fancy your/somebody's chances
fancy (one's) chances
To think that one is likely to succeed. I fancy my chances in the competition because I know I can run faster than the other girls.
fancy someone's chances
to have confidence in someone's [including one's own] ability to be successful. We all think she will refuse to go out with him, but he certainly fancies his own chances. The other contestants are so talented that I don't fancy his chances at all.