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According to this article, Roman dice did not always have the modern cube-shaped form:

[I]n contrast with modern dice, they weren’t always exactly cubes. Sometimes they were noticeably a bit flatter than a true cube, or a bit longer, making them more likely to fall on some faces than on others.

A possible explanation is provided:

Did it matter to game players that these dice were not fair? “We don’t know for sure,” Eerkens says. The way Romans wrote about dice falls suggests they were regarded as signs of supernatural favor or of a player’s fortune, however. The archaeologist Ellen Swift, in her book Roman Artifacts and Society, writes that high rolls had associations of benevolence and felicity, and that rolling three sixes at the same time seems to have been called a Venus. “Dice potentially played an important role in conceptualizing divine action in the world,” she writes.

If you thought that your prayers had more to do with a roll’s outcome than anything else, perhaps a perfect shape wasn’t required. Eerkens says, “Some of the non-symmetry that we see in the earlier dice might be a by-product [of the idea] that it wasn’t thought to be very important in the function of the dice—that it didn’t matter too much, because other things were controlling whether you would win or lose the game.”

This is ingenious but also a but tenuous, in my opinion.

I have an alternative explanation: as is well known, dice were made of bones and bones naturally tend to have an elongated shape.

Is there some known research on this subject?

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    Sorry to have to tell you, but it's not your theory that dice were made of bones. This story has been around for quite a while. I just don't know a good reference off the top of my head. – jjack Feb 26 '18 at 10:52
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    Getting a "perfect" cube in both size and weight distribution would have required some skill. And as long as both sides of a game use the same set of dice, and the game isn't about betting on a specific roll (where the one "knowing" the dice would be at an advantage), does it really matter? (Personal thoughts. And now off to hunt some sources...) – DevSolar Feb 26 '18 at 12:20
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    Sounds like that article's just talking about the tali, which was an elongated Roman dice for which only the four long sides were numbered and counted. So it's basically an ancient d4 dice. The Romans also had the tesserae which were more properly cubic like a normal modern dice. Both were usually made from bones so it's less effort to make the tali, i.e. no need to file the length down to be equal on all sides. – Semaphore Feb 26 '18 at 12:35
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    @Semaphore : looks like you have the beginning of a good answer... – Evargalo Feb 26 '18 at 13:09
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    Knucklebones: en.wikipedia.org/wiki/Knucklebones – AllInOne Feb 26 '18 at 17:21
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You are correct.

According to this site (unfortunately in German) about the Roman Empire there were many different types of dice in use by the Romans. Apart from the 6-sided cubes we know today there were also rod-shaped dice with four or six sides.

The website reports:

"For many games of dice of the ancient times one required only four possible differentiations (results). They derive from little bones from animals, which were also used for playing dice."

The source given by the website is Marco Fitta, "Spiele und Spielzeug in der Antike".

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The use elongated or long dice has been noted for a number of cultures and they seem to have been associated with particular games over many centuries. Archer St. Clair in Carving as Craft notes that these

had largely been replaced by cubical dice in the Roman world by the second century AD.

St. Clair adds that

they are usually made from the shafts of small long bones, and the numbers 1 and 2 are usually omitted. Even when solid...the ends are usually left blank

Interestingly, parallelepiped dice have also been found in Britainn dating from both before and after the Roman occupation but seemingly made in a similar fashion. On these, Arthur MacGregor in Bone, Antler, Ivory and Horn: The Technology of Skeletal Materials Since the Roman Period, says most were

made from the shafts of small, long bones, comparable with the metapodials of sheep, and indeed their characteristically elongated shape may be seen as resulting from this repeated selection. A corollary of this choice is that the ends are usually open and hence the values are normally restricted to the four elongated sides, the numbers 1 and 2 usually being omitted.

There is little mention of what games the Romans played with these dice, but there is this from Pete Nash in Mythic Rome:

TALI (ROLLED KNUCKLEBONES)

Played with actual knucklebones, or elongated dice (tali) which mimic the elongated shape of the bones....the sides were marked with the numerals 1, 3, 4 or 6.... Played with four bones, the objective of the game is to roll the highest possible value.

F. N. David, in Games, Gods and Gambling, citing Suetonius, mentions that it is unfortunate that the emperor Claudius' book 'How to Win at Dice' has not survived. While Davis does not believe it contained rules on games, it might have told us something.

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