One way karate training will increase your chances is by decreasing some of the negative side effects of being in a fight or flight situation. We practice fighting regularly, and while this isn't completely the same as an actual fight it will decrease the chance/degree to which these disadvantages will have an effect on you. Tunnel vision, tendency to hold one's breath, anger, and wild techniques.
Another effect that your training will hopefully have is that muscle memory will grant you automaticity of techniques. Just like learning your basic multiplication facts by heart, you practice your techniques repeatedly so that you can execute them at a moment's notice without having to think about them. After enough training your techniques will be as natural to you as walking, riding a bike, or your simple reflexes.
That being said, physical conflicts are extremely chaotic. Anything can happen. Students of Master Chibana have quoted him saying, "Do not get into a fight unless you're prepared to die." This can get misinterpreted as being brave enough to put your life on the line. The way I interpret is is that Master Chibana was simply acknowledging the fact that even in a simple fistfight a person can die or be seriously hurt, and so you should avoid them as much as possible. An attacker can be completely unskilled in martial arts but could land a wild blow completely by accident which may take you out of commission.
I'll wrap this up with a favorite quote of mine from Master Kyan...
"If you spend your entire life never needed to use the skills of karate for which you trained diligently for such a long time...you truly have accomplished the goal of your training. Learn the art of killing, without ever taking a life."
-Chan-me-gwa, Kyan Cotoku, 1942