Statistics – Does the shape of a cube affect the probability that a number will be rolled?

Such a habit d8 statistically corresponds to a d4

Assuming the d8 is fair, the odds of getting any result are 1/8. Since each number (1-4) occurs twice in the custom version d8, the probability of throwing each of the numbers is 1/8 + 1/8 = 1/4, which is the same as in a normal d4.

You can also see this anydice program that demonstrates this:

Output 1d4 named "normal d4"
Issue {1,1,2,2,3,3,4,4} named "custom d8"