4 ms·

Perhaps the Romans misunderstood probability, and thought that adding imperfections to dice would make them more random? Also the "primes" configuration of fac

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.

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.