Proficiency Dice

Source: Dungeon Master’s Guide p. 263

This optional rule replaces a character’s proficiency bonus with a proficiency die, adding more randomness to the game and making proficiency a less reliable indicator of mastery. Instead of adding a proficiency bonus to an ability check, an attack roll, or saving throw, the character’s player rolls a die. The Proficiency Die table shows which die or dice to roll, as determined by the character’s level.

Whenever a feature, such as the rogue’s Expertise, lets a character double his or her proficiency bonus, the player rolls the character’s proficiency die twice instead of once.

This option is intended for player characters and nonplayer characters who have levels, as opposed to monsters who don’t.