In brief
Backgammon, known in Romania as "table", is one of the oldest board games. It is played by two people, on a board with 24 points, with 15 checkers each and two dice. Each player moves their checkers around the board towards their own home board, and the first to bear all of them off the board wins. The dice decide how far to move; the player decides which checkers to move and where. That is why backgammon is regarded mainly as a game of skill, in which the dice add an element of luck.
The board and the checkers
The board has 24 narrow triangles, called points, divided into four quarters of six. Between two of the quarters runs the bar, a divider in the middle of the board. Each player has a home board (the six points where the checkers must be gathered at the end) and an outer board. The points are numbered 1 to 24 from each player's point of view, starting in their own home board, so one player's 1-point is the other player's 24-point.
The standard starting position, as each player sees it, is: two checkers on the 24-point, five on the 13-point, three on the 8-point and five on the 6-point. The two players move in opposite directions, each from the high points towards the low ones, that is, towards their own home board.
Moving
At the start, each player rolls a single die. Under the international rules, the higher number starts and plays the two numbers just rolled; on a tie both roll again. Informal play has other customs as well, for example the first player rolling both dice again. Then the players take turns, each rolling both dice:
- each die is a separate move: with 5 and 2, one checker moves five points and one checker (the same or another) moves two;
- a single checker may use both dice, provided the intermediate point where it stops is open to it;
- a double (both dice showing the same number) is played four times: with 4 and 4, the player makes four moves of four points each;
- a checker may not stop on a point where the opponent has two or more checkers; such a point is blocked (it is "made" by the opponent);
- the player must use both dice if possible; if only one can be used, the higher one must be played when possible; if no move is possible, the turn is lost.
Hitting
A single checker on a point, called a blot, is vulnerable. If an opposing checker stops on that point, it hits the blot and sends it to the bar. A player with checkers on the bar may make no other move until they have brought them back into play. The checker re-enters in the opponent's home board, on the point shown by one of the dice, counted from the end where the checkers' journey starts. If the points matching the dice are blocked, the turn is lost. When the opponent has blocked all six points of their home board, the checker on the bar cannot enter until one of them opens.
Bearing off
Only once all 15 checkers have reached the home board may the player start bearing them off. A die removes a checker from the point with the same number. If there is no checker on that point, the player must use the die for a move inside the home board, from a higher point. If there are no checkers on higher points, a checker is borne off from the highest occupied point. A checker hit during this phase must re-enter and return home before bearing off continues.
End of the game and the doubling cube
The first player to bear off all 15 checkers wins. A single win is worth one point. If the opponent has not yet borne off any checker, the win is a "gammon" (in Romanian play usually called "marț") and is worth double. If, in addition, the opponent still has a checker on the bar or in the winner's home board, the win is a "backgammon" and is worth triple. In informal play, scoring rules differ from place to place.
Games played under the international rules also use a doubling cube, with the faces 2, 4, 8, 16, 32 and 64. At the start the cube sits in the middle and the game is worth one point. Before rolling the dice, a player may offer to double. The opponent either refuses and loses the game at its current value, or accepts, and the game continues at double value; the player who accepted takes the cube, and only they may offer the next double. There are also optional rules, such as the Crawford rule in matches and the Jacoby rule in money games, applied differently from one club or tournament to another. The cube decisions (when to offer a double and when to accept one) are among the hardest parts of the game.
Luck and skill
The dice mean that any single game can be won by the weaker player. Over a long series, however, decisions weigh more than the dice: the choice of moves, the risk taken when a checker is left alone, the building of blocked points and the cube decisions. Stronger players win most games in a long series, and analysis programs can evaluate a position and show which move gives up the least of the winning chances. Unlike casino games, backgammon has no bank: the players play against each other, so there is no house edge either.
Dice probabilities
Two dice give 36 equally likely combinations. A particular non-double roll, for example 6 and 5, can come in two ways (6–5 and 5–6), while a particular double, for example 6 and 6, comes in only one. The chance of rolling any double is 16.67%.
When one checker uses both dice, their sum is what matters. The table shows how often each sum appears:
| Sum | Rolls out of 36 | Probability |
|---|---|---|
| 2 | 1 | 2.78% |
| 3 | 2 | 5.56% |
| 4 | 3 | 8.33% |
| 5 | 4 | 11.11% |
| 6 | 5 | 13.89% |
| 7 | 6 | 16.67% |
| 8 | 5 | 13.89% |
| 9 | 4 | 11.11% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 1 | 2.78% |
In backgammon the sum is not the whole story, though, because the dice can also be played separately, and doubles are played four times.
The chance of hitting a blot
The table below shows, for each distance between an attacking checker and an opposing blot, how many of the 36 rolls allow the attacking checker to land exactly on it. A roll counts if one die equals the distance, if the sum of the dice equals the distance, or if a double, played two, three or four times, covers the distance exactly.
| Distance | Rolls out of 36 | Probability |
|---|---|---|
| 1 | 11 | 30.56% |
| 2 | 12 | 33.33% |
| 3 | 14 | 38.89% |
| 4 | 15 | 41.67% |
| 5 | 15 | 41.67% |
| 6 | 17 | 47.22% |
| 7 | 6 | 16.67% |
| 8 | 6 | 16.67% |
| 9 | 5 | 13.89% |
| 10 | 3 | 8.33% |
| 11 | 2 | 5.56% |
| 12 | 3 | 8.33% |
| 15 | 1 | 2.78% |
| 16 | 1 | 2.78% |
| 18 | 1 | 2.78% |
| 20 | 1 | 2.78% |
| 24 | 1 | 2.78% |
The table makes two simplifications. It ignores blocking points: a combination that would have to stop on a point held by the opponent cannot be played, so in a real position the chance may be lower. And it looks at a single attacking checker; when several checkers can hit the same target, the chance rises, but not by simple addition, because the same roll may serve more than one checker.
A few things stand out at once. Up to a distance of 6, the blot can be hit with a single die, and the chances are high: 30.56% at distance 1 and 47.22% at distance 6, the highest in the table, because at 6 the rolls containing a 6, those adding up to 6 and the matching doubles all count. Beyond 6, a hit needs both dice and the chance drops sharply: 16.67% at distance 7. Above 12 only doubles remain, for example 2.78% at distance 15, and some distances, such as 13 or 14, cannot be covered by a single roll at all. That is why players try, as far as possible, not to leave blots within direct range of opposing checkers, that is, six points or less ahead of them in their direction of travel.
For money
Backgammon is usually played as a social game. When it is played for money, its legal treatment depends on the rules of each country.
Terms
- House edge: the share of each stake the house keeps on average; in backgammon, where the players play against each other, there is none.
- Variance: how widely results are spread around the average; in backgammon, the dice make it large over short matches.