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> it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip frequencies We can actually tell from their dice that the

> it's not implausible to me that they soon also had some rudimentary understanding of e.g. coin flip frequencies We can actually tell from their dice that they don’t. I believe in the book Against the Gods the author described ancient dice being—mostly—uneven. (One exception, I believe, was ancient Egypt.) The thinking was a weird-looking dice looks the most intuitively random. It wasn’t until later, when the average gambler started statistically reasoning, that standardized dice became common. These dice are highly non-standard. In their own way, their similarity to other cultures of antiquities’ senses of randomness is kind of beautiful.

kqr 7mo ago
It's not entirely crazy. I believe Thorp described this about roulette wheels. If they had no imperfection at all, it would be computationally laborious but not unthinkable to compute the result from the initial positions and velocities. In order to be unpredictable, roulette wheels need to have imperfections. Those very same imperfections, of course, lead to some statistical regularities. Edit: It wasn't quite that, but very nearly: start reading paragraph 5 in http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_l.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi... In the next article in the series, he explains that in practice, roulette wheels are often tilted and that can be used to gain a further advantage: http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_ll.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi...
- blitzar 7mo ago
  If you are the house you probably want to go around every so often and give the wheel a little bump to reset the entropy seed for the day.
- xyzzy_plugh 7mo ago
  Anecdotally I was on a streak and the dealer was actively concentrating and focusing to get my number again. She managed to get it 4 out of 5 spins. Now she would obviously never admit to this, but I'm positive that she was able to, on this specific wheel, land on the number she wanted. I think we would've kept going but she rotated off and I cashed out. Edit: Thorp and Shannon! What a duo. Great articles, thanks for sharing.
  - bluGill 7mo ago
    The house wants you to think that anyway. If it is possible or not.. The house wants people to win money and tell their friends, and every "winning" strategy is good for them - so long as in the end the house makes money.
    - xyzzy_plugh 7mo ago
      I mean, yes, but also no. The house wants you to lose money, but win just enough to think you have a chance. There's a reason those zeroes are on the board. There's no deep strategy in Roulette, really. I play for fun, and the money I put on the table is already spent. The anecdote was: I wouldn't have seriously believed that you could reliably manipulate the spin outcome, and as an observer, that's true. I didn't believe the dealer could either, but after seeing this dealer pull it off I definitely see the potential for manipulation. It was almost like she was showing off that she could. And besides, she earned a hefty tip.
      - bluGill 7mo ago
        > The house wants you to lose money, but win just enough to think you have a chance The house wants to make money overall. They know that individuals who make money tend to tell more friends than those who lose money - free advertising - so they want some people to make money. The total needs to be the average person loses money, but they need some individuals to make money. On the small stakes systems they may even like it when they lose money like that - the dealer makes a big tip, and it encourages people (or their friends) to move to a higher stakes bet where they will lose more. They have to be careful about the law (which probably doesn't allow that manipulation if possible, even if it isn't in their favor), but again individuals with a story to tell are worth a lot more than than the money they lose on that story.
        xyzzy_plugh 7mo ago
        I'm not sure what point you're trying to make. If you're trying to suggest that the casinos train or encourage croupiers to cheat so that patrons get winning streaks, then what you're describing is a fantasy. Casinos are plenty successful without those sort of shenanigans. If anything it's the opposite: pit bosses actively police croupiers who are spinning too consistently, and croupiers are encouraged to vary their spin throughout their session to avoid bias.
JuniperMesos 7mo ago
Maybe this is because dice were originally made from the bones of animals like sheep, which are inherently irregular.
- Pay08 7mo ago
  I was going to ask how we know if the dice are intentionally uneven, as opposed to it being a result of technological, cost, or time constraints.
calf 7mo ago
I don't see the point of being confident about this in either direction. I will not assert for certain but (or, IF) they had dice for 12000 years (12,000!) and to be so certain they didn't know anything at all on an intuitive level is a bit strong a position to take, I don't see that as a safe null/default hypothesis. I had also said "..., THEN it's not implausible" so I don't love how you quoted a strawman in the first place.
culi 7mo ago
The original work suggests the opposite of your conclusion > In a landmark article, foundational to the field of behavioral economics, Tversky and Kahneman (Reference Tversky and Kahneman1974:1130) argued that humans do not infer the statistical regularities embedded in everyday experience because they “are not coded appropriately”—meaning that the quantitative features inherent in these experiences are not isolated, noted, and organized in ways that reveal probabilistic patterns that are usually obscured by the noise of other incoming experience. Intriguingly, Native American dice games appear to perform such a “coding” function. They produce a simplified stream of random events that are carefully observed and recorded at multiple levels: in the scoring of individual dice throws, in the keeping of cumulative scores in single matches, and in tallying wins and losses in multiple matches over time as recorded by the giving or receiving of goods. Therefore, by observing and recording the patterns appearing in these outcomes, ancient Native American dice players repeatedly presented themselves with the very type of “coded” experiences that Tversky and Kahneman (Reference Tversky and Kahneman1974) argued would allow humans to observe and infer the presence of underlying probabilistic regularities. https://www.cambridge.org/core/journals/american-antiquity/article/-/E38C7B1F4CE7F417D8EFAC5AFEEF20A2 https://www.cambridge.org/core/journals/american-antiquity/a... Also the fact that these games are so widespread (239 sets found across 130 different tribes from 30 different linguistic lots) makes me feel like it's highly implausible that abstractions of the rules of the games did not arise

