Something being incredibly unlikely, to the point of it being nearly mathematically impossible.
Comes from the video game "The Legend of Zelda: Majora's Mask" where a Blue Dog is coded to never win a race unless under very specific circumstances.
That guy is gonna try and throw the ball 100 yards!
He's got a Blue Dog chance of it.
You know, several of the greatest underdog stories could be described as Blue Dogs.
Really, like what?
Oh, Leicester City's 2016 Premier League run comes to mind.