, if the black player takes the 2 with the checker on the 20 point, then it is possible to take the 4 (with that same checker).

Accordingly, taking the 2 with the checker on the 12 point is illegal and, instead, the black player must move the checker on the 20 point.

If there is no way to use all of the dice, then the player is free to use as many of the dice as they can in any way they can. For example, consider this board:

The black player can take the 4 using the checker on the 20 point or the 3 using that checker. Either way, they cannot use the remaining die, so both moves are legal.