The Senryaku, the Art of War, has 36 stratagems for mastering the ability to fight.
Know when your battles are stacked against you and don't waste your resources in these foolhardy pursuits.
So I present that the last mechanism a gamer should have in their repertoire is no mechanism at all.
In my experience, some of the best moments in roleplaying occur when players and GM put aside the rules and let the intimacy of the moment take them. This could be allowing the story to take it's course, truly immersing in a situation and forgetting it's a game at all, or really becoming one with the character.
A good set of mechanisms facilitates this type of moment, a good GM recognises it and allows it to flourish, a good player allows others to have their moment in the spotlight without stealing their thunder and calling for a judgment according to page XX.
It's a lot harder to do than might be first thought, it's almost zen-like in it's attainment. Those players who are sometimes defined as "gamists" latch onto the rules and often find it hard to identify with their characters beyond a killer combo, or brilliant skill. Those players sometimes identified as "narritivists" become so obsessed with the story and their ability to manipulate it through the rules that they forget the notion of spontaneous story development. Those players sometimes referred to as simulationists become so hooked up on the way the rules should replicate the setting, that they forget to smell the roses or take in the nuanced details that might be present.
I'm not tarring all players with a brush of unenlightenment, but virtually every game I've played in has seen one or more players spoiling the moment because things weren't going their way, or because they didn't like the way things were heading from the perspective of story or situation. Even in games where I've written the rules and I'm running them as a demonstration of what can be achieved through those rules...there are still people who get hooked up on certain mechanisms and don't know when to let go...much to the detriment of the game and the other players.
I'm not immune to it either.