Stormreach City of...
5th edition rules
The Eberron campaign setting introduced this concept to reflect characters who are larger-than-life heroes destined for great things. Action points allow a player to add a bonus on any d20 roll so that characters can dodge or at least mitigate the effects of bad luck. You start with 5 action points at 1st level. Each time you gain a level, you lose any unspent action points and gain a new total equal to 5 + half your level.
You can spend an action point whenever you roll a d20 to make an attack roll, an ability check, or a saving throw. You don’t have to decide until after you make the roll, but BEFORE you learn if it succeeded or failed. If you spend an action point, roll a d6 and add it to your d20 result, possibly changing a failure into a success. You can spend only 1 action point per roll.
In addition, whenever you fail a death saving throw, you can spend an action point to make it a success.