Hero Points

Hero points work well in epic fantasy and mythic campaigns in which the characters are meant to be more like superheroes than the average adventurer is.

With this option, a character starts with 5 hero point at 1st level. Each time the character gains a level, he or she loses any unspent hero points and gains a new total equal to 5 + half the character's level.

A player can spend a hero point whenever he or she makes an attack roll, an ability check, or a saving throw The player can spend the hero point after the roll is made but before any of its results are applied. Spending the hero point allows the player to roll a d6 and add it to the d20, possibly turning a failure into a success. A player can spend only 1 hero point per roll.

In addition, whenever a character fails a death saving throw, the player can spend one hero point to turn the failure into a success.

Source: DMG, page 264