A Relatively Modern Idea: Fairness in Dice Rolling

[Image courtesy of Larsdatter.com.]

This may come as a surprise to you, fellow puzzlers, but fairness was not always a priority when it came to rolling dice.

Nowadays, whether you’re going after that elusive Yahtzee, hoping for doubles to earn another roll in Monopoly, or trying to roll sevens in a game of craps, the basic concept behind throwing dice is that every outcome of a six-sided die has an equal chance to appear. Unless you’re dealing with loaded or gimmicked dice, your odds should be 1 in 6.

But a recent study by researchers from the American Museum of Natural History and the University of California, Davis, has revealed that fairness in dice rolling didn’t really become a concern for dice users until the Renaissance. Researchers gathered dice spanning 2000 years of human history to explore why this was the case.

[Image courtesy of Wikipedia.]

From an article on Science Alert:

Roman-era dice, the researchers found, were a mess when it came to shape. They were made from a variety of materials, such as metal, bone and clay, and no two were shaped entirely alike. Many were visibly lumpy and lopsided, with the 1 and 6 on opposite sides that were more likely to roll up.

In fact, it seems like variety was the name of the game in Roman times, since the number configurations, shape, and size were inconsistent across the board, although dice were fairly common in the time period.

[Image courtesy of Pinterest.]

The Dark Ages led to a downturn in dice frequency, as they become very rare between the years 400CE and 1100CE.

The use of dice rebounds after 1100, and are most commonly found in ancient Mesopotamia and Egypt in what is known as the primes configuration, meaning that opposite numbers add up to prime numbers. 1 pairs with 2, 3 pairs with 4, and 5 pairs with 6.

There was a reinvigorated focus on the mechanics of chance and calculating probability, thanks to names like Galileo and Pascal, as well as a spirit of greater scientific understanding overall. Those Renaissance influences led to both a standardized shape for dice and a change in the numbering system. At this point, most dice convert to the sevens configuration, where opposite sides add up to seven (1 pairs with 6, 2 pairs with 5, and 3 pairs with 4).

[Image courtesy of Smithsonian.com.]

And according to lead researcher Jelmer Eerkens, cheating may have been on the mind of manufacturers going forward. “Standardizing the attributes of a die, like symmetry and the arrangement of numbers, may have been one method to decrease the likelihood that an unscrupulous player had manipulated the dice to change the odds of a particular roll.”

That change from variable shapes, sizes, and designs reflects a sea change in thinking towards dice and chance. Before, the shape didn’t matter because the results were attributed to Fate or some greater outside force, but later on, an understanding of chance and probability pushed standardization of dice forward.

In the end, it’s amazing how much of our culture and worldview, both past and present, can be revealed by exploring how we solve puzzles and play games.

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The Puzzly Art of Carmina Figurata

We don’t discuss poetry all that often in the blog. To be fair, when it comes to poetry and crosswords, all you really need to know are E’ER, O’ER, ODE, E’EN, and ‘NEATH.

But there is one form of poetry that lends itself quite handily to our favorite field of study, sitting at the crossroads of art, poetry, and puzzles. Today, we’re going to talk about carmina figurata.


[A poem shaped like an altar, a work by Publilius Optatianus Porphyrius.
Image courtesy of Some Grey Matter.]

A carmina figuratum is a poem wherein either the entire body of the poem or select parts form a shape or pattern. Often this shape reflects the subject of the poem.

But that’s what the term has come to mean over time, as poetry has evolved and grown. The original carmina figurata were religious-based poems where letters were colored red to stand out from the regular black lettering in order to draw attention to or highlight a certain religious figure.


[“De laudibus sanctae Crucis” by Oliverus.
Image courtesy of WTF Art History.]

For instance, in this image, titled “Praises to the Holy Cross,” you can see “rex,” meaning “king” in red above Christ’s head and “virtu” on his stomach, among other words. Obviously, having the image superimposed over the text helps highlight the words, representing John 1:14, ““And the Word became flesh and made His dwelling among us.”

Quite a bit to unpack in such a small piece.

Other carmina figurata have no color or imagery, relying on the cleverness of the reader to uncover the hidden messages within the text. This was particularly true of the poet Publilius Optatianus Porphyrius, who wrote dozens of carmina figurata of increasing complexity.

Some of these hidden messages honored the same rulers the poems were meant to impress. Other messages referenced the date the poem was written or the poet himself. Some even concealed drawings or designs.





[Several of Porphyrius’s most ambitious creations, revealing just how far a reader would have to delve to uncover the hidden messages. Images courtesy of Some Grey Matter.]

From the article on Some Grey Matter:

The poems contain supplementary text ‘hidden’ within the main body of the individual poems and intended to be ‘discovered’ by the reader. These versus intexti poems were apparently intended to dazzle Constantine with their technical virtuosity and thereby inspire the hoped–for recall of their creator…

Now that’s ambition. Imagine you’re constructing a Marching Bands puzzle, with the overlapping lines and loops of text, but all in the hope of courting favor with a major political player. And to do so, you need to hide even more information in the grid. That’s next-level puzzling, to be sure.

Whether you’re moved by the artistry, impressed by the construction, or intrigued by the puzzly challenges they represent, you must admit: carmina figurata are works of puzzle art unlike anything else.


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