Each of these six-sided dice, when first rolled, is absorbed into the user. This grants them a power far more unreliable than your run-of-the-mill wish-granting object: to roll for their actions! They can choose whether to act normally for their abilities, or whether to push the phenomenal cosmic power of the Dodging Dice to try and probably fail horribly.
The faces of the die:
1 - Epic failure, backfires horribly and causes more problems
2 - Failure to act, no consequences but delay or a mundane fumble (but this might be bad during time-sensitive defense or if there are very fumble-touchable objects nearby)
3 - Partial success, progress toward the goal but requires more work to be deemed a full success (anything from effective-0 to 'take one more mundane action to confirm' could happen, averaging out towards 'you get a sense of the overall scope of this task and take the first major preparation steps')
4 - Success, action is carried out and works moderately or as intended
5 - Epic success, succeeds very positively or better than intended
6 - Overshoot, disproportionately large effect causes other problems.
Penalty conditions usually nudge the dice down (e.g. -1), raw power boosters nudge the dice up (e.g. +1). Skills and reasonably controlled relevant equipment nudge the dice toward 5 (e.g. reduce odds of normal overshoots or crit failures while using the dice on that topic).
A response roll can be done in an attempt to avoid danger. A die can be rolled for several different things in rapid succession or near-simultaneously, though this may become incredibly chaotic if one fails or overshoots. Performing too many rolls effectively-simultaneously (e.g. within one combat without time travel from an unrelated point) may experience significant penalties (e.g. -1 per extra action in the same volley). One die roll can cover something time-consuming or organizationally complicated (such as engineering a sci-fi magic device or starting a business), in which case time is subjectively experienced as going very quickly for a few days (or a necessary objective time) and life-related activities outside the action go okay. Survival is assumed unless the action backfires or is explicitly sacrificial. Using a die to make a massive world-changing wish can be quite disruptive if failed or overshooting. Dice users are explicitly advised to make a device that does something they want done right, so if they fail or overshoot they are more likely to have something they can prevent being used instead of misfiring reality.
Die rollers assisting each other use the highest of contributing actions, but individual rolls affect the individual roller most. Dice rollers interfering with each other can 'botch', where the higher roll inverts the other roll's effect. Unconscious die rollers typically don't activate their Dodging Dice except to instinctively survive something lethal, and don't reduce their roll to below 2 (e.g. they cannot hard-fail the act of surviving without trying, at least not enough to injure themselves further). Dead die rollers are incapacitated, and may take significant time to form a ghost before they can try wishing themselves back to life if they care to resume life.
In addition to the Dodging Dice, other less-omnipotently-scaled action dice exist in the world or can be created by status effects. The Dodging Dice are the 'default ruleset', where other dice powers might have different random tables and use conditions (e.g. more like a slot machine that can be activated every few seconds, or following RPG stat rules, or transforming body parts as per other entries).
Assume a die roller becomes aware of the basic rules of their ability once their die is first obtained, and is informed of anything edge-case on encountering it. They are also aware of what they roll, and of any conditions of sufficient intensity to cause a roll/penalty/skill effect. It is possible for them to forget this afterward or not be in a state of mind to use it properly, but they generally know what they're doing to start off. In the event of not knowing they have dice, unaware usage tends to occur when narratively dramatic or overly invested in doing something that's not realistic for their abilities (e.g. dramatically transforming someone while having zero logical ability to do so, fixing all the collateral damage from someone else's die rolls). Certain conditions may force it to happen more often than that, and amnesia overshooting or undershooting very often may cause those conditions.