Hope you can help me to answer this tricky question. I´m posting here as I got the impression that it needs a linguist or at least a native to answer it.
When you say: I may go to the party. Does this mean that you have permission to go there? Kind of - your mum allowed you to go there... or does it mean that you´ll probably go there? I´d say it´s the second case.
Or: I may play the guitar. I´d understand that the person means that there is a probability that they will play the guitar. Just as when you say the same thing by using "might".
I use may just to ask for permission or to give permission to somebody.
So, I´d say I´m allowed to go to the party/to play the guitar if I want to express that I (!!) have permission to do something.
I did a lot of research, but examples with MAY are always:
a) questions - May I take a seat?
b) using YOU - you may leave the room once you´ve finished the exam.
I´d really appreciate it if you could give me more information about this issue.