Backgammon dice roller

How to use this backgammon dice roller

The page has two modes. In normal mode you throw both dice on your turn and see the two numbers separately, which is how they are used in backgammon: each number moves one checker, or both numbers move the same checker one after the other. When the two dice match, a double message appears showing the number four times, for example 5-5-5-5.

1. Opening roll. Switch this mode on before the game starts. Each player throws one die; whoever throws higher goes first and plays both numbers that came up, their own and their opponent's. If the two dice tie, the page asks you to roll again.
2. Game. After the opening roll the page goes back to two dice by itself and alternates turns between the two players.
3. Doubles counter. It keeps a tally of the doubles each player has thrown during the game, which settles the old argument about who has had the luckier dice.

You can roll with the button or by dragging the dice with your finger or mouse and letting go over the tray. The result stays on screen until the next throw.

Backgammon dice rules

Modern backgammon rules are the same all over the world, and the part about dice is very specific:

The dice also decide when a hit checker comes back. A checker on the bar enters the opponent's home board on the point shown by one of the dice; if that point is closed (two or more opposing checkers), that number cannot be used. While you have a checker on the bar you cannot move any other.

Odds: direct and indirect shots

The most useful question in backgammon is this: if I leave a blot at a certain distance from an opposing checker, how many throws hit it? There are 36 possible throws. A specific number, say a 6, appears on at least one die in 11 out of 36, or 30.6%. But at a distance of 6 you can also be hit by combinations that add up to 6 (5-1, 4-2, 3-3, 2-2), so the total goes up.

This table counts every throw that reaches a blot at each distance, with no blocking points in the way. It was worked out by going through all 36 combinations and applying the doubles rule (2-2 reaches 2, 4, 6 and 8).

Up to 6 pips away are direct shots, which can be hit with a single die, and the risk is above 30% and close to half at 6. From 7 upwards are indirect shots, which need both dice together, and the risk falls below 17%. That is where the players' rule of thumb comes from: if you must leave a blot, leave it 7 or more pips away rather than 6 or fewer. In a real game the figures are usually lower, because your own made points block some of the combinations.

Entering from the bar

With a checker on the bar you come in if at least one die shows an open point in your opponent's home board. The more points closed, the harder it gets:

Doubles and the counter

There are six possible doubles (1-1, 2-2, 3-3, 4-4, 5-5 and 6-6) among 36 throws, so the chance of a double on any throw is 1 in 6, or 16.7%. That is the same as rolling a given number on a single die. The chance of a specific double, such as 6-6, is 1 in 36, or 2.8%.

The counter helps keep things in proportion. Going 10 throws without a double happens about 16% of the time, so it is nothing unusual; two doubles in a row happen once in every 36 pairs of throws. With 20 to 30 throws each in a normal game, each player can expect three to five doubles, and a gap of two or three between players is well within normal variation.

Another useful figure: counting doubles as four moves, an average throw moves 8⅙ pips (49/6). That is the number players use with the pip count to judge who is ahead in the race.

The doubling cube

The doubling cube is a large die with the faces 2, 4, 8, 16, 32 and 64. It is never thrown; it tracks the stake. It starts in the middle with 64 facing up, which means the game is worth 1.

Some optional rules are common in money play: automatic doubles (if the opening dice tie, the stake doubles and the cube stays in the middle), the Jacoby rule (gammons and backgammons only count once the cube has been turned) and the beaver (a player who is doubled may immediately redouble while keeping the cube). Agree on them before the first throw.

A short history of backgammon

Backgammon is the best-known survivor of a very old family of dice race games, the tables games. These are the milestones that can be documented:

• Royal Game of Ur (around 2600 to 2400 BC). Leonard Woolley found five boards in the Royal Cemetery at Ur, in present-day Iraq, between 1922 and 1934; one is in the British Museum. It was played with four-sided pyramid dice. Its rules are known from a Babylonian tablet of around 177 BC translated by Irving Finkel. It is considered a probable ancestor of the backgammon family, not the same game.
• Rome: duodecim scripta and tabula. The Romans played ludus duodecim scriptorum and later tabula, with 24 points, 15 counters per player and three dice.
• Emperor Zeno (fifth century). A Greek epigram describes a game of tabula played by the Byzantine emperor Zeno, who reigned at the end of the fifth century. From what it describes, the rules were already very close to today's.
• Persia: nard. Between the third and sixth centuries nard appears in Persia, played with two dice. Persian tradition credits the sage Bozorgmehr with its invention.
• 1283: the Book of Games. The manuscript made for Alfonso X of Castile describes several tables games with rules and illustrations, among them todas tablas, very close to backgammon.
• Seventeenth century: the name. The word backgammon appears in writing in England in the middle of the seventeenth century.
• 1743: Edmond Hoyle publishes a treatise on the game in London.
• 1920s: the doubling cube is invented in New York gaming clubs and changes the strategy of the game for good.
• 1960s: Prince Alexis Obolensky organises the first big international tournaments and the game becomes fashionable.

What backgammon is called around the world

Modern backgammon is played with the same rules everywhere, but each country keeps its own names, sometimes for the same game and sometimes for related tables games with different rules.

Practical tips with the dice