The sixth level Circle of the Stars feature, Cosmic Omen, allows the druid to, for the remainder of a day, use their reaction to either help their allies or hinder their foes:
Whenever you finish a long rest, you can consult your Star Map for omens. When you do so, roll a die. Until you finish your next long rest, you gain access to a special reaction based on whether you rolled an even or an odd number on the die:
Weal (even). Whenever a creature you can see within 30 feet of you is about to make an attack roll, a saving throw, or an ability check, you can use your reaction to roll a d6 and add the number rolled to the total.
Woe (odd). Whenever a creature you can see within 30 feet of you is about to make an attack roll, a saving throw, or an ability check, you can use your reaction to roll a d6 and subtract the number rolled from the total.
―Cosmic Omen, Tasha's Cauldron of Everything, pg. 38
Note, however, that in the description of this feature, the player is simply instructed to roll "a die", without qualifying what kind of die it has to be. This poses no issue for the "standard issue" dice used in 5e D&D, since the d4, d6, d8, d10, d12, and d20 all have an even number of sides, and therefore an [assumed, with fair dice] equal probability of rolling an even or odd number.
However, there are dice that have odd numbers of sides. In this situation, a player could pick up a three-sided die, for example, and they'd have a 2/3rds chance of rolling an odd number, biasing their feature towards hindering enemies.
Is there any rule in 5th Edition D&D that forbids a player from choosing to do this?
Best Answer
The fact that it says to roll a die, but doesn't say which one, indicates that it's not supposed to matter.
In general, any mechanic that tells you to roll a die tells you what kind. In this case you're not told which die to roll, or which ones you can choose from, or even that you are supposed to choose one. This strongly indicates that there's no gameplay choice being made, and the mechanic expects all dice to be equivalent, which all the standard dice are.
If you're allowed to just invent arbitrary kinds of dice, then why pick a d3? Why not roll a "d1" and get an odd result every time?