I know that the dice they use in Vegas are supposed to be exactly the balance so that no one size is favored over the others.
But clearly, the side that has 6 dots, (painted on, or embedded, or carved out) has less material (if carved out) or more material (if painted on, or embedded with an alternative color, which would need some sort of cement to hold the embedded color in place.
Is it possible that for the player, this is completely unperceptable (1 to 6 odds). For the casino, which deal with dice rolls in the millions per day, could it be closer to 1.0000000003 to 6 (or some other almost unperceptable amount) that can translate into another 50-100K per week? (or some other amount)
If you’re going to carry this argument to such extremes, you may as well argue that all dice are imbalanced, because the dice-making process could be inducing a minor bias (of, say, several molecules thick) towards one side, thus giving it more weight.
Which means that all the dice in Vegas are (infinitesmally) crooked, and there’s no point in playing Craps. Which means there’s no point in going to Vegas, so the local economy collapses, and the mob sends Fourteen-Week Freddie to pay you a visit, bcullman.
Me, I’ll keep playing Craps. Especially since it’s the closest thing Vegas has to even odds.
I believe (large) casinos in Las Vegas go to great lengths to engineer their games to rigorous standards. They have a vested interest in removing all possibility of any sort of unfairness from their games.
Their profits are high enough by virtue of the games alone that they do not need to eek out any margins. If there are any margins to be eeked out, it is in the realm of keeping gamblers happy so they stay vs. taking their money.
My guess is that the major casinos have deliberately engineered their games to be fair to standards beyond what is required by fair gaming comissions.
You can be certain that the engineer who was hired to design casino dice did not overlook the effect of the nibs on the die. I don’t personally know if they have a significant effect, but the design was for a die that post production was statistically fair to a certain number of significant digits. The design was rigorously and successfully tested. So to a certain number of significant digits all of the dice are fair. This number of significant digits is undoubtedly far more stringent than the smallest margin in craps, and thus, essentially has no effect on the game.
Likely the weights of the sides vary in production in some reasonably bell-shaped curve, so it is just as likely that the 1 would be infinitesimally heavier as the 6.
BTW, if you regard 1.0000000003 as 1 for every purpose, for the remainder of your life, you won’t be any worse for it. In fact, you’d probably do just fine with 1.003 = 1.
To see the effect in practice, you’d have to take a very large number of trials. Let’s say there are 100 million trials in your set. With that, you could measure to a resolution of about 1.00005.
But dice aren’t used for that long. I believe they only roll them a certain number of times before the dice are retired and made into keychains to be sold in the gift shops.
The dice ARE perfectly balanced, to within the precision of the casino’s measuring equipment. In fact, the pit boss will come by periodically and check the balance the dice right at the table - he has a little gizmo that you insert the die into. Then you spin the die, and if it’s not in balance it will visibly wobble.
This, of course, is done to make sure a crooked player hasn’t palmed the casino dice and swapped them with ‘loads’.
Some loaded dice trivia: The easist way to load the dice is to drill a hole through one of the dots, fill it with lead, then paint back over it. That’s why casino dice are transparent - a slug inside the dice will show just by holding it up to the light.
So the real professional dice cheats use extremely dense metal, then they burr out every single dimple slightly deeper, fill them back up with the heavy element, and then paint over the hole. The loaded wafers are thin enough that you can’t really see them by looking through the die.
The problem with those professional ‘loads’ is that they can’t weight the dice as heavily, so they can’t shift the odds in their favor as much. That means the cheats have to risk more money or play longer to make the same profit. These types of loaded dice don’t have that much effect - a die that always comes up 7 is pretty much a fiction. More likely, the weighting will just shift the odds of a certain outcome by a few percentage points - just enough to overcome the house vig plus make a profit. On any given roll or even a handful of rows, you wouldn’t perceive the bias on the dice. Maybe not even in hundreds of rolls. All it takes is one less craps out of every 50 rolls and you’ve got the edge. That’s probably not perceptible. So the house’s best defense is to just make sure the dice are clean, and to maintain good databases of cheats so they can spot them quickly when they enter the place.
