
The Shape of Ancient Dice Suggests Shifting Beliefs in Fate and Chance - curtis
https://www.theatlantic.com/science/archive/2018/02/dice-dice-baby/553742/?single_page=true
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OscarCunningham
Perhaps the Romans misunderstood probability, and thought that adding
imperfections to dice would make them more random?

Also the "primes" configuration of faces could be an attempt to minimise bias.
A weighted die is less useful if the high numbers are opposite each other.

~~~
Retric
As long as all players use the same dice, bias may not be that important.

~~~
analog31
This is a fair point, but I think it gets more complicated if betting becomes
involved, because the players may use the same dice, but the player who
understands how the dice work has a betting advantage.

Differing beliefs in how games of chance work may still be an arbitrage that
works to the advantage of casinos and lotteries.

~~~
plopz
There was a post on here awhile ago[0] about using loaded dice to cheat at
Settler of Catan. All the benefit goes to the person who knows the bias.

[0]
[https://news.ycombinator.com/item?id=15921322](https://news.ycombinator.com/item?id=15921322)

~~~
gxs
This makes intuitive sense with just a basic level of understanding.

A biased dice may appear random, but over time youre bound to roll a given
number or set of numbers more often. Over time, it adds up to a big advantage.

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emptybits
This reminds me of observations some have when looking at the I Ching.

The I Ching is elegant from a modern binary/math perspective because it
appears to be an ancient hierarchy of 1-bit symbols (yin/yang), stacked into
3-bit symbols (triagram=element), and finally stacked into 6-bit symbols
(hexagram). These are, apparently, descriptions of situations at hand or
situations to come. The arrangements of these 64 hexagrams make a modern math
mind speculate about binary counting and the reason for a particular ordering
[1] and it all seems very orderly and balanced and evenly distributed. Or so
you would think.

Then one learns that the traditional methods of division _using_ those 64
hexagrams (e.g. the yarrow stalk method) is quite unevenly distributed. The
dice are weighted, so to speak, to give some outcomes more often than
others.[2]

Did the Chinese ancients _know_ this and design it this way? Did they care?
Was it a mistake? ¯\\_(ツ)_/¯

[1]
[https://www.biroco.com/yijing/sequence.htm](https://www.biroco.com/yijing/sequence.htm)

[2] [https://aleadeum.com/2013/07/12/the-i-ching-random-
numbers-a...](https://aleadeum.com/2013/07/12/the-i-ching-random-numbers-and-
why-you-are-doing-it-wrong/)

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coldtea
I call BS. The romans (and earlier peoples) were just as cunning and you and
me in those matters -- such beliefs didn't play a role in playing other games,
and shouldn't play a role in dice.

Those artifacts could be sacrificial or similar special use dice, not
something people would use on a game or bet on thinking that some god will
even their odds.

~~~
ziftface
That's possible, but it's also possible that they believed in supernatural
intervention when playing dice games. It seems they did for other parts of
their lives, why would this be different?

~~~
coldtea
Because people in general weren't more stupid than us in everyday matters --
and you don't need a theoretical knowledge of combinatorics to know when
you've been had.

~~~
DanAndersen
Is it really just a matter of "being stupid"?

We _know_ that cleromancy (casting of lots) was practiced among Hebrew
populations and in ancient Rome [0]. Under a worldview in which the knowledge
and will of the divine is made manifest through natural acts, where things
aren't just "happenstance" but are inherently infused with meaning, this makes
complete sense.

This is also why trial by ordeal was a thing in many ancient societies, and
why it was seen to be legitimate enough to have as part of a judicial system.
The idea is that divine forces will show their favor based on the outcome of
what would seem to us to be chance. Now there were probably some that were
more cynical or less so about all this, and that may be part of how such
systems actually gained legitimacy, because those in authority could tip the
scales occasionally [1].

I don't think we can compartmentalize the beliefs and mindsets of people,
especially ancient people, into "secular" and "religious" domains. It was all
intertwined in a way that is hard for us to relate to in modern times, even
among modern religious people.

[0]
[https://en.wikipedia.org/wiki/Cleromancy](https://en.wikipedia.org/wiki/Cleromancy)
[1] [https://aeon.co/ideas/why-the-trial-by-ordeal-was-
actually-a...](https://aeon.co/ideas/why-the-trial-by-ordeal-was-actually-an-
effective-test-of-guilt)

\---

EDIT: I did some more reading and found something interesting -- there is a
mention of "loaded dice" in the Mahabharata: [2]

>Shakuni's dice were off course made of his father's thigh bone and is
believed to possess that special power of giving the number according to
Shakuni's will.

From this the idea that dice could be manipulated or used to cheat in various
ways seems to have been known far in the past, but there is still an
interesting connection between dice-rolling and supernatural influences, even
in the case of loaded dice. One of these days I should learn more about the
Mahabharata.

[2] [https://www.quora.com/Mahabharata-Hindu-epic-How-did-
Shakuni...](https://www.quora.com/Mahabharata-Hindu-epic-How-did-Shakuni-
cheat-in-the-game-of-dice)

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mkempe
I strongly recommend "Against The Gods: The Remarkable Story of Risk" (1996)
[1] for a fascinating, historical perspective on people's growing
understanding of probability and statistics over the last few millennia.

The author, Peter Bernstein [2], was brilliant and his other works also merit
your attention if you are interested in economics and finance.

[1] [https://www.amazon.com/Against-Gods-Remarkable-Story-
Risk/dp...](https://www.amazon.com/Against-Gods-Remarkable-Story-
Risk/dp/0471295639)

[2]
[https://en.wikipedia.org/wiki/Peter_L._Bernstein](https://en.wikipedia.org/wiki/Peter_L._Bernstein)

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rdiddly
If imperfect dice including one with an extra 3 were found in a big heap,
mightn't that be because they were deemed inferior dice unworthy of play?
Maybe the local constabulary went around to all the gambling dens, and
confiscated & buried all the crooked dice.

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swah
> 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.

As if someone would play dice (and have fun) with a completely rational
mind...

~~~
coldtea
There's nothing preventing someone to play dice and have fun with a
"completely rational mind".

Don't confuse accepting small odds and the spending money with being
"irrational".

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pradn
It seems to me that some of the ancients had a better appreciation for chance
than we do, especially in public affairs. Many of the speeches in Thucydides'
History of the Peloponnesian War caution that though a warring party may be
strong, luck is a huge part of war. We hardly have George Bush saying "we are
pretty strong, but Iraq could go either way depending on luck." Our
politicians speak with such certainty about the future.

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rbobby
> including one cheater’s die with an extra three

I can't imagine that going undetected for long. Which probably means the owner
was also capable of sleight of hand.

~~~
pbhjpbhj
One would notice on the first roll that the 3 and 4 weren't opposite. Perhaps
it's just for a particular game.

