Fair Dice in Backgammon
Backgammon is a game of skill played with a random element. That element only works if the dice are fair: every face of each die must be equally likely, and no player may influence the result. Over the board this depends on good equipment and good rolling habits; online it depends on the quality of the random number generator.
What "fair" means
A fair die lands on each of its six faces one time in six. With two fair dice, each of the 36 combinations is equally likely, so a particular double such as 6-6 comes up 1 time in 36 and some double comes up 6 times in 36. The figures on our probability page all assume fair dice.
Precision dice
Ordinary dice from a toy shop often have rounded corners, slightly uneven sides and pips scooped out of the faces. Because the 6-face loses more material than the 1-face, such dice can be very slightly unbalanced. Precision dice, the kind used in tournaments, are made to tighter standards:
- sharp, square edges and corners, so the die does not favor rolling in one direction;
- sides cut to the same length within a very small tolerance;
- pips drilled and then filled with paint of similar weight to the removed material, keeping the faces balanced;
- often transparent material, so hidden weights or bubbles would be visible.
Dice cups
Tournament players roll from a dice cup instead of by hand, which makes it much harder to control how the dice land. Good cups have a lip, or "trip", around the inside of the rim that catches the dice and makes them tumble. Accepted etiquette is to shake the dice well, roll them out together into the section of the board on your right, and let them land flat there. If a die lands on top of a checker, tilts against the board edge ("cocked dice") or falls off the playing surface, both dice are rolled again. Many players also agree that a roll made before the opponent has finished his move does not count.
Baffled boxes
A baffled box, sometimes called a dice tower, is the strongest protection against controlled rolling. The dice are dropped into the top of a small box or tower and bounce off internal baffles before coming out at the bottom. No skill of the hand can survive the trip. Baffled boxes are popular in clubs where players want no arguments about rolling technique.
Dice online
When you play on a computer, dice come from a random number generator (RNG). No program can be checked by watching a few games, but you can look for signs that a generator is sound:
- A well-known method. Reputable services say which generator they use and how it is seeded, often a cryptographically strong one, instead of keeping it secret.
- Independent testing. The generator has been checked by people outside the company, for example with standard statistical test suites.
- Open source. In open source software such as GNU Backgammon, anyone can read the code that produces the dice.
- Exportable records. You can download your matches and check the rolls yourself, for instance by counting how often doubles appear over thousands of rolls.
Why the dice seem unfair
Almost every player has lost a game they were sure to win after a run of bad rolls, and that game is easy to remember. The other games, where the dice behaved normally, fade from memory. A position that wins 95% of the time still loses 1 game in 20. Before you blame the dice, count: records of many games, not a single painful loss, are the only fair test. To keep the swings in perspective, read our backgammon tips.