9 ms·

How dice changed over 2k years to be more fair (2018)

69 points by Hooke 6y ago

abiogenesis 6y ago
I was expecting to read things like rounded edges and corners but the article seems to mostly discuss the configuration of numbers on opposite faces. > When dice reappear around 1100 they are predominantly in the "primes" configuration, where opposite numbers tally to prime numbers (1-2; 3-4; 5-6) Does this have really anything to do with primes? It looks like they simply chose sequential numbers.
- Talanes 6y ago
  The "sevens" configuration could also be arrived at by the opposite approach of splitting up the largest and smallest numbers, with everything adding up to seven being a by-product. I took the names as more a classification than actually ascribing intent.
  - abiogenesis 6y ago
    But adding up to seven is something that is expected, and a generic by-product (they would've added up to 9 with a 8-faced dice). The "prime" explanation only works with a 6-faced dice and it's purely accidental.
    - mc32 6y ago
      Yeah the prime explanation is just the result of successive numbers.
- barbegal 6y ago
  No it's just a term used in that area of study such that researchers have consistent terminology. The three common configurations are "sevens", "primes" and "turned" where the opposite sides are 1-3 2-4 5-6
  - abiogenesis 6y ago
    Thanks for the pointers. I have found an insightful article (that also explains where the term "turned" comes from): https://www.theatlantic.com/science/archive/2018/02/dice-dice-baby/553742/ https://www.theatlantic.com/science/archive/2018/02/dice-dic...
- TomK32 6y ago
  Just a side-note: D20 are either random or snaking from 1 to 20 if the player uses them as a life counter.
smogcutter 6y ago
> Gamblers may have seen dice throws as no longer determined by fate, but instead as randomizing objects governed by chance. Going by the principal that people in the past weren’t dumb, just different, and had less access to information, I’m not convinced by the conclusion “they didn’t understand the odds, it was up to the gods”. That may be true for Joe Legionary losing his pay every week over dice, but you can bet your ass that the guy running the game, who probably supplied the dice and maybe even made them had a very good idea of how unfair they were.
- dt5702 6y ago
  I agree. People are people, those in the past didn’t have as much information as we do now but that doesn’t mean they weren’t as sharp. We do see development in ideas over time, but this is separate to the idea that if we don’t understand what they were doing then it must have been religion. Arguments to religion are a classic trope in archaeology. Although this doesn’t explicitly mention that this is the case, I think it’s worth pointing out that people would have known that all dice were fair, but some were fairer than others.
  - de_watcher 6y ago
    Nowadays you have easier time to actually use hard information: build things faster and have impact. But the soft "information" (the one used to affect people directly) has never gone away, it has diversified and it's going strong.
- wahern 6y ago
  A few years ago a philosopher wrote an article in the New York Times that suggested that maybe the gods were real in antiquity, on the tacit presumption that belief in gods was then universal, such universality being a consequence of common and widespread divine manifestations that eradicated doubt. Of course, he was trying to be provocative, but I took issue with the presumption of universality. When I wrote to remind him that Plato briefly discussed atheists in The Laws, implying that atheism among young adults was common, though invariably transitioning to adherence to the local faith as they grew older and wiser[1], he replied with, "Oh, yeah, I forgot." [1] Of course, there's multiple ways to interpret Plato's argument, including 1) older, wiser people came to see the truth of the existence of the gods and 2) older, wiser people came to see the usefulness of shared belief in the gods, regardless of the actual existence of the gods.
cachvico 6y ago
This Reddit post is much more informative: https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_holes_on_a_dice_which_represent_the/ https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_h...
- shawndumas 6y ago
  https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_holes_on_a_dice_which_represent_the/ https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_h...
ARandomerDude 6y ago
