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What is inspiration?
Inspiration is a mechanic which can be used to help incentivise players to get into their character. It teaches players that sometimes role play is more fun than the ideal tactical decision.
Basically it works like this. You have ideals, flaws, bonds, and traits that are unique behaviors and quirks of your character. Sometimes, these personality quirks will cause/inspire the character to behave in a way that somebody without those quirks would not. When a player chooses to play their character’s quirks rather than the ideal tactical move they get inspired for following their ethos. This inspiration can then later be used to grant them advantage on an attack, saving throw, or ability check roll, or even inspire another character, however once used, it can not be used again until the DM grants you inspiration again. You also can not “collect” inspiration, you either have it or you don’t.
Use this mechanic to encourage memorable moments at your table.
Source: Page 35 of the free D&D 5e Basic Ruleset