There are several synonyms for the phrase "flip of the coin" that can be used to describe an outcome that is determined by chance or luck. These include "toss of the coin," "coin toss," "heads or tails," "luck of the draw," and "chance outcome." Each of these phrases conveys the idea that the result is unpredictable and uncontrollable, and that there is an equal chance of either outcome occurring. Whether you are describing a game of chance, a business decision, or a personal choice, using one of these synonyms for "flip of the coin" can add variety and interest to your writing.