> Dice are very rare between 400 and 1100, corresponding to the Dark Ages. How dark these ages weren't. I'm always a bit sad to see such an obviously polemical term used to describe the period.
- dfee 6y ago
  Curious if you’d share more? Is there a faction of historians who don’t share this viewpoint? I’ve always been curious as I studied the Classics (Greece and Rome) and then European History (which in American high schools is 1400AD+). I have no insight into that intermediate period.
  - scambier 6y ago
    From https://en.wikipedia.org/wiki/Dark_Ages_(historiography) https://en.wikipedia.org/wiki/Dark_Ages_(historiography) Relevant excerpts: > The term employs traditional light-versus-darkness imagery to contrast the era's "darkness" (lack of records) with earlier and later periods of "light" (abundance of records) > As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
  - eesmith 6y ago
    https://en.wikipedia.org/wiki/Dark_Ages_(historiography) https://en.wikipedia.org/wiki/Dark_Ages_(historiography) > As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
  - bedobi 6y ago
    I'm also interested in this. Apparently recently there's an aversion to using terms like "dark ages", because they imply the period between antiquity and the renaissance was poorly recorded or objectively worse, and historians shouldn't make value judgements, they should just accurately account for what happened in any given period. I do get that, and I'm no expert, but... It sure seems to me like things were a whole lot objectively worse during the dark ages. Literacy, trade and all kinds of other objectively good things were replaced by more or less complete chaos, constant fighting between countless warlords, plagues... Like yes the large empires of antiquity did their own share of fighting and other bad things but regular people within any given empire seem to have had better lives than more or less anyone during the dark ages. Would love to be corrected because I love learning about history!
simik 6y ago
What's "unbalanced" about the 1-2, 3-4, 5-6 arrangement of numbers? And how is "primes" superior?
- mcv 6y ago
  That arrangement is primes. The other arrangement is sevens: 1 and 6 opposite each other, 2 and 5, and 3 and 4. Both of them can be unfair. Assuming rolling high is better, when 1 and 2 are opposite each other, those faces could be slightly smaller and therefore have a smaller chance of landing on them. This is especially easy with hand-made dice, which are bound to be somewhat irregular. With "sevens", 1, 2, and 3 meet in a single point. If that point is somehow heavier than the opposite point, you're more likely to roll 4, 5 or 6. I think I'd actually consider the "primes" arrangement to be superior to the modern one. No idea why that switch was ever made.
lihaciudaniel 6y ago
The history of dice is older than that. I would say around three times as long, since earliest dice were found in pyramids
- bmm6o 6y ago
  It's not clear in TFA but the paper it's based on focuses on the history of dice in the Netherlands and doesn't claim that dice didn't exist elsewhere earlier.
jhallenworld 6y ago
I've been trying other non-roman dice: Indian four-sided dice: https://averweij.web.cern.ch/averweij/india.htm https://averweij.web.cern.ch/averweij/india.htm Two-sided dice (cowry shells) for Indian Pachisi- they are terrible! https://joyofplaying.wordpress.com/play-by-rules/164-2/ https://joyofplaying.wordpress.com/play-by-rules/164-2/ More binary dice for the Royal Game of Ur: https://www.youtube.com/watch?v=WZskjLq040I https://www.youtube.com/watch?v=WZskjLq040I
seesawtron 6y ago
I don't really understand if the difference in two configurations of numbers appearing on the dice is related to the dice being biased? Nevertheless, the role of geometry in probability became clear to me when I read about Fano Planes and their role in winning Transylvania lottery [0,1]. [0] https://en.wikipedia.org/wiki/Transylvania_lottery https://en.wikipedia.org/wiki/Transylvania_lottery [1] https://en.wikipedia.org/wiki/Fano_plane https://en.wikipedia.org/wiki/Fano_plane
kgwgk 6y ago
A few blog posts on the subject of dice fairness: https://www.lesswrong.com/posts/zd89utY4afA59p58k/wolf-s-dice https://www.lesswrong.com/posts/zd89utY4afA59p58k/wolf-s-dic... https://books.google.ch/books?id=pGRsCQAAQBAJ&pg=PA258&lpg=PA258&dq=wolf+dice&source=bl&ots=9lgmeQE-tk&sig=ACfU3U1yNXs81m9hz8W4-HKXJ1KWTt2UlA&hl=en&sa=X&ved=2ahUKEwjNu6v5n_rpAhXGxMQBHQU7BxEQ6AEwC3oECAYQAQ#v=onepage https://books.google.ch/books?id=pGRsCQAAQBAJ&pg=PA258&lpg=P...

