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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Roll with it!

When it comes to games, there’s probably no component more common or familiar than the six-sided die. From craps to Yahtzee, backgammon to Monopoly, everyone has played a game where the dice controlled your destiny.

And there are several games where the dice are integral to the puzzly gameplay.

The most obvious example is Boggle and its numerous variants. Boggle is played with a 4×4 grid of dice with letters on them, shaken up in order to randomize the letters shown. Players have a limited amount of time to spell out as many words as possible, moving from one letter to an adjacent one.

Testing both your vocabulary and anagramming skills, Boggle is great fun and a terrific challenge, depending on the letters you get. (It can also depend on which edition of the game you purchase, since some have different available letters in order to facilitate gameplay.)

Along that line, I actually received a great puzzly dice game as my Secret Santa gift in the office this year. (How did they know I like puzzles and games!?)

It’s called Campbell’s Alphabet Dice Game, and it’s a marvelous mix of Boggle, Yahtzee, and anagramming games, challenging the players to conjure words from the letters they roll.

The packaging is clever, and the game is designed with all sorts of puzzly references to cooking. With higher-valued letters and a low-stress game mechanic — if you’re stumped, everyone rerolls their letters instead of making one player suffer with crummy letters — it’s a nice addition to my puzzle game treasure chest.

And when it comes to letter-dice games, we have to talk about one of my all-time favorites, Scattergories.

In Scattergories, you roll a giant 20-sided die with numerous letters on it, determining what letter everyone will be using that round. Then players are required to come up with one word for each category that starts with that letter.

The puzzly aspect comes not only from coming up with appropriate words to fit each category, but trying to figure out which words your fellow players WOULDN’T come up with themselves, since answers duplicated by one or more players are worth zero points.

It can be a real challenge to not only come up with ten answers on the fly, but to then try to get into the heads of your opponents and guess what words THEY’D write. More than once, I’ve psyched myself out by assuming one answer was too easy and changing it, only to discover a friend had done the exact same thing. *laughs*

Of course, I would be be remiss if I didn’t mention Dungeons & Dragons, a dice game that goes far beyond the average board game-playing experience.

When it comes to conquering puzzles, some of the best puzzle-solving experiences of my life have been in sessions of Dungeons & Dragons with friends.

Whether it was unraveling a curious mechanical puzzle in order to unlock a door, solving a devious riddle to avert some horrible outcome, or devising a clever way to combine the tools at hand to overcome an unexpected obstacle, my puzzle skills often served me well, allowing me to match wits with dark wizards and perilous foes.

This weekend marked the 40th Anniversary of the birth of the world’s most famous roleplaying game, and it’s hard to deny the incredible legacy sparked by those curiously-shaped dice.

Dice games come in all shapes and sizes — as do the dice themselves! — but they add a marvelous wrinkle of randomness and challenge to the puzzle-game community.

What are your favorite puzzly dice games? Did I miss any major ones? Let me know in the comments!

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