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
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
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.”
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.
**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)
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