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

https://www.theatlantic.com/science/archive/2018/02/dice-dice-baby/553742/?single_page=true

by curtis • 8 years ago

77 25 8 years 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_• 8 years ago

Both great points. The thesis of the article (and title!) seems a little premature but interesting stuff.

Retric2• 8 years ago

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

analog31• 8 years 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.

mkempe2• 8 years 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• 8 years 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...

coldtea3• 8 years 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".

mkempe2• 8 years 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...

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

rbobby• 8 years 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• 8 years ago

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

coldtea3• 8 years 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.

itsjustme2• 8 years 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• 8 years 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• 8 years 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?

coldtea3• 8 years 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.

rdiddly2• 8 years ago

"such beliefs didn't play a role in playing other games..."

Source?

tinymollusk• 8 years ago

Given how bad the modern human is at understanding probability, I see no reason to think the ancients were better.

rdiddly2• 8 years 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• 8 years 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

[2] https://aleadeum.com/2013/07/12/the-i-ching-random-numbers-a...

pradn• 8 years 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.

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

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