When aiming to roll for a 50/50, does the die size matter?

I noticed how D&D 5e’s Hexblade Warlock subclass feature Armor of Hexes imposes a chance to miss regardless of the attacker’s roll. That chance is based on a d6: if it’s a 4 or higher it misses, and anything else it hits if the attack should have hit. To my understanding, this is simply a 50/50 roll on the d6 (success on 4, 5, 6, failure on 1, 2 and 3).

Out of curiousity, does it matter if the dice is a d4, d8, or even d100, as long as it’s an even-sided die and that it’s still 50/50? (On a d4 it would be a success on a 3 and 4, on a d10 it’s 6 and up, and so on.)