The trusting strategy is the course of action based in trust. For instance, in the Prisoner's Dilemma game, if you trust the other person, and the other person trusts you, you both cooperate and overall get a better outcome.
Another example would be any time you do something for a long term benefit that sacrifices something in the short term. You trust that there even is a long term.
You can take the trusting strategy even when you don't feel trusting. A case of willful trust. Perhaps you're a young, struggling artist, such as those whom Ira Glass talks to. You want to quit. Everything tells you to quit. But because Ira Glass encourages you, you keep going. The status quo "wants" you to fail at doing that thing that people don't tend to do that you want to do (if it didn't "want" that, more people would do it), so you have fight hard. And then someday you see the fruits of your actions -- maybe Ira sees them too.
When you're in distress, you want to "sell your birthright" like Esau did. But your perspective isn't necessarily the best, and if you could just see outside where you are, you would see that you're not the kind of person to fail, so you don't need to compromise. But you may need to willfully trust something or someone outside your own point of view for that to happen.