6 ms·

The Shape of Ancient Dice Suggests Shifting Beliefs in Fate and Chance

77 points by curtis 9y ago

OscarCunningham 9y ago
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.
- gt_ 9y ago
  Both great points. The thesis of the article (and title!) seems a little premature but interesting stuff.
- Retric 9y ago
  As long as all players use the same dice, bias may not be that important.
  - analog31 9y ago
    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 9y ago
      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 9y ago
        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.
    - notahacker 9y ago
      In many games greater familiarity with the biases of the dice would be no more an advantage (sometimes considerably less) than greater familiarity with the game rules and strategy. It's not clear what games were played, or whether they were played repeatedly amongst groups or by strangers competing against a "house". The article does suggest the biases were visible enough for such games to not hinge upon a particular participant's false believe in the uniformity of the dice though, as well as hint most people's betting strategy probably wasn't sophisticated enough for them to care
    - Retric 9y ago
      This depends on the rules of the game. To use a classic example a coin flip that simply requires HT vs TH (TT or HH get new flips) is unbiased even with a biased coin. Assuming people had less trust in these dice you end up with different games.
- mkempe 9y ago
  In the 1560s Cardano's Liber de ludo aleae attempted to calculate probabilities of dice throws. His work was not published until 1663. There is no earlier known work on the calculus of probability.
swah 9y ago
> 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 9y ago
  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".
mkempe 9y ago
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/0471295639 https://www.amazon.com/Against-Gods-Remarkable-Story-Risk/dp... [2] https://en.wikipedia.org/wiki/Peter_L._Bernstein https://en.wikipedia.org/wiki/Peter_L._Bernstein
rbobby 9y ago
> 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 9y ago
  One would notice on the first roll that the 3 and 4 weren't opposite. Perhaps it's just for a particular game.
coldtea 9y ago
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.
- tinymollusk 9y ago
  Given how bad the modern human is at understanding probability, I see no reason to think the ancients were better.
- itsjustme2 9y ago
  I agree. And I don't think you need to understand probability to see that a flattened cube will fall on the top and bottom more often than the edges. Another possibility in addition to what you mentioned is that the games the dice were used in took into account that some sides were more probable than others and people trial-and-errored until more-or-less appropriate payoffs/penalties emerged.
  - SubiculumCode 9y ago
    These were the points I was about to make. Also, in modern dice when we want nonequal chance of outcomes we use two dice and sum. This wouldn't be needed if a die had unequal probabilities per face.
- ziftface 9y ago
  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 9y ago
    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.
rdiddly 9y ago
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.
emptybits 9y ago
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-and-why-you-are-doing-it-wrong/ https://aleadeum.com/2013/07/12/the-i-ching-random-numbers-a...
pradn 9y ago
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.

77 points by curtis 9y ago

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.

gt_ 9y ago
Both great points. The thesis of the article (and title!) seems a little premature but interesting stuff.
Retric 9y ago
As long as all players use the same dice, bias may not be that important.
- analog31 9y ago
  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 9y ago
    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 9y ago
      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.
  - notahacker 9y ago
    In many games greater familiarity with the biases of the dice would be no more an advantage (sometimes considerably less) than greater familiarity with the game rules and strategy. It's not clear what games were played, or whether they were played repeatedly amongst groups or by strangers competing against a "house". The article does suggest the biases were visible enough for such games to not hinge upon a particular participant's false believe in the uniformity of the dice though, as well as hint most people's betting strategy probably wasn't sophisticated enough for them to care
  - Retric 9y ago
    This depends on the rules of the game. To use a classic example a coin flip that simply requires HT vs TH (TT or HH get new flips) is unbiased even with a biased coin. Assuming people had less trust in these dice you end up with different games.
mkempe 9y ago
In the 1560s Cardano's Liber de ludo aleae attempted to calculate probabilities of dice throws. His work was not published until 1663. There is no earlier known work on the calculus of probability.

swah 9y ago

> 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 9y ago
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".

mkempe 9y ago

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/0471295639 https://www.amazon.com/Against-Gods-Remarkable-Story-Risk/dp... [2] https://en.wikipedia.org/wiki/Peter_L._Bernstein https://en.wikipedia.org/wiki/Peter_L._Bernstein

rbobby 9y ago

> 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 9y ago
One would notice on the first roll that the 3 and 4 weren't opposite. Perhaps it's just for a particular game.

coldtea 9y ago

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.

tinymollusk 9y ago
Given how bad the modern human is at understanding probability, I see no reason to think the ancients were better.
itsjustme2 9y ago
I agree. And I don't think you need to understand probability to see that a flattened cube will fall on the top and bottom more often than the edges. Another possibility in addition to what you mentioned is that the games the dice were used in took into account that some sides were more probable than others and people trial-and-errored until more-or-less appropriate payoffs/penalties emerged.
- SubiculumCode 9y ago
  These were the points I was about to make. Also, in modern dice when we want nonequal chance of outcomes we use two dice and sum. This wouldn't be needed if a die had unequal probabilities per face.
ziftface 9y ago
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 9y ago
  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.

rdiddly 9y ago

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.

emptybits 9y ago

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

pradn 9y ago

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.