69 points by Hooke 6y ago

I was expecting to read things like rounded edges and corners but the article seems to mostly discuss the configuration of numbers on opposite faces. > When dice reappear around 1100 they are predominantly in the "primes" configuration, where opposite numbers tally to prime numbers (1-2; 3-4; 5-6) Does this have really anything to do with primes? It looks like they simply chose sequential numbers.

Talanes 6y ago
The "sevens" configuration could also be arrived at by the opposite approach of splitting up the largest and smallest numbers, with everything adding up to seven being a by-product. I took the names as more a classification than actually ascribing intent.
- abiogenesis 6y ago
  But adding up to seven is something that is expected, and a generic by-product (they would've added up to 9 with a 8-faced dice). The "prime" explanation only works with a 6-faced dice and it's purely accidental.
  - mc32 6y ago
    Yeah the prime explanation is just the result of successive numbers.
barbegal 6y ago
No it's just a term used in that area of study such that researchers have consistent terminology. The three common configurations are "sevens", "primes" and "turned" where the opposite sides are 1-3 2-4 5-6
- abiogenesis 6y ago
  Thanks for the pointers. I have found an insightful article (that also explains where the term "turned" comes from): https://www.theatlantic.com/science/archive/2018/02/dice-dice-baby/553742/ https://www.theatlantic.com/science/archive/2018/02/dice-dic...
TomK32 6y ago
Just a side-note: D20 are either random or snaking from 1 to 20 if the player uses them as a life counter.

smogcutter 6y ago

> Gamblers may have seen dice throws as no longer determined by fate, but instead as randomizing objects governed by chance. Going by the principal that people in the past weren’t dumb, just different, and had less access to information, I’m not convinced by the conclusion “they didn’t understand the odds, it was up to the gods”. That may be true for Joe Legionary losing his pay every week over dice, but you can bet your ass that the guy running the game, who probably supplied the dice and maybe even made them had a very good idea of how unfair they were.

dt5702 6y ago
I agree. People are people, those in the past didn’t have as much information as we do now but that doesn’t mean they weren’t as sharp. We do see development in ideas over time, but this is separate to the idea that if we don’t understand what they were doing then it must have been religion. Arguments to religion are a classic trope in archaeology. Although this doesn’t explicitly mention that this is the case, I think it’s worth pointing out that people would have known that all dice were fair, but some were fairer than others.
- de_watcher 6y ago
  Nowadays you have easier time to actually use hard information: build things faster and have impact. But the soft "information" (the one used to affect people directly) has never gone away, it has diversified and it's going strong.
wahern 6y ago
A few years ago a philosopher wrote an article in the New York Times that suggested that maybe the gods were real in antiquity, on the tacit presumption that belief in gods was then universal, such universality being a consequence of common and widespread divine manifestations that eradicated doubt. Of course, he was trying to be provocative, but I took issue with the presumption of universality. When I wrote to remind him that Plato briefly discussed atheists in The Laws, implying that atheism among young adults was common, though invariably transitioning to adherence to the local faith as they grew older and wiser[1], he replied with, "Oh, yeah, I forgot." [1] Of course, there's multiple ways to interpret Plato's argument, including 1) older, wiser people came to see the truth of the existence of the gods and 2) older, wiser people came to see the usefulness of shared belief in the gods, regardless of the actual existence of the gods.

cachvico 6y ago

This Reddit post is much more informative: https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_holes_on_a_dice_which_represent_the/ https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_h...

shawndumas 6y ago
https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_holes_on_a_dice_which_represent_the/ https://www.reddit.com/r/askscience/comments/4t4o3a/do_the_h...

ARandomerDude 6y ago

> Dice are very rare between 400 and 1100, corresponding to the Dark Ages. How dark these ages weren't. I'm always a bit sad to see such an obviously polemical term used to describe the period.

