I had a friend who used to be just like this and it made me sooo mad. but honestly, I just don’t think they know any better. they don’t want to damage their pride and at that point (even though its unfair) you end up having to take the losing hand even if you don’t deserve it. people like that are frustrating. I wish I could help, but if she is naturally very competitive and stubborn, I don’t know if you can really change that. you can try telling her about how you feel but that could damage you’re friendship, but it’s up to you really.