There are many synonyms for the phrase "trusting to luck." One common alternative is "rolling the dice," which refers to leaving things to chance and hoping for the best outcome. Another similar phrase is "taking a chance," which suggests taking a risk without knowing the outcome. "Winging it" also expresses a lack of preparation and a reliance on fate. "Playing it by ear" implies a willingness to adjust one's plans on the fly. Finally, "leaving it up to chance" indicates a willingness to let things unfold without active involvement. Regardless of the expression used, trusting to luck generally involves a degree of uncertainty and a lack of control over the situation at hand.