Dice are extremely sensitive to minor imperfections in weight on a given side. The side with six indentations would weigh less than the side with one indentation if measures weren’t taken to compensate.
Today it’s easy. Six indentations are made on each side but then colored over to make the holes invisible. In the very old days, dice were imperfectly cut from a natural substance like bone so slight variances were lost in the larger imperfections.
At some point in the middle dice got very good and were usually made from ivory. How did makers deal with the weight differentials to get true dice?
You might need to clarify what “middle” means timewise and how “true” the dice need to be for the purpose.
Until computers and large casinos I’m guessing people really couldn’t tell the difference between a good vs ok set of dice and didn’t really care. And if the dice get swapped regularly, the outcomes will always vary because of variable imperfections. It shouldn’t be that hard for a craftsman (jeweler or watchmaker) to craft a fairly true set from any reasonable material provided there is consistent density(stone, metal).
Googling “ivory consistency snooker” brings up an article on billiard balls which also needed to be true, but had to deal with a nerve hole in the tusk which was plugged and also with moisture absorption by the ivory. But it seems the issues were dealt with to the level of precision needed to play the game well versus other material options.
Presumably, if a large hole on the “1” side removed as much material as the 6 smaller holes on the “6” side, the balance would be maintained.
<off-topic>I once read a story about a crooked casino where the pigment in the holes on the “6” side was iron, so that the casino could use an electromagnet under the table to increase the odds of the dice coming up 1’s.
Is this feasible? Would it have a big enough effect to matter?
I have a very old pair of ivory dice, and you can easily see, with the naked eye, how they aren’t “square.” The sides are (slightly) rectangular. They were hand-carved, and none too skillfully.
If everyone is playing with the same dice, they won’t favor any one player over any other, although they might be unfairly beneficial or detrimental to the guy trying to make his point.
Another point is that any die is fair, the first several times you use it. Sure, it’ll probably have some bias, and once you roll it enough, you’ll figure out what that bias is, but until you do, it’s as good as random.
Now put your dice in with a whole bunch of other dice, all superficially identical, but each with its own bias. Whenever you need a die, grab one at random. Now they’ll stay fair indefinitely.
Well, no, not “extremely.” The lack of randomness introduced by removing material for the divots is pretty minor, and would only really be noticeable at an “industrial” scale - such as modern casinos, where dice are rolled millions of times.
That would have to be seven holes, not six - the five and the three have a divot in the middle of the face. Also, nobody makes dice like that.
Modern casino dice - which are pretty much the only dice in the world where anyone makes any real effort to keep them perfectly random* - certainly aren’t made like that. Rather, the divots are dug out, then filled with a different colored material that has the same density as the removed plastic. They’re also transparent, so you can see that they aren’t weighted - which, providentially, also means you can see that there aren’t any “painted over” divots in them.
They didn’t. The main concern in getting “true” handmade dice was in getting a proper cube. Any loss of randomness caused by removing material for the divots is small beer compared to the loss of randomness caused by imperfections in the basic shape of the die, or variances in density of the material the die is made out of. It wasn’t until modern machining (and modern statistical analysis) that the variance caused by the divots was even recognized as a problem.
*Well, casinos and Lou Zocchi, and his dice aren’t anywhere near Vegas standards.
If a divot is filled with material that has the same density then the weight doesn’t change. So why do it? I know that’s the wording used when talking about dice, but I’d like a better explanation.
The minimalness of the change was always a possible explanation but I haven’t been able to find any confirmation with actual numbers.
Players don’t have dice, operators do, and they don’t want fair dice to be used. No one running a dice game would allow a player to supply their own dice. The operators will notice if the dice are unfair to their disadvantage and not use them, or change the game.
As far as using some iron pigment in the pips along with a magnet to ‘load’ them, it’s not plausible. I recall that there were know cases of magnets used in roulette wheels which makes a lot more sense for something using a sizable steel ball.
I have handled novelty loaded dice, the imbalance is obvious, and even then they don’t always land in the loaded position. Any loading based on weight that isn’t obvious can still pay off long term for the operator though.
… so that you can see what number you rolled? Here, look at these casino dice again. See how the white pips have depth? They’re not painted on: paint on the surface of the die would unbalance it. Minimally, but enough that it would make a difference in a large enough number of rolls. Likewise, leaving a divot would unbalance it, as you described in your OP. A perfectly balanced die has identical, machine-tolerance dimensions on all six sides, with the pips made out of identical density-plastic and sunk into the surface, maintaining a uniform density throughout the cube while keeping each individual side perfectly flat and true.
These are all techniques that are only really possible with modern machine tooling. Handmade dice would always be imbalanced, and very few people making dice in hte pre-modern era were in a position to do the sort of broad statistical analysis necessary to pick out the non-random variances caused by carving pips into the dice.
Also:
Where does that cite say anything about iron in the paint? The iron slug would be inserted into the body of the die itself, off center so that face would be the most likely one to end up face-down.
Which, incidentally, is why casino dice are always transparent.
When adding pips, the pips are created by replacing the plastic with a different color plastic. There is no removal of total material from any side. Sides with fewer pips do not have any material removed or replaced, except where the pips are.
There were a huge number of dice thrown a huge number of times by a huge number of people throughout history. Did nobody test dice by throwing them a million times and recording outcomes? That sounds exactly like something the Victorians would have loved.
It doesn’t. But I was responding to t-bonham@scc.net’s post, which was about pigment.
Yeah, after I posted, I realized where you were misreading me. Sorry for the ambiguity.
Well, sure, probably. But up until the industrial age, imperfections caused by the dice being hand-carved would overwhelm any statistical bias caused by material removed for the pips. Plus, who would really care about the results? Gambling done between private individuals - soldiers on guard duty, say - would likely be done with dice carved by one of the players. Gambling houses were quasi-legal at best, and weren’t subject to a whole lot of government oversight, so there’d be little impetus for fair dice there. And even those people selling dice to private citizens - fancy ivory ice, for example. Well, what’s the better sales pitch there? “These dice are perfectly random,” or “These dice are lucky?”
It’s only when you get the combination of legalized gambling and modern government oversight that people start getting really interested in making dice that are perfectly fair.
Incidentally, I was incorrect above in describing casino dice: the pips aren’t separate pieces of plastic. Rather, they’re thick paint with the same density as the plastic that makes up the rest of the die.
BTW, the easiest way to test the balance of a die is by dropping it into a glass of water a few times and see if it lands with the same number most of the time. No need to do millions of rolls.
Not as precise, of course, but good enough in the old days with handmade dice or when loaded dice are suspected.
The water test will pick out some sources of bias (mostly those due to uneven weight distribution), but not all of them (such as those due to irregularity of shape).
