"Dog's chance" is an idiom that is used to describe a hopeless or unlikely situation. Instead of using this phrase repeatedly, there are several synonyms that can be used to express the same sentiment. Some of the commonly used synonyms for "dog's chance" include "slim chance", "faint hope", "remote possibility", "long shot", "lost cause" and "no chance in hell". Using these alternate phrases can make your language more interesting and varied, while still conveying the same meaning. So, next time you encounter a situation that seems hopeless, consider using one of these synonyms instead of defaulting to "dog's chance".