kqr 7mo ago

It's not entirely crazy. I believe Thorp described this about roulette wheels. If they had no imperfection at all, it would be computationally laborious but not unthinkable to compute the result from the initial positions and velocities. In order to be unpredictable, roulette wheels need to have imperfections. Those very same imperfections, of course, lead to some statistical regularities. Edit: It wasn't quite that, but very nearly: start reading paragraph 5 in http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_l.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi... In the next article in the series, he explains that in practice, roulette wheels are often tilted and that can be used to gain a further advantage: http://www.edwardothorp.com/wp-content/uploads/2016/11/PhysicalPredictionOfRoulette_ll.pdf http://www.edwardothorp.com/wp-content/uploads/2016/11/Physi...

blitzar 7mo ago
If you are the house you probably want to go around every so often and give the wheel a little bump to reset the entropy seed for the day.
xyzzy_plugh 7mo ago
Anecdotally I was on a streak and the dealer was actively concentrating and focusing to get my number again. She managed to get it 4 out of 5 spins. Now she would obviously never admit to this, but I'm positive that she was able to, on this specific wheel, land on the number she wanted. I think we would've kept going but she rotated off and I cashed out. Edit: Thorp and Shannon! What a duo. Great articles, thanks for sharing.
- bluGill 7mo ago
  The house wants you to think that anyway. If it is possible or not.. The house wants people to win money and tell their friends, and every "winning" strategy is good for them - so long as in the end the house makes money.
  - xyzzy_plugh 7mo ago
    I mean, yes, but also no. The house wants you to lose money, but win just enough to think you have a chance. There's a reason those zeroes are on the board. There's no deep strategy in Roulette, really. I play for fun, and the money I put on the table is already spent. The anecdote was: I wouldn't have seriously believed that you could reliably manipulate the spin outcome, and as an observer, that's true. I didn't believe the dealer could either, but after seeing this dealer pull it off I definitely see the potential for manipulation. It was almost like she was showing off that she could. And besides, she earned a hefty tip.
    - bluGill 7mo ago
      > The house wants you to lose money, but win just enough to think you have a chance The house wants to make money overall. They know that individuals who make money tend to tell more friends than those who lose money - free advertising - so they want some people to make money. The total needs to be the average person loses money, but they need some individuals to make money. On the small stakes systems they may even like it when they lose money like that - the dealer makes a big tip, and it encourages people (or their friends) to move to a higher stakes bet where they will lose more. They have to be careful about the law (which probably doesn't allow that manipulation if possible, even if it isn't in their favor), but again individuals with a story to tell are worth a lot more than than the money they lose on that story.
      - xyzzy_plugh 7mo ago
        I'm not sure what point you're trying to make. If you're trying to suggest that the casinos train or encourage croupiers to cheat so that patrons get winning streaks, then what you're describing is a fantasy. Casinos are plenty successful without those sort of shenanigans. If anything it's the opposite: pit bosses actively police croupiers who are spinning too consistently, and croupiers are encouraged to vary their spin throughout their session to avoid bias.

JuniperMesos 7mo ago

Maybe this is because dice were originally made from the bones of animals like sheep, which are inherently irregular.

Pay08 7mo ago
I was going to ask how we know if the dice are intentionally uneven, as opposed to it being a result of technological, cost, or time constraints.

calf 7mo ago

I don't see the point of being confident about this in either direction. I will not assert for certain but (or, IF) they had dice for 12000 years (12,000!) and to be so certain they didn't know anything at all on an intuitive level is a bit strong a position to take, I don't see that as a safe null/default hypothesis. I had also said "..., THEN it's not implausible" so I don't love how you quoted a strawman in the first place.

culi 7mo ago

The original work suggests the opposite of your conclusion > In a landmark article, foundational to the field of behavioral economics, Tversky and Kahneman (Reference Tversky and Kahneman1974:1130) argued that humans do not infer the statistical regularities embedded in everyday experience because they “are not coded appropriately”—meaning that the quantitative features inherent in these experiences are not isolated, noted, and organized in ways that reveal probabilistic patterns that are usually obscured by the noise of other incoming experience. Intriguingly, Native American dice games appear to perform such a “coding” function. They produce a simplified stream of random events that are carefully observed and recorded at multiple levels: in the scoring of individual dice throws, in the keeping of cumulative scores in single matches, and in tallying wins and losses in multiple matches over time as recorded by the giving or receiving of goods. Therefore, by observing and recording the patterns appearing in these outcomes, ancient Native American dice players repeatedly presented themselves with the very type of “coded” experiences that Tversky and Kahneman (Reference Tversky and Kahneman1974) argued would allow humans to observe and infer the presence of underlying probabilistic regularities. https://www.cambridge.org/core/journals/american-antiquity/article/-/E38C7B1F4CE7F417D8EFAC5AFEEF20A2 https://www.cambridge.org/core/journals/american-antiquity/a... Also the fact that these games are so widespread (239 sets found across 130 different tribes from 30 different linguistic lots) makes me feel like it's highly implausible that abstractions of the rules of the games did not arise