DnD House Rules Player Bonuses aka Benefits (or Bennies)
Dungeons and Dragons 5e has a mechanic called inspiration. It encourages role playing by awarding players an additional d20 dice on a subsequent roll. At any given time, a player can have only one inspiration which encourages them to use it. Overall it provides some additional strategy to a roll of the dice and overall encourages role-playing.
There are a other RPGs that give players a bonus at the beginning of the session that they can use anytime during the game. In Savage Worlds for instance, players receive bennies (benefits) usually distributed as a set of poker chips allowing them to re-roll dice or add a d6 to their die roll. Fate has a resource called Fate Points which drive a mini economy that injects drama and interest into characters. Players earn fate points portraying character aspects that lead to disadvantages and complications. Players can spend fate points in order to get a positive result from a character aspect.
I really like the concept of giving bennies to players in order to encourage good character behavior and having something tangible to hold and exchange. In our game, we have a set of oversized d20s that are used for inspiration. This keeps them prominent and provides a physical transferral when they are awarded or spent. In addition, I like to give players a bonus in the form of a single poker chip which can be used once during the course of the session in order to re-roll any die roll they have rolled. Both of these bonuses add another dimension to the game and provide a way for players to exert themselves when they really want it to count. Try this variation in your next game:
At the start of the session, give each player a poker chip. Allow them to spend the chip in order to re-roll any single dice roll during the session.
The chips do not always get used, but when they do get spent, the overall effect generates a bit of tension and heroism. They are heroes after all. This is particularly helpful for new players who may get frustrated around a bad roll. Overall it adds to the enjoyment of the game.