** Dice**

Dice were invented innumerable times tens of thousands of years ago. They often turn up in archeological digs.

Dating from 2,000 years ago, 90% of Roman dice were typically asymmetrical and would not roll randomly. The Romans knew how to make symmetrical dice but chose not to. Perhaps they thought other forces were at work in determining the outcome of a roll – dice as tumbling Ouija boards.

Only from the mid-15th century were dice typically symmetrical, as gamblers began demanding steady odds.

The arrangement of numbers on dice evolved as well. There are a variety of ways to arrange the numbers 1 to 6 on a die. Several were seen in Roman-era dice.

Between 1250 and 1450, a single arrangement was dominant: 1 opposite 2, 3 opposite 4, and 5 opposite 6. This configuration is called “primes” because opposite faces sum to prime numbers (3, 7, and 11).

Then die denominations suddenly changed. Primes were replaced by the modern “sevens” configuration: 1 opposite 6, 2 opposite 5, and 3 opposite 4, where opposite faces sum to 7.

A standard arrangement makes it easy to check that a die is authentic. Primes and sevens are readily verified.

Primes might have become unpopular because the configuration was perceived as unbalanced, whereas sevens has a symmetry in that the opposite faces all add to 7; symmetry as a proxy for fairness.

As dice design became more ‘regular’, successful players were better able to see patterns in play that might have led to early probabilistic thinking. ~ American mathematician Edward Packel