"Ran the risk" is an expression commonly used to convey a situation where someone has put themselves in danger or jeopardy. There are other phrases that can be used to convey a similar meaning like "took a gamble," "assumed a peril," "ventured a danger," "put oneself in harm's way," "chanced it," "played with fire," etc. Synonyms are useful because they allow for better clarity and variety when writing or speaking, as well as a more nuanced understanding of a given situation. Therefore, it's essential to explore various synonyms to better express oneself and convey the intended message more effectively.