Are the number on the dice placed on these sides for a reason?

Question

To further explain the title:

Is there a probabilistic reason as to why a 6-sided die has the opposing sides suming to 7?

My argument begun when a friend decided to use this die instead of this die.

I understand that having 20 sides, each is as likely to come up, but does the different pattern affect the subsequent rolls?

Thanks in advance!

Answer 1

If the dice are unbiased, there is no reason for choosing any particular arrangement. You could as well pull a card from a deck of six. No difference.

Answer 2

If dice were cuboids rather than cubes due to a manufacturing defect, then each face would no longer have equal probability, but by symmetry the expected value of each throw would still be $\dfrac{7}{2}$.

I have no idea whether this was a consideration.

Answer 3

In the 20-sided dice linked, there is actually a good reason not to use the die with numbers of equal size clustered closely together.

Just as in a roulette wheel, it is harder to cheat if a slight difference in movement totally changes the number, and in addition, it is much more suspenseful to watch if you can only tell at the very end which size/color the number has.

However, for an ordinary die, it is impossible to avoid neighbouring sides having neighbouring numbers, so it makes sense to go for a symmetric arrangement instead.