The phrase "leave to luck" denotes an attitude of indifference towards a particular outcome and relying solely on chance or fortune. However, there are several synonyms for this phrase that can convey different degrees of optimism or pessimism. "Leave to fate" implies a feeling of resignation towards an inevitable result, while "trust to chance" suggests a more careless or risky approach. "Depend on Providence" conveys a sense of faith in a higher power, while "roll the dice" emphasizes the uncertainty and unpredictability of the situation. Finally, "leave it to the gods" invokes ancient mythology and the belief in divine intervention.