Unfortunately I have not been able to sit down playing Trollbabe. I’ve read through several times and like the simple fashion of mechanics in the game, and always look for ways to try out house-rules that emulate elements of Trollbabe. More than the other games, Trollbabe is targeted as a collaborative story-telling game with very few precise mechanics about interacting with the stuff of the world. It is clearly focused on giving mere guidelines of interacting with the NPCs of the world.
Over the course of the game, a PC faces opportunities to reroll attempts to resolve conflicts and overcome obstacles. Regarding the reroll mechanic, each reroll comes with a small cost. Also, each reroll relates to something in-game. The cost of conditions related to rerolls ensures the player must choose whether to accept the cost or back-off and look for alternatives. Also, rerolls are not narrative mulligans; the attempt isn’t working out toward success, and the PC must look for new avenues of success.
Each reason for which a player might invoke a reroll refreshes for each session. This might change if the player and GM decide the refresh rate needs to change. But, the refresh is not at all connected to a mechanic for resting. It is entirely decided by a group agreement of the refresh rate. Any reroll not used is lost rather than accumulated at the refresh point.
A remembered spell or other magical effect
A reroll might be called upon because the PC has remembered some bit of magic; a spell effect might have an aftereffect that was unexpected. There are no defined listed spells; the player describes how the PC calls upon magic, then they may make a reroll on their attempt to resolve the action.
A handy geographical feature
A reroll might be called upon because the PC discovered or recognized a handy terrain feature that can be used to their advantage. The player describes the terrain and how it is advantageous. This is not a question posed to the GM; it is a declaration by the player.
A found or reached item
In the course of action, the PC may find a bit of useful loot or be able to reach something of value to aid in resolving the task. With the new item, the player describes its purpose and earns a reroll. A player might describe reaching an item the GM already brought up, or they might bring something else into play on their own.
A carried object
Of course any sort of personal gear is available to call into a conflict for a reroll. In this case, it is a listed item of gear from the character sheet being used. It might get used as intended or as an improvised tool in some unintended way.
A sudden ally
Trollbabe is a game more centrally focused on interactions with NPCs. It is less focused on the loot, monsters, or traps. So, an important reroll is made through calling in a sudden new ally. Since this is part of a player’s choices, it is not intended to be a deus ex machine by the GM; the player makes the call to bring in an ally seeming from nowhere to aid the scene.
A final note is the introduction of relationships. While a reroll can be gained by introducing a sudden ally, this sudden ally doesn’t have to become part of the ongoing adventure. It could be they arrive to solve a problem, stick around briefly, and disappear as readily as they arrived.
By introducing a relationship, a player can bring in one more reroll, but they place that relationship in threatened space. Now, they have an NPC which ought to matter enough that circumstances wherein the NPC is threatened, pulls the PC deeper into the action. It works as a trade-off; the player has another source of a reroll, but that one extra reroll can be endangered by the GM.
Often, a sudden ally is a good candidate for a relationship.