why do (most) dice have the same face placements? As in, why is the 6 usually opposite to the 1, likewise with the 3 and 4? Does this affect the “fairness” of a dice roll, making it a 1/6 chance every roll as opposed to a different value?

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why do (most) dice have the same face placements? As in, why is the 6 usually opposite to the 1, likewise with the 3 and 4? Does this affect the “fairness” of a dice roll, making it a 1/6 chance every roll as opposed to a different value?

In: 576

Tradition. And no, it in no way affects the outcome, no matter what you put on a face as long as the faces are identical in weight

Mostly it’s just tradition. It actually can affect the odds, if you aren’t careful about distributing the die’s mass evenly among all six sides, which is why casinos fill in their dice’s holes using a resin of the same density used to make the dice themselves. But for most gaming dice, the effect isn’t large enough for people to care about.

You’re asking about rolling dice versus counting dice. While it’s not very obvious with a six sided dice, a 20- sided die is usually put together the same way, so that opposing sides sum to the same number, and adjacent sides are farther apart. Some such die have numbers next to each other so it’s easy to turn the top face from 20 to 19 to 18, etc. With some practice, you could roll the counting die to give your preferred high or low result.

It’s a bit more than tradition.

If your dice is not perfectly equilibrated (e.g. one half is heavier than the other and these faces will show up less often), then opposite face adding up to always the same number (7, on six-faced dice) will ensure that the mean outcome will still be the same.

The pattern is so that the two sides opposite eachother will always add to 7.

Is there any real reason for this? Not really, it’s just how they have always been done.

If you’re rolling the dice properly, it doesn’t matter and it’s just tradition. But, it’s theoretically possible to hold and throw the dice in a particular way and have certain faces come up more often, or to have slight manufacturing defects that cause one half to come up a bit more often. It’s more of a thing with 20 sided or larger, more round, dice, but it’s basically impossible to hit one face in particular. So, if you have 20, 19, 18, 17 and so on all right next to each other, someone could roll it in such a way that that general half of the dice comes up more often. Scattering the numbers so the high and low numbers are evenly dispersed compensates for that possibility.

I.e. if you have a 6 sided dice, you could theoretically roll it like a wheel so it’s just rolling on 4 of the sides, and the other 2 will basically never be landed on. But you can’t control which of the 4 it lands on. If you put the numbers so the 2 impossible sides are 1 and 2, you can get an unfair advantage, but if they are 1 and 6, or 2 and 5, you’re eliminating both good and bad outcomes, not just bad ones, and you don’t really benefit from rolling it that way. It’s a pretty easily detectable method of cheating at dice, and pretty hard to execute, but it is possible, and placing the numbers the way they do helps to counter it.

Or there’s a bubble in the resin that makes one half of the dice more likely to come up. If all the high numbers are on that half, it could be considered loaded and cheating. If there’s high and low numbers on that half equally, there’s an increased chance of both the good and bad numbers, so it’s not as advantageous to the roller.

Each opposing face has 7 “pips” total – 6+1, 5+2, 4+3. This minimizes differences in mass per face pair such that each number statistically will appear approximately the same number of times. You’re looking for a even distribution of the 6 numbers over time.

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On 6 sided die, the opposing numbers add up to 7
You have 1-6, 2-5, and 3-4. This is just a convention, to make the dices uniform wherever you emcounter them; though it makes it easier to check if they’re not incorrectly labelled, having two sides of 5 or 6.
Plus, 7 is regarded as a lucky number

The sum of the opposing dice faces is always 7. So the center of mass of the die remains the same.

Here’s the ELI5 I haven’t seen yet: let’s assume the dice are fair and perfectly made. Now, imagine one with no numbers at all. Mentally label one face. When you roll, there will be exactly 1/6 of a chance it’ll land on that face. So in terms of strict probability, there’s no difference created by rearrangement. As others have pointed out, you can use sleight of hand to manipulate the outcome, but that’s not really about the arrangement, either, just about *knowing* the arrangement and physically influencing the result. You could not use sleight of hand with a pair of dice whose numerical arrangement is unknown to you. So, especially if the dice are properly crafted, and preferably do not have divots, there’s literally no difference where the numbers go unless you’re playing a game that hinges on what number is on the opposite side, like “when you roll a six that’s a perfect outcome but you suffer a penalty of one next round because that’s the number facing down” kind of thing. But that’s not statistics in action, that’s just the game rules making that important. No idea if there’s a game like that, but I’m sure you can picture the rough concept. To prove this at home, take a few dice, roll them a hundred and twenty times (this gives you a good amateur sample size) and see what happens. Then do an analysis for the spread at 20, 40, 60, 80, 100, and 120. You should see that as the rolls increased, the value for each face closer approaches 16.6…%. Mystery managed! Oh, and you’ll also see “streaks”, but as you increase the rolls, you’ll realise that those are evened out later by other “streaks” or “droughts.”

in ‘regular’ dice (regular referring to traditional, and those used by casinos) the opposite faces always add up to 7. such as 6+1, 3+4, 2+5

i’m not sure about it affecting the fairness but checking this arrangement of the faces is how casinos ensure the dice haven’t been switched to fakes

Others have explained why opposite sides add to 7. TL/DR: If the dice are “short” on one side, and/or somebody knows how to blanket roll, then you get a relatively fair outcome.

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**Weird side-note**: There are only two ways to lay out a D6 so that opposite sides add to 7. 6 is on top, 1 on the bottom. 5 is at the front, 2 is at the back, then you can put the 4 on either the right or the left, with the 3 on the opposite side.

As it turns out, the “west” chose to put the 3 on the right, while the “east” chose to put the 4 on the left. If you look at the 4/5/6 vertex, then those numbers will be clockwise (east) or counter-clockwise (west).

I’m not sure if “east” means only China here, or if it’s a larger territory that goes clockwise.

If you add up the opposite sides, it always equal 7
(6+1)
(2+5)
(3+4)
It is done to make the odds always the same. Every time your roll the dice, the odds are equal.

I also think the opposite sides always add up to 7 to make it harder for people to try cheat by switching dice (to one that has replicated numbers)