dfee 6y ago
Curious if you’d share more? Is there a faction of historians who don’t share this viewpoint? I’ve always been curious as I studied the Classics (Greece and Rome) and then European History (which in American high schools is 1400AD+). I have no insight into that intermediate period.
- scambier 6y ago
  From https://en.wikipedia.org/wiki/Dark_Ages_(historiography) https://en.wikipedia.org/wiki/Dark_Ages_(historiography) Relevant excerpts: > The term employs traditional light-versus-darkness imagery to contrast the era's "darkness" (lack of records) with earlier and later periods of "light" (abundance of records) > As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
- eesmith 6y ago
  https://en.wikipedia.org/wiki/Dark_Ages_(historiography) https://en.wikipedia.org/wiki/Dark_Ages_(historiography) > As the accomplishments of the era came to be better understood in the 19th and 20th centuries, scholars began restricting the "Dark Ages" appellation to the Early Middle Ages (c. 5th–10th century),[6][7][8] and now scholars also reject its usage in this period.[9] The majority of modern scholars avoid the term altogether due to its negative connotations, finding it misleading and inaccurate.
- bedobi 6y ago
  I'm also interested in this. Apparently recently there's an aversion to using terms like "dark ages", because they imply the period between antiquity and the renaissance was poorly recorded or objectively worse, and historians shouldn't make value judgements, they should just accurately account for what happened in any given period. I do get that, and I'm no expert, but... It sure seems to me like things were a whole lot objectively worse during the dark ages. Literacy, trade and all kinds of other objectively good things were replaced by more or less complete chaos, constant fighting between countless warlords, plagues... Like yes the large empires of antiquity did their own share of fighting and other bad things but regular people within any given empire seem to have had better lives than more or less anyone during the dark ages. Would love to be corrected because I love learning about history!

simik 6y ago

What's "unbalanced" about the 1-2, 3-4, 5-6 arrangement of numbers? And how is "primes" superior?

mcv 6y ago
That arrangement is primes. The other arrangement is sevens: 1 and 6 opposite each other, 2 and 5, and 3 and 4. Both of them can be unfair. Assuming rolling high is better, when 1 and 2 are opposite each other, those faces could be slightly smaller and therefore have a smaller chance of landing on them. This is especially easy with hand-made dice, which are bound to be somewhat irregular. With "sevens", 1, 2, and 3 meet in a single point. If that point is somehow heavier than the opposite point, you're more likely to roll 4, 5 or 6. I think I'd actually consider the "primes" arrangement to be superior to the modern one. No idea why that switch was ever made.

lihaciudaniel 6y ago

The history of dice is older than that. I would say around three times as long, since earliest dice were found in pyramids

bmm6o 6y ago
It's not clear in TFA but the paper it's based on focuses on the history of dice in the Netherlands and doesn't claim that dice didn't exist elsewhere earlier.

jhallenworld 6y ago

I've been trying other non-roman dice: Indian four-sided dice: https://averweij.web.cern.ch/averweij/india.htm https://averweij.web.cern.ch/averweij/india.htm Two-sided dice (cowry shells) for Indian Pachisi- they are terrible! https://joyofplaying.wordpress.com/play-by-rules/164-2/ https://joyofplaying.wordpress.com/play-by-rules/164-2/ More binary dice for the Royal Game of Ur: https://www.youtube.com/watch?v=WZskjLq040I https://www.youtube.com/watch?v=WZskjLq040I

seesawtron 6y ago

I don't really understand if the difference in two configurations of numbers appearing on the dice is related to the dice being biased? Nevertheless, the role of geometry in probability became clear to me when I read about Fano Planes and their role in winning Transylvania lottery [0,1]. [0] https://en.wikipedia.org/wiki/Transylvania_lottery https://en.wikipedia.org/wiki/Transylvania_lottery [1] https://en.wikipedia.org/wiki/Fano_plane https://en.wikipedia.org/wiki/Fano_plane

kgwgk 6y ago

A few blog posts on the subject of dice fairness: https://www.lesswrong.com/posts/zd89utY4afA59p58k/wolf-s-dice https://www.lesswrong.com/posts/zd89utY4afA59p58k/wolf-s-dic... https://books.google.ch/books?id=pGRsCQAAQBAJ&pg=PA258&lpg=PA258&dq=wolf+dice&source=bl&ots=9lgmeQE-tk&sig=ACfU3U1yNXs81m9hz8W4-HKXJ1KWTt2UlA&hl=en&sa=X&ved=2ahUKEwjNu6v5n_rpAhXGxMQBHQU7BxEQ6AEwC3oECAYQAQ#v=onepage https://books.google.ch/books?id=pGRsCQAAQBAJ&pg=PA258&lpg=P...