Backgammon against the computer

The rules of backgammon

In brief

  • Two players, 15 checkers each, on a board of 24 points. You have the white checkers, the computer has the black ones.
  • Each die is a separate move; a double is played 4 times.
  • A point holding two or more opposing checkers is blocked. A single checker can be hit: it goes to the bar.
  • You must play both dice if possible, otherwise the higher one.
  • The first player to bear off all 15 checkers wins 1, 2 or 3 points, multiplied by the doubling cube.

These rules are those of the app, which follows the official rules (see the sources) with a few differences, listed at the end of the page. Every position shown was checked by the app's engine and by a second program.

  • your checkers (white), moving from 24 toward 1
  • computer checkers (black)
  • points of the move shown

The board and the starting position

The board has 24 points, numbered from your point of view: your checkers move down from the 24 point to the 1 point. The 6 final points, at the bottom right, make up your home board. The bar divides the board in two; borne-off checkers are stacked on the right.

At the start, you have 2 checkers on the 24 point, 5 on the 13 point, 3 on the 8 point and 5 on the 6 point. The computer has the same position mirrored: 5 checkers on the 19 point, 3 on the 17 point, 5 on the 12 point and 2 on the 1 point. Each side must then move 167 pips in total to bear off its checkers: this is the pip count, shown by the app.

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The app's starting position. Black moves in the opposite direction.

Dice and doubles

On your turn, you roll two dice. Each die is a separate move: you can move two checkers, or the same checker twice. A double is played 4 times. You can never move backward.

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First roll: 3 and 1. The app offers 7 opening moves, and this roll can be played 16 different ways. Here 8/5 6/5: two checkers on the same point, which becomes blocked.

Open points, blocked points and blots

A checker can land on an empty point, on a point where you already have checkers, or on a point where the opponent has only one checker. A point holding two or more opposing checkers is blocked: you can neither land on it, nor touch down on it midway using the first die.

Hitting and the bar

Landing on a point where the opponent has only one checker hits it: that checker goes to the bar. As long as a checker is on the bar, its owner must enter it before moving any other checker. You enter in the black home board, points 19 to 24, counting from the edge of the board: the lowest die face leads to the 24 point, the highest to the 19 point. If both dice land on blocked points, you lose your turn.

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Roll 5 and 1: 13/8 8/7* hits the lone black checker; it goes to the bar.
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One checker on the bar, roll 6 and 4: the only legal first move is bar/19, because the 4 lands on a blocked point.

The both-dice rule

You must play both dice if possible, even if it forces you into a move you would rather not make. If only one of the two can be played, it must be the higher one, when it is playable. The app applies this rule move by move: it does not offer a first move that would prevent the other die from being played.

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Roll 6 and 2: only the sequence 7/5 6/off plays both dice, so the app offers only that.
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Roll 6 and 5: only one die can be played, and it must be the higher one, 13/7.

Bearing off

When all 15 of your checkers are in your home board, you can bear them off. A die removes a checker from the point with the same number. A die higher than your highest point removes a checker from that point; otherwise, it must be played inside the home board. A checker hit during bearing off must enter and come back to the home board before bearing off resumes.

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Roll 6 and 4: 5/off 3/off bears off two checkers; the other permitted way, 5/1 3/off, bears off only one.

The end of the game and scoring

The first player to bear off all 15 checkers wins. The points depend on the loser's position, and are then multiplied by the value of the doubling cube.

End of gameWhenPointsChecked example
Single gamethe loser has already borne off at least one checker1cube at 1: 1 × 1 = 1 point
Gammonthe loser has not borne off any checkers2cube at 2: 2 × 2 = 4 points
Backgammonno checkers borne off, and a checker still on the bar or in the winner's home board3cube at 4: 3 × 4 = 12 points
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You have borne off all 15 checkers; the computer has borne off none and still has a checker in your home board. Backgammon: 3 × 4 = 12 points.

The doubling cube

The doubling cube is a die that carries the stake of the game. At the start, it is in the center and shows 1. On your turn, before rolling the dice, you can offer to double. Your opponent chooses:

  • Accept: the stake goes up to 2 and the cube moves to their side. Only they can offer to redouble, which would bring it to 4.
  • Decline: they immediately lose the value of the cube before doubling, that is 1 point with the cube in the center, or 2 if the cube was already at 2.

In the app, the cube is chosen for each game (the "Cube" row of the "New game" window) and does not go above 64. The computer offers and accepts the cube based on the difference in pip counts: this is a simple rule, not an expert analysis.

Some cube rules are habits of money play, not rules of the game, and the app does not apply them: Jacoby rule (gammon counts only if the cube has been turned), Beaver (redoubling immediately while keeping the cube), Automatic doubles (cube doubled when the first roll is a double).