( informal ) to have a good chance of winning sth or of achieving sth
BE IN WITH A SHOUT (OF STH / OF DOING STH)
Meaning of BE IN WITH A SHOUT (OF STH / OF DOING STH) in English
Oxford Advanced Learner's English Dictionary. Оксфордский английский словарь для изучающик язык на продвинутом уровне. 2005